Novel Concepts for Versatile and High-Power Thin-Disk Laser Oscillators

Research Collection

Doctoral Thesis

Author(s): Saltarelli, Francesco

Publication Date: 2020

Permanent Link: https://doi.org/10.3929/ethz-b-000449261

Rights / License: In Copyright - Non-Commercial Use Permitted

This page was generated automatically upon download from the ETH Zurich Research Collection. For more information please consult the Terms of use.

ETH Library DISS. ETH NO. 26982

NOVEL CONCEPTS FOR VERSATILE AND HIGH-POWER THIN-DISK LASER OSCILLATORS

A thesis submitted to attain the degree of DOCTOR OF SCIENCES of ETH ZURICH (Dr. sc. ETH Zurich)

presented by FRANCESCO SALTARELLI Laurea Magistrale in Fisica, Sapienza, Università di Roma

born on 22.07.1992 citizen of Italy

accepted on the recommendation of Prof. Dr. Dr. h. c. Ursula Keller, examiner Prof. Dr. Thomas Südmeyer, co-examiner

2020

“Don’t fake it till you make it. Fake it till you become it” — Amy Cuddy

Contents

List of Figures ...... v List of Tables ...... vii List of Acronyms ...... ix List of Symbols ...... xi Publications ...... xiii Abstract...... xvii Sommario (abstract in Italian) ...... xxi 1 Introduction and motivation ...... 1 1.1 Ultrafast lasers ...... 2 1.2 High-power laser oscillators ...... 5 1.3 Motivation and outline of the thesis ...... 6 2 Framework of this thesis ...... 9 2.1 Thin-disk laser concept ...... 9 2.2 Cavity stability and gas-lens effect ...... 11 2.3 Active multi-pass cavities ...... 14 2.4 SESAM and Kerr-lens modelocking ...... 15 2.5 Requirements for high-power modelocking ...... 19 2.6 SESAM’s thermal lensing ...... 19 2.7 Self-phase modulation cancellation ...... 21

Contents

2.8 Nonlinear mirror modelocking ...... 23 2.9 Power scaling of modelocked thin-disk lasers ...... 25 3 Thermal effects in thin-disk lasers ...... 29 3.1 Gas-lens effect in kW-class thin-disk lasers...... 30 3.1.1 Introduction ...... 30 3.1.2 High-power single-transverse-mode TDL operation ...... 34 3.1.3 Thermal-lensing measurements ...... 35 3.1.4 Simulation of the gas-lens and gas-wedge effects ...... 41 3.1.5 Conclusion...... 45 4 Cascaded quadratic nonlinearities ...... 47 4.1 Self-phase modulation cancellation in a high-power ultrafast thin-disk laser oscillator ...... 48 4.2 Supplementary material: Self-phase modulation cancellation in a high-power ultrafast thin-disk laser oscillator ...... 58 4.2.1 Coupled wave equations ...... 59 4.2.2 Pulsed second harmonic generation...... 60 4.2.3 Cavity design ...... 64 4.2.4 Thermal behavior of the nonlinear crystal ...... 65 5 Nonlinear mirror modelocking ...... 67 5.1 Modelocking of a thin-disk laser with the frequency-doubling nonlinear-mirror technique ...... 69 5.1.1 Introduction ...... 69 5.1.2 NLM operating principles...... 73 5.1.3 Experiment ...... 74 5.1.4 Numerical model of the NLM device ...... 81 5.1.5 Conclusion and outlook ...... 85 5.2 Power-scaling of nonlinear-mirror modelocked thin-disk lasers . 87 ii

Contents

5.2.1 Introduction ...... 87 5.2.2 High-power NLM-modelocked oscillator ...... 91 5.2.3 Study of the nonlinear-mirror modelocking regime ...... 97 5.2.4 Conclusion and outlook ...... 105 6 Power scaling results ...... 109 6.1 Power scaling of ultrafast oscillators: 350-W average-power sub-picosecond thin-disk laser ...... 111 6.1.1 Introduction ...... 111 6.1.2 Cavity design ...... 115 6.1.3 Laser performance in continuous wave and modelocked operation ...... 119 6.1.4 Conclusion and outlook ...... 123 6.2 Further power scaling to 430-W average power ...... 125 6.2.1 Cavity design ...... 127 6.2.2 Modelocking and laser performance ...... 129 6.2.3 Conclusion and outlook ...... 132 7 Conclusion and outlook ...... 133 Author contributions ...... 137 Bibliography ...... 141 Curriculum Vitae ...... 153 Acknowledgements ...... 154

iii

List of Figures

Fig. 1.1 Overview of state-of-the-art ultrafast lasers ...... 4

Fig. 2.1 Thin-disk concept ...... 10 Fig. 2.2 Cavity design and stability in thin-disk lasers ...... 12 Fig. 2.3 Structure and saturation properties of a SESAM ...... 18 Fig. 2.4 Cascaded quadratic nonlinear processes ...... 23 Fig. 2.5 Overview of state-of-the-art thin-disk laser oscillators ...... 27

Fig. 3.1 Beam quality for thin-disk laser operation in air vs vacuuum ...... 33 Fig. 3.2 Disk’s thermal lensing in thin-disk lasers ...... 38 Fig. 3.3 Beam quality in a cw thin-disk oscillator ...... 40 Fig. 3.4 Model to simulate the gas-lens and gas-wedge effects ...... 42 Fig. 3.5 Results of gas-lens and gas-wedge simulations ...... 45

Fig. 4.1 Overview of intracavity GDD used in thin-disk lasers ...... 50 Fig. 4.2 Schematic of the laser cavity ...... 51 Fig. 4.3 SPM cancellation in thin-disk lasers ...... 54 Fig. 4.4 Laser power slopes ...... 55 Fig. 4.5 Modelocking diagnostics at 210-W average output power ...... 57 Fig. 4.6 SHG efficiency in a SHG minimum, approximated formula ...... 63 Fig. 4.7 Evolution of the 1/e2 mode radius in the laser cavity ...... 66

Fig. 5.1 Overview of nonlinear-mirror modelocked lasers ...... 72 Fig. 5.2 Operating principle of nonlinear-mirror modelocking ...... 74 Fig. 5.3 Schematic of the laser cavity and cavity mode ...... 76 Fig. 5.4 Modelocking diagnostics at 21-W average output power ...... 77 Fig. 5.5 Numerical model of a NLM modelocked laser ...... 80

List of Figures

Fig. 5.6 Analysis of the performance of a NLM modelocked laser ...... 84 Fig. 5.7 Overview of ultrafast thin-disk oscillators ...... 90 Fig. 5.8 Operating principle of NLM modelocking ...... 93 Fig. 5.9 Schematic of the cavity and power slopes for the SESAM- assisted NLM modelocked oscillator ...... 95 Fig. 5.10 Modelocking diagnostics for the SESAM-assisted NLM modelocked oscillator ...... 97 Fig. 5.11 Reflectivity of the NLM device and design of the OC ...... 99 Fig. 5.12 Experimental characterization of the NLM ...... 103

Fig. 6.1 Timeline of record-power thin-disk laser oscillator results ...... 115 Fig. 6.2 Cavity design and beam profile of the 350-W average power thin-disk oscillator ...... 118 Fig. 6.3 Cavity mode and stability zone ...... 119 Fig. 6.4 Power slopes and SESAM properties ...... 122 Fig. 6.5 Modelocking diagnostics at 350-W average power ...... 123 Fig. 6.6 Timeline of record-power thin-disk laser oscillator results ...... 127 Fig. 6.7 Power slopes in cw for different active multi-pass cavities ...... 128 Fig. 6.8 Cavity mode and stability zone ...... 129 Fig. 6.9 Power slope in modelocked operation and beam profile ...... 130 Fig. 6.10 Modelocking diagnostics at 430-W average power ...... 131

List of Tables

Table 3.1 Disk’s thermal lensing for different gas environments ...... 39 Table 3.2 Thermal and optical properties of helium, N2 and air ...... 43

Table 4.1 SPM cancellation in TDL, laser parameters ...... 56

vii

List of Acronyms

AlAs Aluminium Arsenide AMP Active Multi-Pass AOI Angle Of Incidence AR Anti-Reflective at.% Atomic Percent BBO Beta Barium Borate (BaB2O4) CC ConCave CTE Coefficient of Thermal Expansion cw continuous wave CX ConveX CWE Coupled Wave Equation DBR Distributed Bragg Reflector DTC Dielectric Top Coating FEM Finite-Element Method FW Fundamental Wave FWHM Full Width at Half Maximum GaAs Gallium Arsenide GDD Group Delay Dispersion GTI Gires-Tournois Interferometer GVM Group Velocity Mismatch He Helium HD High Dispersive HHG High Harmonic Generation HR High-Reflective IBS Ion-Beam Sputtering InGaAs Indium Gallium Arsenide

List of Acronyms

IR InfraRed KLM Kerr-Lens Modelocking Laser Light Amplification by Stimulated Emission of Radiation LBO Lithium triborate (LiB3O5) MBE Molecular Beam Epitaxy MM MultiMode MSA Microwave-Spectrum Analyzer Nd:YAG Neodymium-doped Yttrium Aluminum Garnet (Y3Al5O12) NLM NonLinear Mirror NPR Nonlinear Polarization Rotation OC Output Coupler OPA Optical Parametric Amplification OSA Optical-Spectrum Analyzer QW Quantum Well RBW Resolution BandWidth RF Radio Frequency ROC Radius Of Curvature SESAM SEmiconductor Saturable Absorber Mirror SH Second Harmonic SHG Second-Harmonic Generation SiO2 Silicon Dioxide SPM Self-Phase Modulation SVEA Slowly-Varying-Envelope Approximation TBP Time-Bandwidth Product TDL Thin-Disk Laser TEM Transverse ElectroMagnetic TFP Thin Film Polarizer Ti:Sapphire Titanium-Sapphire TPA Two-Photon Absorption XUV eXtreme UltraViolet Yb:CALGO Ytterbium-doped Calcium Gadolinium Aluminum Oxide (CaGdAlO4) Yb:YAG Ytterbium-doped Yttrium Aluminum Garnet (Y3Al5O12) Yb:LuO Ytterbium-doped Lutetium Oxide (Lu2O3)

List of Symbols

B B integral Brt Round-trip B integral χ Electric susceptibility deff Second order nonlinear coefficient D Amount of group delay dispersion δ Group-velocity mismatch ∆k Phase mismatch

∆Fdisk Disk’s thermal lensing

∆Fgas Disk’s thermal lensing due to the gas-lens effect

∆Ftotal Overall disk’s thermal lensing ΔFvacuum Disk’s thermal lensing in vacuum ∆R SESAM modulation depth

∆Rns SESAM non-saturable losses ∆T Disk’s temperature increase Drt Round-trip GDD E Electric field EIC Intracavity pulse energy Ep Pulse energy F Fluence F2 SESAM inverse saturable absorption coefficient Fsat SESAM saturation fluence γ SPM coefficient

γair SPM coefficient due to the air

γavg SPM coefficient for a pulse with a gaussian spatial profile

List of Symbols

γCQN Effective SPM coefficient due to CQN processes

γsoliton SPM coefficient from soliton pulse formation Ipk Peak intensity L Cristal length 2 M Beam quality factor M2x Beam quality factor in the x direction M2y Beam quality factor in the y direction n Index of refraction n2 Nonlinear refractive index nmin SHG minimum order nrefl Number of reflections on the disk per cavity round trip η Efficiency ω Angular frequency PIC Average intracavity power Pout Average output power R Disk’s radius of curvature Rlin Reflectivity of a SESAM at very low fluence Rnl NLM nonlinear reflectivity Rns Reflectivity of a fully saturated SESAM sech2 Squared hyperbolic secant

τp FWHM pulse duration Tnl NLM nonlinear transmission TOC Output coupler transmission vg Group velocity wcam beam waist on camera wlaser beam waist on the disk wdisk pump-beam waist on the disk

xii

Publications

Within the scope of this thesis, the following journal papers and conference contributions were published. The original manuscripts of the journal publications are re-printed with permission in this cumulative thesis. The text and figures are printed as published, while the formatting of those publication has been adapted to fit the page format of this thesis. Further, the numbering of the figures, tables, and references has been adjusted. The reference list of the publication has been included in the reference list at the end of this thesis. The copyright of the publications is held by the respective copyright holders. Journal papers 1. I. J. Graumann, F. Saltarelli, L. Lang, V. J. Wittwer, T. Südmeyer, C. R. Phillips, and U. Keller, “Power-scaling of nonlinear-mirror modelocked thin-disk lasers,” Opt. Express 27, 37349-37363 (2019) 2. F. Saltarelli, I. J. Graumann, L. Lang, D. Bauer, C. R. Phillips, and U. Keller, "Power scaling of ultrafast oscillators: 350-W average- power sub-picosecond thin-disk laser," Opt. Express 27, 31465- 31474 (2019) 3. F. Saltarelli, A. Diebold, I. J. Graumann, C. R. Phillips, and U. Kel- ler, "Self-phase modulation cancellation in a high-power ultrafast thin-disk laser oscillator," Optica 5, 1603-1606 (2018) 4. A. Diebold*, F. Saltarelli*, I. J. Graumann, C. J. Saraceno, C. R. Phillips, and U. Keller, "Gas-lens effect in kW-class thin-disk lasers," Opt. Express 26, 12648-12659 (2018) *These authors contributed equally to this work

xiii

Publications

5. F. Saltarelli, A. Diebold, I. J. Graumann, C. R. Phillips, and U. Kel- ler, "Modelocking of a thin-disk laser with the frequency-doubling nonlinear-mirror technique," Opt. Express 25, 23254-23266 (2017) Conference papers 1. F. Saltarelli, I. J. Graumann, L. Lang, D. Bauer, C. R. Phillips, and U. Keller, "Soliton-Modelocked Thin-Disk Laser Oscillator with 350 W Average Power and Sub-ps Pulses," in Laser Congress 2019 (ASSL, LAC, LS&C), talk 2. F. Saltarelli, D. Koenen, L. Lang, I. J. Graumann, C. R. Phillips, and U. Keller, "Beam quality in high-power thin-disk lasers: influence and measurement of the radial inversion profile," in Laser Congress 2019 (ASSL, LAC, LS&C), poster 3. F. Saltarelli, I. J. Graumann, L. Lang, D. Bauer, C. R. Phillips, and U. Keller, “Power Scaling of Ultrafast Laser Oscillators: 350-W Out- put Power Sub-ps SESAM-Modelocked Thin-Disk Laser,” Conference on Lasers and Electro-Optics (CLEO), San Jose, CA, (2019), talk 4. F. Saltarelli, A. Diebold, I. J. Graumann, C. R. Phillips, and U. Kel- ler, “Recent advances in SESAM-modelocked high-power thin disk lasers,” Conference on Lasers and Electro-Optics (CLEO), San Jose, CA, (2019), talk 5. I. J. Graumann, F. Saltarelli, L. Lang, V. J. Wittwer, T. Südmeyer, C. R. Phillips, and U. Keller, “Power-Scaling Nonlinear-Mirror Modelocked Thin-Disk Lasers,” European Conference on Lasers and Electro-Optics and European Quantum Electronics Conference, (Optical Society of America, 2019), talk 6. F. Saltarelli, A. Diebold, I. J. Graumann, C. R. Phillips, and U. Kel- ler, “Overcoming the challenges in power scaling ultrafast thin-disk oscillators: nonlinearity management and thermal effects,” European Conference on Lasers and Electro-Optics and European Quantum Electronics Conference, (Optical Society of America, 2019), talk 7. F. Saltarelli, I. J. Graumann, L. Lang, D. Bauer, C. R. Phillips, and U. Keller, “350-W Average-Power SESAM-Modelocked Ultrafast Thin-Disk Laser,” European Conference on Lasers and Electro- xiv

Publications

Optics and European Quantum Electronics Conference, (Optical Society of America, 2019), talk 8. F. Saltarelli, A. Diebold, I. J. Graumann, C. R. Phillips, and U. Kel- ler, "Self-Phase Modulation Cancellation in 210-W SESAM- Modelocked Thin-Disk Oscillator Operated in Air," Laser Congress 2018 (ASSL), OSA (2018), talk 9. F. Saltarelli, A. Diebold, I. J. Graumann, C. R. Phillips, and U. Kel- ler, "Soliton-Modelocked 153-W Thin-Disk Laser Oscillator in Air Enabled by Negative Nonlinearities in a Phase-Mismatched χ(2) Crys- tal," Advanced Photonics 2018, OSA (2018), talk 10. F. Saltarelli, A. Diebold, I. J. Graumann, C. R. Phillips and U. Keller, "Nonlinear-Mirror Modelocked 323-fs Thin-Disk Oscillator," Con- ference on Lasers and Electro-Optics (CLEO), San Jose, CA, (2018), talk 11. F. Saltarelli, A. Diebold, I. J. Graumann, C. J. Saraceno, C. R. Phil- lips and U. Keller, "Gas Lens in kW-Class Thin-Disk Lasers," Conference on Lasers and Electro-Optics (CLEO), San Jose, CA, (2018), talk 12. F. Saltarelli, A. Diebold, I. J. Graumann, C. R. Phillips, and U. Kel- ler, "210-W Ultrafast Thin-Disk Laser Oscillator in Air Enabled by Negative Nonlinearities from Cascaded χ(2) Processes," Conference on Lasers and Electro-Optics, OSA (2018), post-deadline talk 13. F. Saltarelli, A. Diebold, I. J. Graumann, C. R. Phillips, and U. Kel- ler, "Nonlinear-Mirror Modelocked Thin-Disk Laser Delivering 21 W Average Power with 324-fs Pulses," Laser Congress 2017 (ASSL, LAC), OSA Technical Digest (Optical Society of America, 2017), talk 14. A. Diebold, I. J. Graumann, F. Saltarelli, F. Emaury, C. Phillips, C. J. Saraceno, and U. Keller, “Optimized components for high-power ultrafast thin-disk lasers,” in OCLA Symposium 2017 Optical Coat- ings for Laser Applications, Buchs, Switzerland, (2017), invited talk

Abstract

Ultrafast high-power lasers underwent a tremendous development over the last twenty years, enabled by the combination of Ytterbium-doped gain materials with gain medium geometries optimized for heat extraction. These laser sources are nowadays pivotal to many industrial and scientific applications. The thin-disk laser technology has been at the forefront of this field and laser sources based on this technology today exceed the kilowatt-level average power in both continuous wave and ultrafast operation. Such laser sources can be commercially bought and are routinely used in the micromachining industry and research laboratories worldwide. A compelling strategy to develop high-power ultrafast laser sources is to directly scale up the output power from oscillators, bypassing the complicated chain of amplifiers traditionally used. In this way, the laser output is obtained directly from a comparatively simple, high-performance, and potentially cost- effective source. Moreover, oscillators offer a low-noise output, exceptional temporal pulse shape, diffraction-limited beam quality, and high repetition rates. Research on laser oscillators is thus of great interest to the optics community. The scientific motivation behind this thesis is the development of high-power laser sources for high-field physics experiments. In this context, we explored and pushed the limits in high-power modelocked lasers based on the thin-disk technology. The lasers developed expand our experimental capabilities and offer proof of concepts for potential use within the laser industry. In the course of this thesis, we set a record for the highest average output power from any ultrafast oscillator demonstrating 430-W average power from

xvii

Abstract a thin-disk laser oscillator at 6.29-MHz repetition rate and 769-fs pulse duration (1 fs = 10-15 s). This result improved a long-standing record of 275-W average power set in 2012. For this result we relied on a SEmiconductor Sat- urable Absorber Mirror (SESAM), which is the leading modelocking technique for high-power oscillators. This achievement hinges on a deep understanding of the sources of thermal lensing in thin-disk lasers and improvements on the laser cavity design, which were both investigated as part of this thesis. Regarding thermal lensing, we discovered a gas-lens effect which occurs in thin-disk lasers. It consists of a lensing effect due to the presence of heated air in front of the thin disk. This lens significantly contributes to the disk’s overall thermal lensing. The understanding of this effect is crucial for the development of high-power laser oscillators and helped us to achieve the record- power levels. Until now, record-power oscillators were based on short cavities with one or two reflections on the disk. While this approach is attractive because of the few optical components involved, it likely reached its limit and could not be used for further power scaling due to the associated excessive intracavity power. Therefore, we developed a new thin-disk laser approach which combines an active multi-pass imaging scheme with laser operation in a low- pressure environment. The active multi-pass approach enables several reflections on the disk per round trip, while the low-pressure environment removes the gas-lens effect and the nonlinearity of air. For a given output power, the multi-pass cavity can operate at a reduced intracavity power, thereby mitigating thermal effects on the intracavity mirrors and the SESAM. Another aspect we investigated is nonlinearity management in thin-disk lasers. A large amount of self-phase modulation is picked up in the intracavity air due to the high peak power in thin-disk oscillators. This can destabilize modelocking and, in fact, many high-power thin-disk oscillators, including the previous record average power result, have been operated in a low-pressure environment. However, this substantially increases the cost and the complexity of the laser system making it less attractive for applications. We thus explored cascaded quadratic nonlinear processes to compensate the self- phase modulation and hence allow high-power laser operation in air. By xviii

Abstract combing this technique with thin-disk technology, we demonstrated a SESAM-modelocked laser delivering 210-W average power. This result represents the highest-power recorded for any SESAM-modelocked oscillator operated in air. Additionally, our result paves the way to the use of cascaded quadratic nonlinearities for high-power laser development. Through our exploration of quadratic nonlinear processes, we also demonstrated the first nonlinear-mirror modelocked thin-disk laser. We obtained pulses as short as 323-fs compared to the few-picosecond long pulses previously achieved with this technique. The nonlinear mirror combines the flexibility of SESAM modelocking in terms of cavity design with the possibility of obtaining short pulses due to the fast saturable loss, as in Kerr-lens modelocking. This combination is particularly attractive for scientific applications. Later, we combined a SESAM with the nonlinear mirror modelocking to obtain close to 100-W average power and defined a set of guidelines to use the nonlinear mirror in high-power sub-picosecond oscillators. The laser sources developed in this thesis, especially if combined with a modern multi-pass cell compression stage, are of immediate interest for various applications in micromachining and nonlinear-optics experiments such as extreme-ultraviolet generation and terahertz generation at megahertz repetition rate. In particular, these sources are a promising candidate for the development of table-top cost-effective extreme-ultraviolet sources. We foresee the possibility to further power scale the developed oscillators using SESAMs with improved thermal performance together with active optics to correct for the residual thermal lensing effects. Additionally, the combination of the nonlinear mirror and the SESAM offers a concrete path to obtain shorter pulses directly from the oscillator. Lastly, by making the laser cavity longer, pulse energies above 100 µJ are well within reach, which would expand the range of applications of these laser oscillators even further.

xix

Sommario (abstract in Italian)

Negli ultimi vent’anni vi è stato uno sviluppo impetuoso dei laser ultrabrevi ad alta potenza, permesso dalla combinazione di mezzi attivi drogati ad itter- bio con geometrie del mezzo attivo ottimizzate per estrarre il calore. Queste sorgenti laser sono oggi fondamentali per molte applicazioni industriali e scientifiche. La tecnologia laser a disco è stata all’avanguardia nello sviluppo di queste sorgenti laser. Oggi, i laser a disco hanno potenze in uscita superiori al kilowatt sia in modalità ad emissione continua, sia ad impulsi ultrabrevi. Tali laser sono stati sviluppati come prodotti commerciali e fanno parte degli stru- menti impiegati quotidianamente nell’industria della microlavorazione a macchina e, più in generale, in laboratori di ricerca in tutto il mondo. Una strada per sviluppare sorgenti laser ultrabrevi consiste nell’aumentare direttamente la potenza in uscita dagli oscillatori. Questa interessante strategia permette di fare a meno della complicata catena di amplificatori tipicamente necessaria per gli amplificatori laser. In questo modo, il fascio laser è ottenuto direttamente da una sorgente più semplice, ad alte prestazioni e potenzial- mente conveniente. In aggiunta, gli oscillatori sono sorgenti laser a basso rumore che emettono un fascio con eccezionale forma temporale e la cui qua- lità spaziale è limitata dalla sola diffrazione. Inoltre, gli oscillatori hanno elevate frequenze di ripetizione. Per tutti questi motivi, lo sviluppo di oscillatori è un argomento di grande interesse in ottica. La motivazione scientifica di questa tesi è lo sviluppo di sorgenti laser ad alta potenza per esperimenti di fisica con campi elevati. In questo contesto, abbiamo esplorato e spinto i limiti di potenza nei laser basati sulla tecnologia a disco in regime di modelocking. I laser sviluppati espandono le nostre capacità

xxi

Sommario (abstract in Italian) sperimentali e indicano la percorribilità di strategie che possono essere usate nell’industria dei laser nel prossimo future. Nel corso di questa tesi, abbiamo stabilito il record di potenza per un oscillatore laser ultrabreve, raggiungendo una potenza media di 430 W da un oscillatore a disco con una frequenza di ripetizione di 6.29 MHz e impulsi dalla durata di 769 fs (1 fs = 10-15 s). Questo risultato migliora un record sto- rico di potenza media di 275 W che è stato segnato nel 2012. Per ottenere questo risultato ci siamo affidati ad uno specchio saturabile a semiconduttore (SESAM), che è la tecnologia di modelocking leader per lo sviluppo di oscillatori ad alta potenza. Questo risultato si basa su una comprensione profonda delle sorgenti di lente termica nei laser a disco e su miglioramenti nella progettazione delle cavità laser. Entrambi questi aspetti sono il risultato dei temi studiati in questa tesi. Riguardo gli effetti di lente termica, abbiamo scoperto un effetto di lente termica nel gas (effetto di gas lens) che avviene nei laser a disco. Esso è dovuto alla presenza di aria calda di fronte al disco. Questo fenomeno contribuisce in modo significativo all’effetto di lente termica complessivo del disco. La comprensione di questo fenomeno è importante per lo sviluppo di oscillatori laser ad alta potenza e ci ha aiutato a raggiungere livelli record di potenza. Fino ad oggi, gli oscillatori con potenza record erano basati su cavità brevi con una o due riflessioni sul disco. Questo approccio risulta allettante per i pochi componenti ottici richiesti. Tuttavia, esso sembra aver raggiunto il suo limite e non poteva quindi essere usato per incrementare ulteriormente la potenza dei laser, a causa dell’eccessiva potenza nella cavità laser che esso comporta. Pertanto, abbiamo sviluppato un nuovo approccio per i laser a disco frutto dell’unione di uno schema di imaging per passate multiple con una camera a vuoto in cui operare il laser. Lo schema di imaging permette di ottenere molte riflessioni della luce laser sul disco prima che essa lasci la cavità laser. Allo stesso tempo, l’ambiente a bassa pressione rimuove l’effetto di gas lens e le non linearità dell’aria. Per una data potenza in uscita, la cavità a passate multiple può operare con una potenza laser nella cavità ridotta, mitigando quindi gli effetti termici sugli specchi nella cavità e sul SESAM.

xxii

Sommario (abstract in Italian)

Un altro aspetto che abbiamo studiato in questa tesi è il controllo delle non linearità nei laser a disco. Una grande quantità di auto modulazione di fase viene accumulata nell’aria presente nella cavità a causa dell’elevata potenza di picco nei laser a disco. Questo può destabilizzare il processo di modelocking e, di fatto, molti dei laser a disco ad alta potenza, compreso il precedente record di potenza media, sono stati operati in un ambiente a bassa pressione. Tuttavia, questo aumenta sostanzialmente il costo e la complessità del sistema laser rendendolo meno attraente per le applicazioni. Per tentare di risolvere il problema, abbiamo esplorato le possibilità offerte dai processi quadratici a cascata per compensare l’auto modulazione di fase e permettere dunque il funzionamento di laser ad alta potenza in aria. Combinando questa tecnica con la tecnologia dei laser a disco, abbiamo realizzato un laser che opera in modalità di modelocking grazie ad un SESAM e che produce 210 W di potenza media in uscita. Questo risultato rappresenta la più alta potenza mai registrata per un oscillatore laser che opera in regime di modelocking con un SESAM in aria. In aggiunta, il nostro risultato apre la strada all’uso dei processi quadratici a cascata nello sviluppo di laser ad alta potenza. Attraverso la nostra esplorazione dei processi quadratici, abbiamo anche realizzato il primo laser a disco che opera in regime di modelocking grazie allo specchio non lineare. Abbiamo così ottenuto impulsi dalla durata di soli 323 fs, il che rappresenta un miglioramento notevole rispetto agli impulsi di qualche picosecondo ottenuti precedentemente con questa tecnica. Lo specchio non lineare combina la flessibilità del modelocking con il SESAM in termini di progettazione della cavità con la possibilità, come nel modelocking con la lente di Kerr, di ottenere impulsi brevi grazie alla veloce perdita saturabile. Tale combinazione è di particolare interesse per le applicazioni scientifiche. In seguito, abbiamo combinato un SESAM con lo specchio non lineare per ottenere quasi 100 W di potenza media e definire un insieme di linee guida per utilizzare lo specchio non lineare in oscillatori ad alta potenza con impulsi più brevi di un picosecondo. Le sorgenti laser sviluppate in questa tesi, in particolare se combinate con un moderno sistema di compressione degli impulsi a passate multiple, possono essere particolarmente interessanti per varie applicazioni nel campo della microlavorazione a macchina e per esperimenti di ottica non lineare, come la

xxiii

Sommario (abstract in Italian) generazione di impulsi nell’estremo ultravioletto e generazione di radiazione al terahertz a frequenze di ripetizione del megahertz. In particolare, queste sorgenti sono molto promettenti per lo sviluppo di convenienti sorgenti da tavolo nell’estremo ultravioletto. Dal nostro lavoro emerge la possibilità di incrementare ulteriormente la potenza degli oscillatori laser ultrabrevi a disco tramite lo sviluppo di SESAMs con proprietà termiche migliori e tramite l’uso di ottiche attive per correggere gli effetti di lente termica nel laser. In aggiunta, la combinazione dello specchio non lineare con il SESAM offre una via concreta per ottenere impulsi più brevi direttamente dall’oscillatore. Da ultimo, aumentando la lunghezza della cavità laser, siamo convinti che impulsi con energia superiore ai 100 µJ siano a portata di mano. Questo aumenterebbe ulteriormente le possibili applicazioni per questi oscillatori laser.

xxiv

Introduction and motivation

1 Introduction and motivation

Lasers have a profound impact on our modern society. They find application in everything from industrial processes to science, medicine, and defense. La- sers generate revenues in excess of $12 billion (2018) with a compound annual growth rate (CAGR) above 5% in the last 10 years. The main segments are material processing (35%) and communications (33%)1. Lasers equip everyday devices like checkout scanners and computer mice, enable high-speed optical communication, empower optical storage devices, and are used in sensors for consumer goods. Additionally, they are used in the material processing industry, particularly, laser cutting in the automotive and garment industry. Lasers find applications in the medical domain, for example, for ophthalmology, prostatectomy, cancer treatment, and tattoo removal. Beyond industry, lasers are nowadays ubiquitous in research laboratories around the world. For example, physicists and chemists use them for spectroscopy and to resolve fast processes, while biologists use them for imaging living tissues and sequencing DNA. Also in fundamental research, lasers play a crucial role, since they enable many high-precision measurements. For example, the Nobel Prize in Physics 2019 was awarded for the detection of gravitational waves. The experiment was performed using a large-scale laser interferometer.

1 The Worldwide Market for Lasers – Trends and five-year forecast (2017 – 2023). Strategies Unlimited 1

Chapter 1

The laser was invented in 1960 by T. Maiman [1] and originated as an acronym for “Light Amplification by Stimulated Emission of Radiation”. It emits light through the quantum process of stimulated emission discovered theoretically by A. Einstein in 1917 [2]. Due to this process, laser light is coherent in space and time which makes it fundamentally different from the light emitted by a light bulb. In fact, due to spatial coherence, laser light can be focused to a small spot and due to temporal coherence, light with a very narrow spectrum or short pulses in time can be formed. Practically, a laser consists of an optical resonator, a gain medium, and a pump source. The optical resonator is an arrangement of mirrors able to confine and store light at specific resonance frequencies. In this thesis, we will use linear resonators, where the light bounces back and forth between two end mirrors forming a standing wave. The resonator includes the gain medium, which amplifies the laser beam through the process of stimulated emission. The pump source provides energy to the gain medium enabling the stimulated emission process. There is an extremely wide variety of lasers in terms of physical size, type of the gain medium, wavelength, linewidth, and power. A major classification of lasers is based on how they deliver power with time. With this respect, they are grouped into continuous-wave (cw) lasers and pulsed lasers. The former corresponds to lasers whose power output is steady over time. The latter corresponds to lasers whose output is made up of pulses. In particular, ultrafast lasers generate pulses with a duration of some picoseconds (1 ps = 10-12 s) or femtoseconds (1 fs = 10-15 s). 1.1 Ultrafast lasers The possibility of obtaining such short pulses is a very attractive aspect of lasers. In fact, by tightly focusing the output of ultrafast lasers, very high peak intensities can be reached, which lead to nonlinear interactions with materials. For example, in industry, femtosecond lasers with high peak power are used for high-precision micromachining of metals and glasses, and in medicine for surgery. Moreover, ultrafast lasers opened the door to a new branch of chem- istry, termed femtochemistry [3], which consists in the study of chemical processes on the femtosecond timescale.

Introduction and motivation

The workhorse of ultrafast laser science is the Ti:sapphire laser technology. In fact, as a gain medium, Ti:sapphire allows the generation of pulses down to some femtoseconds in duration, due to its exceptionally broad emission spectrum. On the other hand, Ti:sapphire lasers require high pump intensity, the crystal quality degrades for high doping concentrations, and they suffer from thermal issues due to the high quantum defect. Those properties make it not suitable for high-power laser development and limit the achievable average power to a few watts. In an ultrafast laser source, the average power determines the product between the number of pulses per second, i.e., the repetition rate (frep), and the energy of each pulse (Ep) according to Pav = Ep frep. It follows that for applications requiring a given pulse energy, the limited average power forces a compromise on the laser repetition rate. For example, in science, ultrashort pulses are used for nonlinear processes like terahertz (THz) and extreme ultraviolet (XUV) light generation. Those processes require tens of microjoules to millijoules pulse energy, hence, the repetition rate of Ti:sapphire laser systems for those applications is limited to some kilohertz. The low conversion efficiency of those processes leads to a low flux at the generated wavelengths. Increasing the average power of the laser source and hence the repetition rate would translate in a much higher flux. This, in turn, would dramatically speed up the measurement time for experiments requiring terahertz and XUV pulses and allow new experiments [4, 5]. For industrial applications, higher power often leads to a higher throughput and, in general, industrial applications greatly benefit from megahertz repetition rate sources and multi-hundreds of watts average power [6]. In fact, a significant part of the development of high- power laser sources has been driven by private industrial research. In the last twenty years the output power of ultrafast laser systems increased dramatically due to the development of lasers based on Yb-doped gain materials. Such materials are ideal for high-power operation as they allow for efficient and cost-effective diode pumping and a high doping concentration is possible, while maintaining a good material quality. Such favorable propri- eties combined with laser geometries optimized for heat extraction, namely fiber [7], thin disk [8], and slab [9], enabled the development of high-power laser sources.

Chapter 1

Amplifier systems based on these technologies exceed the kW-level average power milestone (Fig. 1.1). They are usually multi-stage systems composed of a low-power oscillator, pulse stretcher, amplification stages, and pulse compressor. The record results in terms of average output power have been achieved by combining the output of multiple fiber amplifiers, with the current record being 3.5 kW of average power [7].

Fig. 1.1 Overview of pulse energy versus repetition rate of cutting-edge high-power ultrafast sources. Dashed lines at the average power in the label are drawn. Amplifier systems exceed one kilowatt in average power while high-power thin-disk oscillators reach multi-hundreds of watts average power at high repetition rates from a single-box device. The points highlighted in yellow are results demonstrated in this thesis. Refs: [7-21].

Compared to Ti:sapphire laser systems, Yb-doped systems increased the achieved output power by three orders of magnitude. On the flipside, Yb- doped gain materials suitable for high power have a much narrower gain bandwidth compared to Ti:sapphire, hence they cannot deliver multi-hundreds of watts output powers with pulse durations below 100 fs. Such short pulse durations are desirable for many applications, especially in science, and hence a significant research effort has been put into compressing the output of high-power lasers. A key finding has been the recent demonstration of multi-pass cell compression schemes [22]. They allow the compression of a high-power laser output with minimal impact on the spatial and temporal beam quality and have a high overall transmission (in the order of 90%). This

Introduction and motivation simplifies the issues of obtaining short pulses from a high-power laser and paves the way for Yb-doped lasers to become the workhorse of the ultrafast scientific community. 1.2 High-power laser oscillators A compelling route to high-power laser sources is to directly scale up the power of the laser oscillator. In this way, a multi-stage amplifier system is replaced by a conceptually simple and cost-effective single-box device [23]. Developing high-power laser oscillators brings new challenges intrinsic to the delicate physical process of pulse formation. The thin-disk laser (TDL) technology [24] stands out for the development of these ultrafast high-power oscillators. The key idea behind thin-disk lasers is to shape the gain medium as a thin disk. This allows an efficient heat extraction compared to a bulk geometry and a short interaction length between the pulses and the gain medium. This short interaction length keeps nonlinear effects low, which would otherwise hinder pulse formation. In order to obtain pulsed operation from an oscillator, a device which provides a saturable loss behavior is required. Such a device ensures that pulsed operation is energetically favorable for the cavity compared to cw operation. The most common techniques to achieve modelocking in high power operation are Kerr-lens modelocking (KLM) and semiconductor saturable absorber mirror (SESAM) modelocking. In this thesis, we focus on SESAM modelocking and explore a new modelocking technique in the context of thin-disk lasers: the nonlinear-mirror modelocking (NLM). The SESAM [25] is a very versatile modelocking device. In fact, its properties can be adjusted through its thin-film design (semiconductor engineering), and by depositing a dielectric thin-film coating on top of it. Additionally, the thin structure of the SESAM compared to the beam size, is beneficial for efficient heat extraction analogous to the gain disk. SESAMs have been used to modelock lasers with repetition rates ranging from few megahertz to tens of gigahertz and pulse durations from sub-50 fs to nanoseconds at wavelengths from the visible to the mid-infrared (mid-IR), and average powers from mil- liwatts to several hundreds of watts [26].

Chapter 1

The development of high-power oscillators encompasses two main aspects: cavity stability and pulse formation. Regarding cavity stability, the oscillator needs to be designed in such a way that it delivers a single transverse mode. However, due to the high thermal load at kilowatt-level intracavity average power, optical components tend to deform causing beam quality degradation. The resonator has to be designed in such a way that those deformations have minimal impact. Regarding pulse formation, it is a delicate process in high- power oscillators governed by the saturable absorber and the interplay between the group-delay dispersion and the phase accumulated through nonlinearities during the pulse propagation in the laser cavity. Once these challenges are addressed, SESAM-modelocked thin-disk laser oscillators offer a low-noise output, megahertz repetition rates, and diffraction- limited beam quality from a single-box, diode-pumped laser source. In fact, they are already being used for a variety of nonlinear optics experiments. Among the most promising and recent applications of high-power thin-disk oscillators we highlight XUV generation both intra- [27] and extra- [28] cavity and terahertz generation by optical rectification [5, 29, 30]. 1.3 Motivation and outline of the thesis The scientific motivation behind this thesis is the development of high-power laser sources for high-field physics experiments. In this context, we focused on the study and the development of high-power ultrafast lasers based on the thin-disk laser technology. In particular, we thoroughly investigated the two key aspects of cavity stability and pulse formation. The laser sources developed can enable new experiments in research and offer a proof of concept for industry to pick up on those and develop commercial products. This thesis is based on a cumulative format and includes five publications representing the main results achieved. The chapters are organized as follows. Chapter 2 provides an overview of the challenges in developing high-power oscillators, showcases the results achieved in this thesis, and highlights the connections between the results. Chapter 3 focuses on the disk’s thermal lensing. We study the effects that the heated air in front of the disk has on cavity stability. In particular, we introduce

Introduction and motivation the gas-lens effect [31], which we discovered during this thesis. It significantly contributes to the overall disk’s thermal lensing and has important implica- tions for the development of high-power thin-disk lasers. Chapter 4 and Chapter 5 focus on the use of second order nonlinear processes in thin-disk lasers. In particular, Chapter 4 discusses the use of cascaded quadratic nonlinearities (CQN) to assist the pulse formation process. We show how CQN can be used for nonlinearity management in high-power lasers, demonstrating a thin-disk laser with more than 200-W average power which is operated in air [32]. This result set a record for the highest power achieved by a SESAM-modelocked oscillator operated in air. Chapter 5 introduces the nonlinear mirror (NLM) modelocking technique. We demonstrated the first proof-of-concept NLM-modelocked thin-disk laser [33] and later power scaled it close to 100-W average power [34]. This technique can offer the flexibility of the SESAM together with the possibility of obtaining shorter pulses, which are of interest especially for scientific applications. Chapter 6 describes our power scaling results. Prior to this thesis, the average- power record from an ultrafast oscillator was 275 W. We first improved it to 350 W [21] and later to 430 W. In this chapter, we describe how leveraging the learnings of the previous chapters, we combined an improved cavity design with vacuum operation to set the new benchmark. Lastly, Chapter 7 provides an outlook and discusses the prospects in high- power thin-disk lasers development.

Framework of this thesis

2 Framework of this thesis

A significant part of this thesis has been devoted to deeply understand what limits the performance in thin-disk oscillators. In this chapter, we first introduce the thin-disk laser technology and the concepts behind cavity design highlighting the new insights developed during this thesis. Next, we discuss modelocked operation with a focus on the challenges associated with high- power modelocking. In particular, we underline the novel concepts we demonstrated in terms of nonlinearity management and introduce an alternative modelocking technique in the context of thin-disk lasers. Lastly, we conclude presenting our latest high-power results. 2.1 Thin-disk laser concept The thin-disk gain medium was introduced by Giesen et al. in 1994 as a “scalable concept for diode-pumped high-power solid-state lasers” [24]. The disk has a typical thickness of a few hundreds of microns and a diameter of several millimeters. The front side of the disk has an anti-reflective (AR) coating and the backside a high-reflective (HR) coating for both pump and laser wavelengths. In this way the disk can be directly used in a laser as an active mirror which provides the laser gain. The disk is contacted with its backside on a water-cooled heatsink [Fig. 2.1(a)]. The thermal properties of the disk are determined by its material, its dimen- sions, and how effectively the heat can be extracted. The growing market for thin disks pushed industry to optimize all these aspects. This led to improvements to the materials and highly reproducible and optimized contacting

Chapter 2 techniques. In particular, the heatsink on which the disk is contacted plays a crucial role in determining the thermal properties of the disk. Today state-of- the-art disks are directly glued on diamond, owing to the excellent thermal conductivity of diamond. In the laser cavity, the thin disk is used in reflection with the pump and laser beams impinging on the front face [Fig. 2.1(b)]. The pump light, coming from the diodes, is homogenized and focused on the disk through a set of collimation lenses and a parabolic mirror. Due to the small thickness of the disk, only few percent of the pump light are absorbed for each pass on the disk. In order to overcome this limitation, thin-disk lasers encompass an optical arrangement composed by the parabolic mirror and a set of rooftop mirrors to recycle and reimage the pump light on the disk after each pass. This optical arrangement including the aforementioned collimation lenses is called thin-disk head. The thin-disk head has to be manufactured with a high mechanical precision which is done by specialized laser companies such as TRUMPF GmbH and Dausinger & Giesen GmbH. State-of-the-art thin-disk heads offer up to 72 passes on the disk gain medium.

Fig. 2.1 Thin-disk concept. (a) Schematic of the disk (not to scale); (b) schematic of a thin-disk head. The pump beam (in green) and the laser beam (in red) impinge on the front face of the disk. The disk is water cooled from the backside through a heatsink.

The large surface to volume ratio of the disk and the cooling directly through the backside ensure an almost one-dimensional heat flow through the disk. This leads to minimal detrimental disk’s thermal effects even at high power. Additionally, power scaling is possible by increasing simultaneously the pump

Framework of this thesis spot and the laser spot size on the disk, thus keeping the pump intensity constant. In this way, the thermal load per unit area on the disk stays approximately constant. This approach combined with substantial improvements in the production of large-area high-quality Yb-doped disks has been extremely successful. Output powers above 10 kW have been achieved from a multimode (M2 > 10) TDL [35], and up to 4 kW with a lower M2 of 1.4 [36]. For those results the maximum output power is only limited by the amount of pump power that the disk can handle and that is available. Laser operation with a M2 value close to 1, i.e., in nearly fundamental mode operation is preferable in cw, since it allows a tighter focusing of the beam and becomes a requirement in ultrafast operation, as we will discuss. 2.2 Cavity stability and gas-lens effect The laser modes in which the laser can operate are determined by the laser resonator. Here, we consider only stable resonators, i.e., resonators where the field distribution of the mode reproduces itself after a round trip, except for a possible power loss. A laser resonator made of parabolic mirrors supports Hermite-Gaussian modes which are designated as TEMl,m, where the TEM0,0 is the fundamental gaussian mode. Compared to higher order modes with l or m larger than 0, the fundamental mode has the smallest beam waist across all. This difference in beam waist is used in thin-disk oscillators to select the fundamental gaussian mode TEM0,0. The pumped thin disk acts as a soft aperture, since the disk offers gain for the beam in the pumped area and losses through absorption in the unpumped area. Denoting the 1/e2 radius of the pump and laser spot on the disk as wpump and wlaser respectively, a ratio of 70% - 80% for wlaser/wpump has been found experimentally to ensure fundamental-mode operation together with a high level of optical-to-optical efficiency. The intracavity components change their optical properties, namely focusing power and aspherical aberrations, during laser operation due to thermal effects. This changes the cavity properties and hence the cavity can depart from fundamental-mode operation. The study of cavity stability as a function of the focusing power of its components is called stability zone analysis. This topic has been extensively studied in literature, in particular for linear resonators [37].

Chapter 2

The main source of thermal lensing in thin-disk lasers is the disk. To understand how the disk’s thermal lensing affects the cavity stability, we consider a simple laser cavity composed of the disk, which has a concave curvature, a convex mirror, an end mirror, and an output coupler [Fig. 2.2(a)]. We define the change in the focusing power of the disk as Fdisk=2/R(T)-2/R(cold), where T is the temperature of the disk, R its radius of curvature (ROC), and R(cold) the curvature of the cold disk. A change in Δthe disk’s radius of curvature causes a change in the beam size through the cavity and in particular on the disk [Fig. 2.2(b)]. This means that if for a given disk’s focusing power we have the optimal ratio for wlaser/wpump, this may change for a different focusing power of the disk and hence cause higher order modes to be excited. Dealing with the disk as a lens with a variable focusing power, the width of the stability zone with respect to the disk’s thermal lensing decreases inversely propor- tionally to the square of the minimum cavity mode size in the zone, i.e., 1/ [Fig. 2.2(c)]. Hence, increasing the pump and the laser spot size on 2 the disk𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 leads to a narrower stability zone with respect to the disk’s thermal lensing≈ 𝑤𝑤 .

Fig. 2.2 Cavity design and stability. (a) Schematic of a thin-disk cavity composed of an output couple (OC), the thin disk, a convex mirror (CX) and an high reflective (HR) mirror; (b) evolution of the 1/e2 mode radius as a function of the position inside the laser resonator; (c) stability zone for disk’s thermal lensing. ∆Fdisk represents the change in disk’s focusing power, 0 m-1 corresponds to the cold disk.

In terms of beam quality, we typically have a good beam quality at low power, i.e., small |∆Fdisk|, when the laser spot size on the disk is optimal. At high power, owing to a large |∆Fdisk|, we have a sub-optimal laser spot size on the disk and hence a degradation of the beam quality. At very high pump power, 12

Framework of this thesis additional aspherical deformations of the disk [38, 39] become significant and contribute to the beam quality degradation. In this thesis we focus on the spherical part of the thermal lensing since this is sufficient to explain the evolution of the beam quality that we observe in our lasers. Reducing the disk’s thermal lensing is pivotal to develop thin-disk laser oscillators able to operate in fundamental-mode over a wide range of output powers. The disk-inherent thermal lensing has been studied in the literature [40] and is due to the temperature gradient, bulging, stress-induced birefrin- gence, and deformation of the disk. Those effects depend on the disk’s material, the bonding, and the heatsink. Since state-of-the-art disks are industrial products, those aspects are outside of our control. In the context of this thesis, we discovered another source of thermal lensing due to the heating up of the air in front of the disk [31]. In particular, the pump spot on the disk has a super-gaussian intensity profile [41], which results in a similarly shaped temperature profile on the disk. This induces a radial gradient in the temperature profile for the air directly in contact with the disk and a smoother temperature gradient going away from the disk due to convection. Variations in temperature translates into variations in index of refraction due to the thermo-optic coefficient dn/dT. A spatially varying index of refraction affects the propagation of the light, in this case the effect can be well approximated with that of a defocusing lens placed on top of the disk. We call this effect the gas-lens effect. In order to assess this effect, we directly measured the overall disk’s focusing power with an interferometer. We backed our experimental observations, with a numerical model developed with the finite-element method (FEM) software COMSOL. We measure a reduction of the disk’s thermal lensing in vacuum compared to air by ≈37%. We would like to point out that this is a rather counter-intuitive behavior, in fact one would expect more severe thermal effects in the absence of air (i.e., in vacuum) due to the lack of convective cooling. The heated air in front of the disk was already known to cause another effect: the gas-wedge effect. It consists in a vertical deflection of the beam caused by an asymmetric vertical temperature profile of the heated gas in front of the

Chapter 2 disk. Our FEM model was able to also predict this effect. Countermeasures to it have been proposed in literature and include helium-flooding the laser [42], introducing an angularly dispersive element [43], or the use of retroreflectors [44]. Operating the laser in helium or in a low-pressure environment makes both the gas-lens and gas-wedge effects negligible. Understanding the gas-lens effect was pivotal to power scale thin-disk oscillators. It allows us to link the behavior of the laser in air with its behavior in a vacuum. The topic of the gas-lens effect is expanded upon in Chapter 3 of this thesis. 2.3 Active multi-pass cavities So far, we focused on understanding the causes of the disk’s thermal lensing and the effects it has on cavity stability. An important consideration is that the disk-related thermal effects are proportional to the heat deposited on the disk. For a given pump power, we can reduce the heat deposited by increasing the amount of power extracted from the disk through stimulated emission, i.e., laser action. Hence, in order to reduce the disk’s related thermal effects, our goal is to maximize the optical-to-optical efficiency of the oscillator by tuning the cavity’s output-coupling rate. This fixes the ratio between the average output power of the laser (Pout) and the intracavity power (PIC) to Pout = PIC * TOC where TOC is the output coupler transmission. We will now discuss the trade-offs associated with TOC. The average intracavity power in the laser oscillator determines the heat deposited on the intracavity components. For very high intracavity powers these components may exhibit aspherical aberrations and ultimately be damaged. Hence, the goal is to increase the output coupling rate to reduce the intracavity power for a given output power. However, only increasing the output coupling rate would negatively impact the optical-to-optical efficiency, leading to a larger disk’s thermal lensing for a given output power. In order to maintain a high optical-to-optical efficiency with a large output coupling rate, we need to increase the gain per round trip. We can do that employing an active multi- pass (AMP) cavity, which has multiple reflections on the disk gain medium. The first thin-disk lasers relying on AMP cavities were shown by Neuhaus, Bauer, et al. [45, 46].

Framework of this thesis

On the flip side, each time the light is reflected on the disk, the effects of the disk’s thermal lensing accumulate. For nrefl reflections on the disk within the cavity, the width of the stability zone scales by a factor of 1/nrefl. On the other hand, multiple reflections on the disk improve the mode filtering effect of the disk and can make the cavity more robust against higher-order modes. This process may mitigate the detrimental effects of the reduced cavity stability. Further investigation through numerical models are planned. Either way, this highlights the importance of minimizing the disk’s thermal lensing. In this thesis, we combined, for the first time, an active multi-pass cavity with vacuum operation in order to reduce the intracavity power while keeping the disk’s thermal lensing as low as possible. The multiple reflections on the disk are achieved through a 4-f like imaging scheme. Such a scheme allows us to easily change the number of reflections on the disk by shifting the position of a mirror and realigning the active multi-pass cell without affecting the mode throughout the rest of the cavity. We implemented this active multi-pass cavity scheme first in [32], next in our power-scaled NLM-modelocked oscillator [34] and, finally in our record- power oscillator presented in [21]. We present a detailed study of the laser performance as a function of the number of reflections on the disk and the output-coupling rate in Chapter 6.2. 2.4 SESAM and Kerr-lens modelocking Until now, we discussed laser operation in cw, we now explore modelocked operation. Pulses with picosecond and femtosecond duration are typically obtained from a laser oscillator through passive modelocking, which is achieved by incorporating a saturable loss inside the cavity. This loss is classified either as fast when the saturation happens on a time scale orders of magnitude shorter compared to the pulse duration or slow otherwise. For Yb-doped gain materials, the gain upper state lifetime is on the order of 1 ms and hence does not play a role in pulse shaping. The two mainstream modelocking techniques for thin-disk oscillators are Kerr-lens modelocking (KLM) and SESAM modelocking. Kerr-lens modelocking (KLM) belongs to the category of fast saturable loss. It achieves a loss modulation combining the self-focusing effect and a cavity

Chapter 2 aperture. An intense laser pulse, compared to cw light, will be focused and hence fit through the cavity aperture, thus experiencing lower losses. The main advantages of this technique are the fast temporal response, the large achievable modulation depth, and the fact that the saturable properties are not achieved through absorption. On the other hand, exploiting the self-focusing effect links the temporal and spatial properties of the oscillator. Additionally, in order to obtain a significant change in beam size, the resonator has to be operated close to a stability limit. These constraints make the cavity design more challenging and prone to instabilities. KLM thin-disk oscillators delivering 270-W average output power with 330-fs pulses at 18.8-MHz repetition rate have been demonstrated [47]. SESAM modelocking belongs to the category of slow saturable loss. In this case, the saturable loss is obtained through an absorption mechanism and hence a proper thermal management is required. The main advantages are the flexibility and a modelocking process decoupled from cavity stability. Modelocking a laser can be as straightforward as replacing a flat end mirror with a SESAM in a cw laser. A SESAM consists of a bottom distributed Bragg reflector (DBR), which has high reflectivity, followed by an absorber layer which provides the saturable absorption [Fig. 2.3(a)]. The DBR is made up of ≈30 pairs of GaAs and AlAs layers, the absorber layer is made up of multiple InGaAs quantum wells (QWs) and saturates for the typical laser fluence in the laser cavity hence becoming transparent. By properly spacing the DBR and the QWs and introducing a GaAs layer after the QWs, we obtain an anti-resonant structure, which reflects part of the light at its surface. Additionally, the position of the QWs is optimized in order to have them close to an antinode of the electric filed standing wave pattern Fig. 2.3(b)]. The saturation properties of an ideal SESAM are described through the following parameters:

- the modulation depth ∆R, i.e., the difference between the reflectivity at low fluences and the reflectivity of the fully saturated SESAM. - the saturation fluence Fsat, i.e., the fluence at which the reflectivity has increased by 1/e of the modulation depth.

Framework of this thesis

- the non-saturable losses ∆Rns, i.e., the losses of a fully saturated SESAM. Such an ideal SESAM [red line in Fig. 2.3(c)] has a reflectivity which increases monotonically with the fluence. However, for a real SESAM, at high fluencies an additional absorption process due to two-photon absorption causes a rollover effect [blue line in Fig. 2.3(c)], parametrized by an additional F2 parameter. The reflectivity of a SESAM as a function of the fluence can be expressed as [48]:

log 1 + lin 1 ns 𝐹𝐹� ( ) = 𝑅𝑅 𝐹𝐹𝑠𝑠𝑠𝑠𝑠𝑠 (2.1) � � �𝑒𝑒 − �� 𝐹𝐹 𝑅𝑅 − �𝐹𝐹2 𝑅𝑅 𝐹𝐹 𝑅𝑅𝑛𝑛𝑛𝑛 𝑒𝑒 ideal𝐹𝐹 SESAM ��𝐹𝐹�𝑠𝑠𝑠𝑠�𝑠𝑠 �� where Rns = 1-∆Rns and Rlin = Rns – ∆R. Additionally, a SESAM is characterized by its recovery time, i.e., the time it takes for the SESAM to recover after it has been saturated by a pulse. This recovery time can be optimized for specific applications by tuning the growth parameters. In our group, we grow the SESAM in the ETH cleanroom facility FIRST using a molecular beam epitaxy (MBE) machine. Over the years, a large effort has been put into optimizing the saturation properties of the SESAMs for high-power lasers and to increase their damage threshold [49]. One of the key points is to use an additional dielectric top coating (DTC), deposited by a separate machine, in order to reduce the intensity of the electric field inside the semiconductor structure. Since the growth aspect of the SESAM had already been studied extensively, we did not focus on this aspect in the context of this thesis. A typical SESAM optimized for high-power oscillators [49] usually has a low modulation depth ∆R ≈ 1%, a high saturation fluence Fsat ≈ 2 30 uJ/cm , and non-saturable losses ∆Rns ≈ 0.1%.

Chapter 2

Fig. 2.3 SESAM structure and saturation properties. (a) Typical SESAM structure showing the bottom DBR, the absorber formed by quantum wells (QWs), and the dielectric top coating (DTC) section; (b) the height of the block for each material corresponds to the refractive index of the material, the black curve shows the square of the electric field normalized to 4 outside of the SESAM; (c) SESAM’s saturation curve, the red curve refers to an ideal SESAM with F2 = ∞, i.e., no inverse saturable losses.

In a SESAM-modelocked thin-disk laser, the saturable absorber starts and stabilizes the modelocking, while pulse formation relies on soliton pulse shaping. In this regime a stable pulse propagates in the cavity as a result of the balance between the phase change induced by the group delay dispersion (GDD) and the nonlinear phase shift induced by the Kerr effect, named self- phase modulation (SPM). The resulting pulses have an intensity profile in time which follows a squared hyperbolic secant (sech2) function. In this regime the full-width-at-half-maximum (FWHM) pulse duration τp of the sech pulses follows the equation:

2| rt| = 1.76 (2.2) avg𝐷𝐷 IC 𝜏𝜏𝑝𝑝 𝛾𝛾 𝐸𝐸 where Drt is the negative round-trip GDD accumulated by the pulse, γavg =

¾ γ the SPM coefficient for a pulse with a gaussian spatial profile, and EIC the intracavity pulse energy. We define the SPM coefficient γ = B/Ppk_IC where B is the B integral accumulated over a cavity round trip and Ppk,IC the intracavity peak power. This formula suggests that the pulse duration does not depend on the saturable absorber parameters. This however is only true within some boundaries 18

Framework of this thesis since the absorber still must initiate and stabilize the modelocking process. Pulses shorter than 1 ps are routinely achieved due to soliton pulse shaping, despite the SESAM having a recovery time of several picoseconds. In high-power thin-disk lasers, the SPM is usually obtained directly through the air in the laser cavity due to the combination of comparatively long cavities with high intracavity peak powers. An additional Brewster plate is added only if more SPM is required. Dispersive mirrors, usually Gires-Tournois interferometer (GTI) type, provide the necessary negative GDD to balance the SPM. 2.5 Requirements for high-power modelocking Modelocking an oscillator imposes some additional requirements on the laser oscillator, compared to cw operation: (i) the laser should operate in a single transverse mode. (ii) the laser must incorporate a saturable-loss device for modelocking. (iii) the intracavity optics must be able to handle the high intracavity optical intensities while providing the required dispersion for soliton pulse shaping. Regarding point (i), different transversal modes have slightly different frequencies hence their superposition lead to interference effects, which may destabilize modelocking. This point is particularly thorny for high-power oscillators, which, due to the high intracavity power, suffer from thermal lensing of the intracavity components. These thermal effects change the cavity properties and hence may cause beam distortions and excite higher order modes. The main sources of thermal lensing are the disk, the SESAM, and the dispersive mirrors. Point (iii) becomes particularly delicate when a large amount of GDD is required. In fact, dispersive mirrors, due to their resonant structure, have worse thermal behavior compared to standard high-reflective mirrors. In our record- power results we tackled this issue by designing active multi-pass cavities in order to reduce the intracavity power. 2.6 SESAM’s thermal lensing The properties of the SESAM are relevant on two different levels for an ultrafast laser oscillator: on the one hand the SESAM should have suitable 19

Chapter 2 saturation properties for modelocking, on the other it should ideally not exhibit any thermal lensing. We discussed the saturation properties in Section 2.4. Regarding the thermal lensing, from a cavity-stability standpoint, the ideal SESAM should be flat (i.e., with a radius of curvature of some hundreds of meters) and insensitive to heat. We assess the impact that a SESAM has on cavity stability calculating a stability zone for the SESAM’s thermal lensing in the same way as we do for the disk. We must consider the cold radius of curvature of the SESAM and the thermal lensing induced by the heat deposited on the SESAM. These aspects have been investigated in detail in [50]. They are determined by the thickness of the substrate on which the SESAM is grown, the heatsink material, and the contacting technique used to bond the SESAM on the heatsink. We grow our SESAMs on a 600-µm GaAs wafer, that is the substrate [Fig. 2.3(a)]. The DBR and the absorber, which is made up by quantum wells, are overall only ≈5 µm thick. In order to extract the heat from the SESAM, our standard procedure consists in bonding the backside of the GaAs substrate on copper through tin soldering. This typically results in an astigmatic surface with a cold radius of curvature <20 m in absolute value, corresponding to a diopter power >0.1 m-1. This standard procedure works well for low- to mid- power oscillators but is not suitable for multi-hundreds of watts oscillators with megahertz repetition rate cavities. For those, we need SESAMs with a flatter cold surface. To improve the flatness of the cold SESAM, we collaborated with our industrial partner TRUMPF GmbH. Due to their industry-level contacting technique, we obtained SESAMs with a cold radius of curvature >500 m. The thermal performance of the SESAM is limited by the fact that the heat generated in the absorber section on the front face of the SESAM travels through the 600-µm substrate, before being extracted from the copper contacted on the backside. A way to improve the thermal performance is by completely removing the GaAs substrate. This approach has been presented in [50] and delivers ≈4 times better performance compared to a standard SESAM in terms of thermal lensing per unit of power absorbed. However, due to errors in the MBE growth and the delicate etching procedure to

Framework of this thesis remove the substrate, we were not able to develop substrate removed SES- AMs with a large enough usable area. To overcome this challenge, we proposed an intermediate solution which consists in lapping the substrate from the original 600 µm to ≈200 µm. In this way the critical etching part is avoided. Our FEM model predicts a roughly two-fold improvement in thermal performance. These improvements on the SESAM in terms of cold-surface flatness and thermal properties helped us in achieving the record power result presented in Section 6.2. During the timeframe of this thesis, I worked on a project to improve the thermal properties of the SESAM. We obtained the first results shortly before the deadline to submit this thesis and decided to fill in an invention disclosure to ETH technology transfer to explore the possibility of patenting the solution. In light of the required confidentiality and the fact that we did not use these improved SESAMs for the results presented in this thesis, I decided to not include that work in this thesis. 2.7 Self-phase modulation cancellation Cutting-edge ultrafast thin-disk laser oscillators deliver tens-of-µJ pulses at megahertz repetition rate with megawatt-level intracavity peak power. This combination would lead to an amount of SPM picked up by the pulses in the intracavity air in the order of some radians. In the soliton modelocking regime, in which those lasers operate, stable pulses are obtained only when the SPM is balanced with an appropriate amount of GDD. An excessive absolute value of SPM or an insufficient amount of GDD can prevent pulse formation. Different solutions have been developed to cope with this challenge. A solution is to introduce a corresponding amount of GDD of the order of several 100’000 fs2 in the laser cavity to compensate for the large amount of SPM. This creates a tradeoff between pulse energy and the GDD introduced in the laser cavity. The issue with this approach is related to the thermal effects of the dispersive mirrors used to introduce the GDD. Those effects, eventually, limit the amount of average power achievable with the laser. Additionally, obtaining such large amount of GDD requires cavity with many passes on the same mirrors, which can be cumbersome from a practical point of view.

Chapter 2

A different solution, which can overcome the mentioned issues, is to operate the ultrafast thin-disk oscillator in a low-pressure environment. This reduces the amount of GDD needed by more than an order of magnitude, but the added complexity makes the laser oscillators less appealing for applications in general and, especially, for industry. Additionally, operating the lasers in a vacuum chamber limits the possibility to perform cavity adjustments, hence, it makes laser development more involved. In this thesis, we explored an alternative approach to nonlinearity management based on cascaded quadratic nonlinearities (CQN). It allows a direct cancellation of the SPM picked up in air. In CQN, a second-harmonic generation (SHG) crystal is used to obtain an effective nonlinear refractive index that is tunable in magnitude and sign. This is achieved through the continuous conversion and back-conversion of light between the fundamental wave (FW) and the second harmonic (SH) in a phase-mismatched SHG crystal. We exploit this by introducing an intracavity SHG crystal and angle tuning its phase mismatch ∆k to set the amount of negative phase shift introduced. This counteracts the positive phase shift picked up in air and allows to operate the laser in air with an amount of GDD comparable with that of vacuum-operated thin-disk lasers. On the flip side, the light converted to the second harmonic in the CQN process is lost to the cavity mode, which is at the fundamental wavelength. This loss is present only for modelocked operation and not for cw. Hence, it will act as in inverse saturable loss counteracting the modelocking action of the SESAM. By operating the crystal in a SHG minimum (for example the third or the fourth), we bring this loss to few 0.1%, such that it does not impact modelocking [Fig. 2.4(a)]. We demonstrated this technique in a high-power thin-disk oscillator using a L = 5-mm-long type-I LBO crystal to obtain the CQN process. In this specific case, the SPM coefficient from the intracavity air was γair ≈ 10.6 mrad/MW. By tuning the phase mismatch of the crystal ∆k, we cancelled up to 80% of the SPM picked up in air operating the crystal close to the 3rd SHG minimum [Fig. 2.4(b)]. The thin-disk oscillator delivered 210-W average output power with 780-fs, 19-µJ pulses (19-µJ point in Fig. 2.5). This is the

Framework of this thesis highest output power of any SESAM-modelocked laser operated in air to date. This result is discussed in detail in Chapter 4.

Fig. 2.4 CQN processes in TDLs: (a) fraction of light converted to the second harmonic; (b) effective SPM coefficient. By tuning the phase mismatch ∆k we can obtain an effective negative SPM coefficient together with negligible SHG losses. For our high-power result, we operated the crystal close to the marked 3rd SHG minimum.

2.8 Nonlinear mirror modelocking Besides SESAM modelocking, which is a well-established modelocking technique for high-power oscillators, we investigated an alternative technique: nonlinear mirror (NLM) modelocking. NLM modelocking hinges on second-order nonlinearities, as does CQN. It was invented in 1988 by Stankov et al. [51] and used to modelock bulk lasers in the picosecond regime. The technique combines a SHG crystal with a dichroic output coupler, which is high reflective for the second harmonic and partially transmits the fundamental wave. Through the processes of second- harmonic generation and optical parametric amplification (OPA), it provides a reflectivity which increases at higher intensities, thereby yielding a saturable loss. This modelocking technique, compared to SESAM modelocking and KLM, offers on one hand a pulse formation process decoupled from cavity stability and, on the other, a fast-saturable loss. The achievable pulse duration is limited by the group velocity mismatch (GVM) between the fundamental wave and the second harmonic in the nonlinear crystal [52]. In particular, the GVM hinders the efficiency of the OPA process for short pulses, creating a rollover

Chapter 2 effect that reduces the reflectivity of the nonlinear mirror device for short pulses. The best performance achieved with this technique, in terms of high average power and short pulses, in the context of bulk lasers were of few-watt output power and 5-ps pulses. In fact, in that context, the limited bandwidth of the gain materials used (Nd:YAG for example) and the limited peak power of those oscillators required long nonlinear crystals for the SHG and OPA processes. Those long nonlinear crystals, because of the mentioned GVM problem, in turn, prevented those lasers from achieving shorter pulses. In thin disk oscillators, due to the high peak power achievable much shorter crystals can be used hence reducing the detrimental effect of the GVM. In our first demonstration [33], using a BBO crystal for the nonlinear mirror, we achieved 21-W average output power with 323-fs pulses from a 17.7-MHz cavity. This result shortened the achieved pulse duration with this technique by a factor of 10 and improved the peak power by a factor of 100. Addition- ally, in the context of ultrafast thin-disk lasers, we demonstrated a pulse duration previously accessible only through KLM using the same gain material. For comparison SESAM-modelocked Yb:YAG thin-disk oscillators usually achieve pulse durations in between 600 fs and 1.5 ps. After our first results, we attempted to scale up the output power of NLM- modelocked thin-disk lasers, keeping the pulse duration as short as possible. To this end, we developed a new laser oscillator incorporating a state-of-the- art thin-disk module and a cavity with multiple reflections on the disk. Addi- tionally, to minimize thermal effects, we employed a low-absorption LBO crystal as nonlinear crystal. Our first attempts to modelock this oscillator relying solely on the nonlinear mirror were unsuccessful due to a tendency of the oscillator to transition in a Q-switched modelocking regime. Q-switching instabilities are particularly dangerous since they cause spikes in the intracavity peak power in the laser and can ultimately damage an intracavity component. In our case it was the output coupler to be damaged. Hence, we decided to combine the nonlinear mirror with a SESAM in order to exploit the rollover behavior of the SESAM to clamp the saturable loss and hence avoid Q-switching. This route proved

Framework of this thesis to be successful and allowed us to obtain stable modelocking at up to 87-W average output power with up to 14.7-MW peak power and sub-600 fs pulses [34]. Additionally, we defined a set of guidelines to use the nonlinear mirror in high-power sub-picosecond oscillators. The topic of the NLM modelocking is expanded upon in Chapter 5. 2.9 Power scaling of modelocked thin-disk lasers The understanding of high-power ultrafast laser oscillators developed in the previous sections allowed us to improve the long-standing average-power record of 275 W set in 2012 by Saraceno et al. [12]. In particular, the ultrafast oscillator designed by Saraceno et al. was based on a comparatively short cavity with one reflection on the disk operating at 16.3 MHz and with an output coupler transmission of 11.4%. Such cavities are appealing due to their simplicity and the few optical components they incorporate. On the flip side, they operate with a comparatively low output-coupler rate and hence have a high intracavity power for a given output power. For example, the 275-W average power oscillator operated with 2.4 kW of intracavity power. Our first attempts to develop a laser oscillator delivering more than 275-W average power were based on a similar cavity design and an increased pump and laser spot size on the disk. However, they failed because of the high intracavity average power, which led to detrimental thermal effects and damages to the intracavity optics and the SESAM. To overcome this challenge, we implemented a strategy based on the following points:

- we designed an active multi-pass cell with multiple reflections on the disk to increase the output coupling rate and hence reduce the intracavity power for a given output power. - we combined the active multi-pass cell with vacuum operation to minimize the thermal lensing effects from the disk and reduce nonlinearities in ultrafast operation. We implemented a cavity with three reflections on the Yb-doped thin-disk gain medium operated with 25% output coupling rate in an atmosphere of 30-mbar N2. For modelocking, we used a standard top-coated SESAM optimized for high power. The oscillator delivered 350-W average output power 25

Chapter 2 with 940-fs, 39-µJ pulses at 8.88-Mhz repetition rate resulting in 37-MW peak power [21] (39-µJ point in Fig. 2.5). To further scale up the output power of this oscillator, we pushed the active multi-pass cell approach one step further and advanced our oscillator in the following directions:

- we increased the number of reflections on the disk from three to five. - we used, for modelocking, a SESAM with a flat cold surface (ROC > 500 m) and enhanced heat extraction capabilities due to the lapped substrate. - we set up an imaging system which monitors the disk’s saturation. It allowed us to optimize the laser alignment in real time and acted as a safety interlock to shut down the pump diodes in case of disk’s overheating. - we optimized the placement of the optical components to minimize stray light reflections and hence thermal drifts due to thermal expansion of the mirror mounts. The second iteration of our oscillator operated with an output coupling rate of 40% in a 47-mbar air atmosphere. It delivered 430-W average output power, with 68-µJ, 769-fs pulses at 6.29-MHz repetition rate (68-µJ point in Fig. 2.5). Those parameters correspond to a peak power of 78 MW, which, to the best of our knowledge, is the highest peak power ever recorded from any ultrafast laser oscillator. The output power of this oscillator is limited by the onset of the SESAM’s rollover, which leads to additional losses and hence clamps the output power. Further power scaling should be possible by using SESAMs with a different top coating and a larger saturation fluence. The laser parameters reached, especially if combined with an extra-cavity pulse compression stage, are compelling for a variety of nonlinear optics experiments such as high-harmonic generation. An in-depth description of our power-scaling results is presented in Chap- ter 6. We discuss first the 350-W average power ultrafast oscillator and then highlight the further advancements which allowed us to reach 430-W average output power.

Framework of this thesis

Fig. 2.5 Overview of state-of-the-art thin-disk laser oscillators modelocked using the techniques: SESAM, KLM, NLM, and nonlinear polarization rotation (NPR). The results obtained in this thesis are highlighted in yellow. In particular we set records for the highest average power overall and the highest average power achieved in air from a SESAM-modelocked laser. Refs: [12, 15, 21, 32-34, 46, 47, 53-57].

Thermal effects in thin-disk lasers

3 Thermal effects in thin-disk lasers

In this chapter, we describe the thermal effects associated with the thin-disk gain medium in a high-power laser oscillator. We operated our laser in cw with up to 1.4 kW of average output power in multimode operation and 800 W in fundamental transversal model operation (M2 < 1.1). We carried out a detailed characterization of the disk’s thermal lensing and separated it in two components: one inherent to the disk and one due to the air heating up in front of the disk. We discovered the existence of the air-induced second component which we called gas-lens effect. Additionally, we developed a numerical model which describes the effects of the heated air in front of the disk and predicts the gas-lens effect. The details are presented in the following journal publication: Title: “Gas-lens effect in kW-class thin-disk lasers”, [31] Journal: Optics Express doi: 10.1364/OE.26.012648

© 2018 Optical Society of America. Users may use, reuse, and build upon the article, or use the article for text or data mining, so long as such uses are for non-commercial purposes and appropriate attribution is maintained. All other rights are reserved.

Chapter 3

3.1 Gas-lens effect in kW-class thin-disk lasers

A. Diebold,1,3 F. Saltarelli,1,3 I. J. Graumann,1 C. J. Saraceno,1,2 C. R. Phillips,1 and U. Keller1 1Ultrafast Laser Physics, Institute for Quantum Electronics, ETH Zurich, Zurich, Switzerland 2Photonics and Ultrafast Laser Science, Ruhr-Universität Bochum, Bochum, Germany 3These authors contributed equally to this work.

Abstract: We unveil a gas-lens effect in kW-class thin-disk lasers, which ac- counts in our experiments for 33% of the overall disk thermal lensing. By operating the laser in vacuum, the gas lens vanishes. This leads to a lower overall thermal lensing and hence to a significantly extended power range of optimal beam quality. In our high-power continuous-wave (cw) thin-disk laser, we obtain single-transverse-mode operation, i.e. M2 < 1.1, in a helium or vacuum environment over an output-power range from 300 W to 800 W, which is 70% broader than in an air environment. In order to predict the magnitude of the gas-lens effect in different thin-disk laser systems and gain a deeper understanding of the effect of the heated gas in front of the disk, we develop a new numerical model. It takes into account the heat transfer between the thin disk and the surrounding gas and calculates the lensing effect of the heated gas. Using this model, we accurately reproduce our experimental results and additionally predict, for the first time by means of a theoretical tool, the existence of the known gas-wedge effect due to gas convection. The gas-lens and gas-wedge effects are relevant to all high-power thin-disk systems, both oscillators and amplifiers, operating in cw as well as pulsed mode. Specifically, canceling the gas-lens effect becomes crucial for kW power scaling of thin-disk oscillators because of the larger mode area on the disk and the resulting higher sensitivity to the disk thermal lens. © 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

3.1.1 Introduction Increasing the average output power from diode-pumped solid-state lasers is motivated by many industrial and scientific applications [4, 58, 59]. Reaching the desired kW-class performance requires gain materials with both excellent

Thermal effects in thin-disk lasers thermal properties and optimized heat-removal designs. In particular, Yb- doped materials have been at the forefront of most high-power continuous- wave (cw) laser developments in the last few decades. In addition to a small quantum defect, they exhibit broad absorption spectra in the near-infrared, which are easily accessible by low-cost high-power diode pump lasers. Three different design architectures have proved especially successful for state-of-the-art thermal management: fiber [60], slab [61], and thin-disk [24] geometries. In the scope of this paper, we focus on the thin-disk design, which, specifically, is well suited for applications requiring excellent spatial beam quality. Here, the gain medium is shaped as a disk with a thickness in the order of 100 μm and used in reflection with cavity mode sizes in the mm range. The large ratio of pump-spot size to disk thickness results in a quasi-1D heat flow through the backside of the disk and strongly reduces thermal-lensing effects. Thanks to this feature, power scaling is possible by simply increasing simultaneously the pump power and the pump-spot size on the disk, while keeping the pump intensity constant. This power scalability led to the demonstration of more than 10 kW of output power in cw operation from a multimode (M2 > 10) thin-disk laser (TDL) with a single disk [35], or up to 4 kW with a lower M2 of 1.4 [36]. However, in this latter result an M2 < 2.0 was only achieved at output powers between 3 kW and 4 kW, thus in a comparatively narrow range of 1 kW. The thin-disk concept allows for exceptional results also in high-power ultrafast operation. In a multi-pass thin-disk amplifier setup, 1.4 kW at 300 kHz repetition rate with 8-ps pulses were demonstrated at an M2 > 1.4 [62]. Also, thin-disk regenerative amplifiers made large progress in recent years with up to 1 kW of average output power at 5 kHz [20] or 500 W at 50 kHz [17], both at 1 ps of pulse duration. For even higher pulse repetition rates in the MHz range, modelocked ultrafast TDLs [63] are particularly attractive as they generate few hundreds of Watts of average power directly from a compact oscillator at sub-ps pulse durations [12, 55]. Furthermore, they offer excellent single-transverse-mode beam quality with an M2 < 1.1 and low noise properties [64]. Often, these systems are operated in helium (He) or vacuum environments to avoid excessive nonlinearities [23, 55, 65]. For a stable intracavity pulse-formation process, 31

Chapter 3 higher-order modes must be prevented [23]. Thus, modelocked TDLs are also very demanding when it comes to the thermal-lensing behavior of the disk. In particular, for high output powers approaching the kW level, a large spot size (i.e., with a diameter close to 10 mm) is required on the disk. In TDLs, the width of the stability zone with respect to disk thermal lensing scales inversely with the square of the pump-spot size, for a fixed number of intracavity passes over the gain material [37]. Thus, increased spot sizes result in an increased sensitivity to the disk thermal lensing, which makes it more challenging to achieve single-mode operation over a wide power range. The disk thermal lensing can be compensated for by using deformable mirrors in TDLs in order to dynamically adjust the cavity during operation [66]. This, however, comes at the expense of additional complexity in the laser setup. Additionally, the thermal load on the disk and consequently the thermal lensing can be mitigated by pumping into the zero-phonon line at 969 nm instead of 940 nm [67]. Through many years of industrial-scale research, thin disks, specifically based on the gain material Yb:YAG, have been optimized in terms of optical and thermal behavior [36]. Yet, in addition to thermo-optic effects intrinsic to the disk, the heated gas atmosphere close to the disk can have a significant impact on the laser performance. One effect, which recently received experimental attention, is the so-called gas wedge. It is a vertical deflection of the beam caused by an asymmetric vertical temperature profile of the heated gas in front of the disk. Measures to compensate for this gas-wedge effect include adjustments of the cavity end mirrors, He-flooding the laser [42], introduction of an angularly dispersive element [43], or the use of retroreflectors in multi-pass thin-disk amplifiers [44]. However, neither a systematic understanding of the gas wedge nor a measurement of the full influence of the gas environment on the thin-disk thermal-lensing behavior has been demonstrated to date. In this paper, we investigate the disk thermal-lensing effects of high-power TDL systems in different gas environments. In our cw TDL setup, we achieve single-mode operation (i.e. M2 < 1.1) over an approximately 70% broader output-power range of about 500 W in vacuum (i.e. 1 mbar) versus about 300 W in air (Fig. 3.1). At a first glance, this result appears counter-intuitive as one might expect more severe thermal effects in the absence of air (i.e. in

Thermal effects in thin-disk lasers vacuum), and thus a narrower output power range of good mode quality. To investigate the observed behavior in detail, we carry out a thermal-lensing measurement for our state-of-the-art disk in different gas environments. We find a reduction of the overall disk thermal lens by ~33% when operating in vacuum or 1 bar of He as compared to 1 bar of air or 1 bar of nitrogen (N2), with the disk temperature being independent of the gas environment. In a newly developed numerical simulation, we modeled our experimental results with a gas lens induced by the heated gas in front of the thin disk, which adds to the disk-material thermal effects analyzed in Ref. [68]. This gas lens is non- existent for vacuum environments and roughly a factor of five smaller for He as compared to air and N2. Our model also predicts the above-mentioned gas-wedge effects and forecasts a reduction of this effect by an order of magnitude when going from air to He.

Fig. 3.1 (a) Schematic of the single mode cw thin disk laser (TDL) cavity setup, including an output coupler (OC), a 2-m convex (CX) mirror, and the highly-reflective (HR) end mirror. The three cavity arms are labeled as a, b, and c, respectively. (b) Output power slope for high-power single mode operation. The power range of good beam quality (i.e. M2 < 1.1) is ~70% broader in vacuum as compared to 1 bar air.

Our findings therefore provide crucial knowledge for the design of the next generation of TDL systems. In particular, we suggest operating the cavity in a low-pressure environment or flooding it with helium in order to remove the gas-lens and gas-wedge effects and significantly increase the operation range of high-power TDLs. Thin-disk cavities with high sensitivity to disk thermal lensing will particularly benefit from our investigation. Such systems include those with output powers in the kW range and consequently large disk spot

Chapter 3 sizes, as well as high-energy thin-disk lasers with multiple passes over the gain crystal [15, 46, 69]. For ultrafast high-power TDLs, the suggested approach is particularly attractive as replacing air with helium or vacuum additionally heavily reduces intracavity nonlinearities [23]. The paper is structured as follows. In section 3.1.2, we present our high-power single-mode TDL cw results in different gas environments. Section 3.1.3 details our thermal-lensing measurements, including the discovery of a gas lens in front of the disk. Our findings indicate a significant difference of operation in 1-bar air and 1-bar N2 as compared to vacuum and 1-bar He and thus explain our laser experiments. Section 3.1.4 theoretically models our experiments, discussing both the gas-lens and the gas-wedge effect. We conclude in section 3.1.5.

3.1.2 High-power single-transverse-mode TDL operation In our experimental high-power single-mode TDL setup, we used a 100-μm- thick, 10-at.%-doped, 3.80-m-curved Yb:YAG disk with a diameter of 20 mm, bonded onto a diamond heat sink. The disk was inserted into a 44- pass thin-disk laser head and pumped with a free-space-coupled diode, delivering up to 3.7 kW at at center wavelength of 940 nm. The pumping scheme resulted in an 8-mm-diameter octagonal-shaped pump spot. The above-mentioned parts were provided by Trumpf. We placed the entire setup inside a vacuum chamber, similar to the one used in [12], which allowed for operation in either air, vacuum (~ 1 mbar), He, or N2 environment. We designed a single-mode cavity with a single reflection on the disk [Fig. 3.1(a)]. It consisted of three arms, with lengths a = 1000 mm, b = 1100 mm, and c = 2308 mm. This cavity setup was convenient due to its independent adaptability of both the laser-mode radius on the disk via arm c, and the center of the cavity stability zone [37, 70, 71] with respect to the disk thermal lens via arm b. For an experimentally optimized beam quality, we chose a laser-mode radius on the disk of 2.87 mm in the center of the stability zone, leading to an overlap with the pump spot of ~72%. The cavity was operated with an output-coupling (OC) mirror transmission of 8% and its alignment was optimized during operation via piezo-controlled cavity end mirrors. We increased the OC rate to 8% from 4% used for the multimode operation in order to reduce the intracavity power. In fact, compared to multimode 34

Thermal effects in thin-disk lasers operation, in the single mode cavity we have a smaller beam on the intracavity mirrors and so higher intensities. In this setup, we measured in cw operation simultaneously the output power and the beam quality (M2) of the output laser mode. We always refer to the average M2 value, i.e. M2 = sqrt(M2x*M2y). Using different gas environments and keeping all other cavity parameters constant, we pumped the disk up to 2.5 kW of pump power, corresponding to a pump intensity of 5 kW/cm2. As we show in Fig. 3.1(b), we achieved good beam quality (M2 < 1.1) for operation in vacuum from ~300 W to ~800 W of output power, i.e. over a power range of ~500 W. In 1-bar air, this range narrowed down to ~200 W to ~500 W, i.e. a power range of ~300 W. In 1-bar He, we achieved similar results as in vacuum, and in 1-bar N2 similar results as in 1-bar air. For the sake of clarity, the data points for 1-bar N2 and 1-bar He are omitted from Fig. 3.1. We could shift the center of the power range of good beam quality to different output power levels by adapting arm b. Yet, the overall span of the ranges stayed unchanged for each gas environment. Our observations suggest a reduced disk thermal lensing in vacuum or 1-bar He as compared to 1-bar air or 1-bar N2. This led us to investigate the origins of thermal lensing in our system in more detail, as a broad power range of good beam quality is crucial, in particular for modelocked operation.

3.1.3 Thermal-lensing measurements Experimental setup We simultaneously employed two independent diagnostics to measure the thermal-lensing behavior of our thin disk. 1. Interferometer: We used the interferometer Trioptics µPhase PLANO S DOWN with a frequency-stabilized HeNe Laser, routed into our vacuum-chamber with a 4-f 1:1 imaging setup. For each gas environment, we treated the radius of curvature of the cold disk as a reference point and we measured deviations from that. In this way, we can measure small changes, independent of the absolute calibration of the reference surface. Given the measured phase profile, to obtain the lensing effect we first set an analysis mask for

Chapter 3

the interferometer laser beam on the disk, filling the whole 8 mm pump spot size, and then perform a fit to obtain a lens value in diopters. Thus, we calculated the total disk thermal lens as

∆Ftotal = 2/R(I) - 2/R(I = 0), where R is the disk’s radius of curvature and I is the pump intensity on the disk. From the fits, the uncertainty -3 that we get on ∆Ftotal is <0.3 x 10 diopters. Thus, we do not expect this to be the limiting factor in the precision of our measurements. 2. Laser focus: As a second method, we directly measured on a beam profiler the focusing effect experienced by a probe beam upon reflection from the disk. For this method, we set up a single-frequency diode laser (Top- tica CTL 1050) and collimated its single-mode output beam with 6.80-mm 1/e2 diameter on the disk. We tuned its wavelength to 1060 nm to minimize the gain effect of the disk on the probe beam. We measured the 1/e2 beam diameter wcam with a DataRay Win- CamD-LCM camera at a distance dcam = 2.40 m from the disk. Given the probe beam size on the disk and the distance dcam, through ABCD matrix calculations it is possible to relate the beam size at the camera position with the disk radius of curvature and, ultimately, with its ther-

mal lensing ∆Ftotal. We chose the position dcam in order to have a good

compromise between the sensitivity to thermal lensing ( cam ∆Ftotal) and the beam diameter wcam with respect to the camera aperture. With ∂w /∂ the chosen dcam, at ∆Ftotal = 0, we have cam = 1.8 mm and a sensitiv- -1 2 ity cam ∆Ftotal = 8 mm/m . With a pixel size of (5.5x5.5) μm , this w sensitivity translates to a minimum measurable variation on ∆Ftotal of ∂w /∂ 0.7 x 10-3 diopters. This value is comparatively small with respect to the measured thermal lensing. Additionally, we took sample profiles every 0.5° in the camera image and for each one we calculated cam. We obtained the final value of cam averaging them. Thus, also in this w case, we do not expect the precision on ∆Ftotal to be limited by the measuring technique. w

Thermal effects in thin-disk lasers

In order to assess the repeatability of our ∆Ftotal measurements, we repeated the same measures in different runs few hours apart. The recorded fluctuations in ∆Ftotal were in the percent-level. In addition to the above measurements, the disk temperature was tracked with a calibrated thermal camera FLIR SC640, looking into the vacuum chamber through a Germanium window. Measurement results and implication for kW-class TDL cavity In all presented configurations, the disk defocused, i.e. the disk focal power decreased, with increasing pump power. However, the rate of change with respect to pump power depended on the exact operating conditions. In fluorescence operation, the disk diopter change, relative to the cold disk, was linear versus pump power, within the range studied. Furthermore, thermal-lensing effects were of the same magnitude for operation in 1-bar air or 1-bar N2, and 33% less pronounced in vacuum or 1-bar He. The disk temperature increased linearly with pump power and was independent of the gas environment. Fig. 3.2(a) shows our fluorescence measurements. For the sake of clarity, we excluded the data points for 1-bar N2. The experimental results from both measurement methods (interferometer and laser focus) stood in good agreement with each other within a ~10% error margin. Additionally, we measured the disk curvature in multimode (MM) laser operation. In this case the laser had an M2 ~ 60, using a V-shaped cavity with a flat highly reflective (HR) mirror and a flat 4% OC mirror. We achieved MM output powers up to 1400 W. Thanks to the low sensitivity of the highly multimode test cavity to the cavity element curvatures, the output power was almost independent of the disk thermal lensing and of the different gas environments. We therefore only show one averaged curve in Fig. 3.2(c) for the output power. Again, thermal-lensing effects in vacuum or 1-bar He were ~33% weaker as compared to 1-bar air or 1-bar N2. The absolute disk thermal lensing and temperature increase were reduced by ~25% in MM operation as compared to fluorescence operation, for the whole range of pump powers used in these experiments. This trend is expected from general heat fraction theory [72].

Chapter 3

Fig. 3.2 (a) Disk thermal-lensing measurements in fluorescence mode, total disk thermal lens ΔFtotal, disk peak temperature change ΔT. Both methods, interferometer (Int.) and laser focus (Focus), stand in good agreement with each other. Measurements in vacuum yielded similar results as 1 bar He, and measurements in 1 bar N2 (not shown here) yielded similar results as 1 bar air. The disk temperature increase is independent of the gas environment. (b) Disk thermal-lensing measurements in multimode (MM) operation, reaching 1.4 kW of output power [see Fig. 3.2(c)]. Due to the low sensitivity of the highly multimode test cavity to the cavity element curvatures, the output power was independent of the gas environment within the uncertainty of the used power meter (~5%). Note also that a slightly wider range of pump intensities (up to 5.5 kW/cm2) is used for the multimode data.

From both the fluorescence and MM measurements we found that the disk thermal lensing relates linearly to the disk peak temperature. We used the experimental data presented in Fig. 3.2 in order to calculate the ratio between the ∆Ftotal and the disk temperature increase ∆Τ through a linear fit with the intercept fixed to 0. We report this scale factor in the first two columns of Table 3.1 for fluorescence operation and multimode operation, respectively. The scale factor mostly depends on the gas environment, but is almost independent of the laser operating conditions (e.g., fluorescence, multimode, single mode). We therefore infer that the disk temperature is a quantitatively accurate metric for disk thermal lensing, with the scale factor found via the measurements presented in this section. From the mentioned linear fits, we could calculate an uncertainty on the presented fitting parameters of ~3%. Then, we use the vacuum measurements to isolate the gas contribution from the disk-material contribution obtaining the results presented in column 3 of Table 3.1. The mentioned uncertainties on the fit parameter allows us to provide an uncertainty on the gas-lens contribution ∆Fgas,exp/∆T.

Thermal effects in thin-disk lasers

Table 3.1 Slope of disk thermal lensing for different gas environments. Total diopter change (ΔFtotal, see also Fig. 3.2) in both fluorescence and multimode operation, diopter change due to the gas lens effect (ΔFgas,exp = ΔFtotal - ΔFvacuum) inferred from the fluorescence measurement, and simulated diopter change due to the gas lens effect (ΔFgas,sim, see section 3.1.4), all per disk peak temperature increase (ΔT). The fit uncertainty of (ΔFtotal/ΔT) is ~3%. The resulting uncertainty of ΔFgas,exp/ΔT is presented in the table.

Gas Fluorescence Multimode , , environ- total total gas exp gas sim ment [10-Δ6 𝐹𝐹1/m/K] [10-Δ6 𝐹𝐹1/m/K] [10Δ-6𝐹𝐹 1/m/K] [10Δ-6𝐹𝐹 1/m/K] Vacuum 228Δ𝑇𝑇 237Δ𝑇𝑇 Δ-𝑇𝑇 Δ-𝑇𝑇 1-bar He 244 263 16 ± 6 26 1-bar air 364 374 136 ± 6 128

1-bar N2 378 369 150 ± 12 143

The air temperature in the laboratory was 24 ºC, and the humidity ~30%. Our measurements in N2 show a difference for the ∆Fgas,exp/∆T with respect to air within 10% for both fluorescence (Table 3.1) and multimode operation. Thus, humidity did not strongly influence the gas-lens effect. Thermal-lensing measurements in our kW-class single-mode setup described in section 3.1.2 (Fig. 3.1) were not possible due to space constraints in our cavity setup. Yet, the disk thermal lensing is directly proportional to the disk temperature. Thus, we measured the disk temperature increase during lasing and then inferred its thermal lens (from the results presented in Table 3.1). In Fig. 3.3(b), we present the measured M2 as a function of the disk thermal lens. We overlap it with the corresponding calculated laser-beam radius at the disk, i.e. the stability zone. As in Fig. 3.1, we show two cases, 1-bar air and vacuum. The same set of measurements are used for both Fig. 3.1(b) and Fig. 3.3(b). For each gas medium, a good M2 occurred over the same range of thermal-lensing values. However, for vacuum and 1-bar He environments, where gas lensing is much weaker, this corresponds to a wider range of pump powers, and hence a wider range of output powers. The beam quality degraded as soon as the laser-beam radius at the disk, and therefore the overlap between

Chapter 3 laser beam and pump beam, deviated from the optimum value at the center of the stability zone.

Fig. 3.3 (a) Sample output beam profile for different values of M2. (b) Calculated stability zone of the single-mode cavity (black solid line) in comparison to the measured 2 mode quality (M ) versus the total disk diopter change (ΔFtotal) for both operation in 1-bar air and vacuum. The overlaid numbers indicate the corresponding output power, see also Fig. 3.1(b). In this particular cavity setup, an ideal overlap of pump spot and 2 - laser spot, leading to an M < 1.1, is achieved for disk thermal lensing between -5*10 3 1/m and -11*10-3 1/m.

It should be noted that in TDLs the width of the stability zone scales inversely with the square of the pump-spot size, for a fixed number of intracavity passes over the gain material [37]. For state-of-the-art kW-level TDL operation large spot diameters (e.g. 8.0 mm as presented here) are required in order to reach sufficient pump powers, which results in narrower stability zones. Thus, minimizing the disk thermal effects as much as possible becomes critical. The stability zone also becomes narrower or splits up when the number of laser passes over the gain material is increased. This concept is frequently employed in high-energy thin-disk lasers in the form of multi-cavity [15, 69] or relay-imaging multi-pass designs [46]. Thus, already at comparatively small pump-spot sizes, these lasers can exhibit a strong sensitivity to the disk thermal lensing. This means that the correct choice of the gas environment can become crucial to reach good beam quality over a broad range of output powers.

Thermal effects in thin-disk lasers

3.1.4 Simulation of the gas-lens and gas-wedge effects We performed simulations to understand, model, and predict the observed thermal-lensing effects in different gas environments. The disk heats up upon the absorption of pump light. On the one hand, this leads to well-studied disk-material defocusing thermal-lensing effects [39, 73], which are mostly due to the disk bending and changes in the disk’s thermo- optic coefficient dn/dT, where n is the refractive index and T the temperature. The deposited heat is transported through the disk’s backside and the diamond heat-sink into the cooling water. Consequently, we experimentally found our disk temperature to be virtually independent of the gas environment [Fig. 3.1(a)]. Nonetheless, a small fraction of heat, accounting for about 0.1% of the total heat dissipated by the disk, is transferred to the gas in front of the disk. The resulting temperature distribution in the gas exhibits a strong radial depend- ency. Due to the gas thermo-optic coefficient, this results in a gas lens, which contributes to the net disk thermal lensing. Additionally, the heated gas rises in front of the disk due to convection effects, ultimately causing a gas wedge [42-44]. In order to quantify both the gas-lens and gas-wedge effects, we carried out a three steps simulation for all different studied gas environments. As input, we used a disk temperature profile based on our thermal-camera measurements. In a first step, we simulated the temperature rise and convection of the air surrounding the disk using the non-isothermal flow and conjugate heat transfer modules of the finite-element method software COMSOL Multiphysics 5.2a. The model includes the thin YAG disk and a 20-mm-long cylinder of gas placed in front of it [Fig. 3.4(a)]. The backside of the disk is set to the cooling water temperature of 24 °C and the front side of the disk has a super- Gaussian temperature distribution. Based on a fit of the thermal-camera images, the disk temperature distribution was modeled with a super-Gaussian radial distribution of order four with a FWHM of 8 mm (a Gaussian distribution would be of order two). The peak value of the super-Gaussian was set to the measured peak value of the disk temperature profile. This temperature profile constitutes a heat source for the gas in front of the disk. The heat

Chapter 3 transfer and gas flow equations (laminar flow), including gravity, were then solved, resulting in the full three-dimensional temperature distribution of the gas. We used open boundary conditions at the surfaces of the gas cylinder. The gas flow was simulated under the assumption of weak compressibility. The calculated maximum Reynolds number is < 4 for a peak disk temperature of 100 °C, which confirms that laminar flow is dominant. In a second step, we used the temperature distribution and combined it with the gas thermo-optic coefficient [74-76] to calculate the n(x,y,z) - 1 distribution in front of the disk, see Fig. 3.5 for 1-bar air and 1-bar He. Using the three-dimensional Helmholtz equation in the paraxial approximation, we sub- sequently studied the evolution of an incoming Gaussian laser beam while impinging orthogonally on the disk and propagating through the gas. Our numerical calculation employed the split-step Fourier method. By fitting the phase profile of the output beam with a second-order polyno- mial, we obtained in a last step the curvature of the output beam in both axes as well as the phase-front tilt. From this, we inferred both the defocusing gas-lens (i.e. , ) and the gas-wedge effects.

Δ𝐹𝐹gas lens sim

Fig. 3.4 (a) Schematic of the model showing, left to right, the diamond heatsink, the disk with the super Gaussian temperature profile on it, and the gas in front of it. (b) Simulated and measured gas lens and vertical gas wedge effect for a disk’s peak temperature increase ∆T = 57 °C. We fitted the gas lens simulation data with the function β ∆Fgas,sim = α (dspot) finding β = -1.4. The gas lens effect increases for smaller pump spot diameter while the gas wedge (black squares) only slightly depends on it.

Thermal effects in thin-disk lasers

Thus, for a given pump-spot configuration, the full simulation takes as input the measured peak temperature on the disk as well as the gas type and pressure, and outputs the gas-induced lens and wedge. In all configurations, our model predicts a linear dependence of the gas-lens effect with respect to the disk temperature. We find a significant and similar gas lens in both 1-bar air and 1-bar N2. The magnitude of the gas lens in air or N2 is ~50% of our measured disk-material thermal-lensing effects, which we inferred from our experiments in vacuum. Thanks to the almost one order of magnitude lower (n-1) and dn/dT for helium (see Table 3.2), its gas-lens effect is roughly five times weaker as compared to air and therefore negligible in comparison to the disk-material thermal-lensing effects. We demonstrate a close agreement between simulation and experiment for the gas-lens effect in Table 3.1.

Table 3.2 Thermal and optical properties of vacuum, helium, nitrogen, and air, at 25°C and 1030 nm [74-76].

Index of Thermo-optic Specific Thermal Gas refraction coefficent heat conductivity (n-1)*104 dn/dT*107 [1/K] [J/(g*K)] [W/(m*K)] Vacuum - - - - 1-bar He 0.32 -1.06 5.19 0.15 1-bar air 2.65 -8.88 1.01 0.03

1-bar N2 2.71 -9.15 1.04 0.03

Additionally, our model predicts the gas-wedge effect, which occurs due to gas convection [42-44]. From our simulations, we infer for 1-bar air and 1-bar

N2 an angular beam deviation θ linear to the disk temperature increase ∆T. This deviation is ~0.14 μrad/K in the vertical direction, and negligible in the horizontal direction (~0.005 μrad/K). For 1-bar He, the gas wedge in the vertical direction is roughly one order of magnitude smaller (~ 0.014 μrad/K), and for vacuum non-existent. Experimental indications of such gas-wedge effects were observed before, but never quantified [42-44]. The influence of the gas wedge on the cavity is

Chapter 3 strongly dependent on the cavity design, particularly on the linear beam displacement ∆y at the disk caused by an angular beam deviation θ at the disk, i.e. ∆y = k * θ, where k is a sensitivity parameter. For the single-mode cavity presented in section 3.1.2, we calculate k = -57 mm/mrad. The sensitivity parameter translates into a gas-wedge-induced ∆y of less than 0.5 mm at the maximum power in single-mode operation (i.e. for ∆T ~ 60K). This is small compared to the 8.0 mm of pump-spot diameter on the disk. In fact, we could not experimentally measure the gas-wedge effect. However, in different cavity designs or with different disk materials, the gas wedge can play a more significant role. For instance, from the beam displacement presented in 4 of Ref. [43] and the corresponding cavity design, we can infer a gas-wedge effect of ~35 μrad in the vertical direction at ~2.5 kW/cm2 of pump intensity. In this case, flooding the cavity with helium would be highly beneficial. With our model, we performed a scan of the pump spot diameter on the disk finding that decreasing the spot size results in an increased gas-lens effect. In Fig. 3.4(b) we show the result of this scan for a disk’s peak-temperature increase ∆T = 57 °C. We fitted the simulations with the function ∆Fgas,sim = β α (dspot) finding β = -1.4. In order to confirm this trend we measured the gas-lens effect in a different laser with 4.4 mm pump-spot diameter finding a very good agreement with the scaling, as showed in the Fig. 3.4(b). Regarding the gas-wedge effect, we found out from the simulations that it only marginally depends on the pump spot diameter on the disk. The provided scaling function for the gas-lens effect can be used in order to estimate the magnitude of this effect in a thin-disk laser with a different pump spot size and thus assess what would be the beneficial effect of going to vacuum or helium flooding the chamber. Finally, we investigated the sensitivity of our model to the shape of the temperature profile on the disk. A super-Gaussian of order 8 (i.e. a more flat-top profile) lead to an increase of the predicted gas-lens effect by ~10%.

Thermal effects in thin-disk lasers

Fig. 3.5 Simulation of the gas refractive index (n(x,y,z)-1) profiles for (a) 1-bar air and (b) 1-bar He. The disk is situated at z = 0 mm with a peak temperature of 81 °C (∆T = 57 °C). Both the gas lens and gas wedge effects are clearly visible. Due to the higher thermal conductivity of He, see Table 3.2, the heat from the disk extends further into the gas. Nonetheless, thanks to the order of magnitude lower n-1, the thermo-optic effects for He are significantly less pronounced as compared to air, as in our experimental data summarized in Table 3.1.

3.1.5 Conclusion We presented a detailed investigation of the disk thermal-lensing effects in high-power thin-disk lasers in different gas environments. We measured, for the first time, a reduction of the overall disk thermal lens by ~33% when operating our state-of-the-art disk in vacuum or 1 bar of He as compared to 1 bar of air or 1 bar of N2. With this knowledge, we achieved in our high-power cw TDL setup single-mode operation, i.e. M2 < 1.1, over a ~70% broader output power range of ~500 W in He or vacuum atmosphere versus a range of ~300 W in air. We anticipate that combining an air-purged environment with pumping at a wavelength of 969 nm, will further increase the power range of optimal beam quality.

Chapter 3

Our simulations accurately modeled our experimental results with a gas lens induced by the heated gas in front of the thin disk, which adds on top of disk-material thermal effects. The gas lens is roughly five times weaker for He as compared to air and N2, and non-existent for vacuum environments. In addition to the gas lens, our model predicts a gas wedge due to the inhomo- geneous vertical temperature profile of the heated gas in front of the disk. Our findings therefore provide crucial knowledge for the design of advanced thin-disk laser systems with output powers in the kW range and consequently large disk spot sizes, this includes high-energy thin-disk lasers with multiple intracavity passes over the gain crystal. Additionally, using vacuum or helium atmospheres cancels the gas wedge and heavily reduces intracavity nonlinearities, which is particularly attractive for ultrafast applications. Funding Swiss National Science Foundation (SNSF) (200020_172644); Sofja Ko- valevskaja Award of the Alexander von Humboldt Foundation; Cluster of Excellence RESOLV (EXC 1069). Acknowledgements We would like to thank Trumpf Laser GmbH for providing the thin-disk equipment.

Cascaded quadratic nonlinearities

4 Cascaded quadratic nonlinearities

In this chapter, we discuss the use of cascaded quadratic nonlinearities in high- power TDL oscillators to generate a phase shift opposite to the one picked up in air due to self-phase modulation. This simplifies the nonlinearity management in high-power lasers and allows us to operate these lasers in air rather than in vacuum. We demonstrated a SESAM-modelocked TDL oscillator delivering 210-W average output power with 19-μJ pulses. This result represents the highest average output power of any SESAM-modelocked TDL operated in air. The details are presented in the following journal publication and in the relative supplementary material. In the journal publication, we put the references of Fig. 4.1 in the supplementary due to the page limits of the letter. In this thesis, for clarity, we indicated the references in the caption of the figure and removed the same figure (originally Fig. S2) from the supplementary (SI). Title: “Self-phase modulation cancellation in a high-power ultrafast thin-disk laser oscillator”, [32] Journal: Optica doi: 10.1364/OPTICA.5.001603 doi SI: 10.6084/m9.figshare.7361048.v1

Chapter 4

4.1 Self-phase modulation cancellation in a high-power ultrafast thin-disk laser oscillator

F. Saltarelli, A. Diebold, I.J. Graumann, C.R. Phillips, and U. Keller Institute for Quantum Electronics, ETH Zurich, 8093 Zurich, Switzerland

Abstract: Ultrafast high-power lasers are employed in a wide variety of applications in science and industry. Thin-disk oscillators can offer compelling performance for these applications. However, because of the high intracavity peak power, a large amount of self-phase-modulation (SPM) is picked up in the intracavity air environment. Consequently, the highest performance oscillators have been operated in a vacuum environment. Here, we introduce a new concept to overcome this hurdle. We cancel the SPM picked up in air by introducing an intracavity phase-mismatched second-harmonic-generation crystal. The resulting cascaded χ(2) processes provide a large SPM with a sign opposite to the one originating from the air. This enables laser operation in air at 210 W average output power with 780 fs, 19 μJ pulses, the highest output power of any semiconductor saturable absorber mirror (SESAM) modelocked laser operated in air to date, to the best of our knowledge. This result paves the way to a novel approach for nonlinearity management in high- power lasers. © 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement Ultrafast laser technologies are a crucial tool for a wide variety of applications ranging from science, such as time-resolved studies and XUV generation, to industry, for instance in high-precision material processing. During the last decade, high-power sources based on Yb-doped gain materials, shaped in the thin-disk [20], fiber [19] and slab geometry [61] had an impressive development, leading to ultrafast amplifier systems exceeding the kW-level average power milestone. Using the thin-disk laser (TDL) technology, oscillators delivering multi-100-W average power and tens-of-μJ pulse energy at MHz repetition rate have been demonstrated [12, 15, 47]. This approach enables to use a table-top and comparatively cost-effective TDL oscillator as an ultrafast

Cascaded quadratic nonlinearities high-power laser source. Hence TDL oscillators, thanks to their excellent beam quality and low-noise properties [28], are a highly attractive alternative to multi-stage amplifier systems composed of a low-power oscillator, pulse stretcher, amplification stages, and pulse compressor [19, 23]. In fact, TDL oscillators are being used for extra- and intra-cavity XUV generation, high- power frequency conversion to the mid-IR, and are potential sources for high- power THz generation [5]. A significant challenge in these TDL oscillators is the high intracavity peak power, which can exceed 100 MW. At such peak powers, the phase accumulated because of the nonlinear refractive index of the intracavity air represents a major contribution to the overall self-phase modulation (SPM). Since the modelocking process relies on soliton pulse formation, which requires a balance between group-delay dispersion (GDD) and SPM [77], this very large amount of SPM ultimately hinders pulse formation. Different methods have been developed so far to overcome this challenge. One is to compensate this large SPM with a corresponding amount of GDD obtained through dispersive mirrors. This creates a trade-off between the amount of GDD in the cavity and the output pulse energy of the laser (‘Standard TDL’ in Fig. 4.1). However, dispersive mirrors have substantially worse thermal behavior compared to Bragg mirrors, making it very challenging to add a large number of them in a high-power oscillator [23, 78]. A different approach consists in operating the oscillator in vacuum or helium environment so that the air contribution to the SPM is almost removed (‘Vacuum/He TDL’ in Fig. 4.1) [23]. This approach led to the record results in average power and pulse energy. However, the advantages in performance offered by operation of the TDL in vacuum are offset by the significantly increased cost and complexity of such a system. For many scientific and industrial applications, a simpler solution would be required. Here, we present a new and much simpler technique to cancel the intracavity SPM picked up in air by exploiting cascaded quadratic nonlinearities (CQN) [79]. In CQN, a second-harmonic-generation (SHG) crystal yields an effective nonlinear refractive index that is tunable in magnitude and sign. CQN have been successfully employed for modelocking of lasers in both the positive and negative dispersion regime [80-84], pulse compression [85, 86], for nonlinear-

Chapter 4 mirror-type modelocking schemes in TDLs [33, 57], and in regenerative amplifiers [87]. Here, we introduce a CQN crystal inside the laser cavity in a phase-mismatched, low-loss configuration. This allows us to cancel up to 80% of the total SPM of air. We balanced the remaining SPM through just five dispersive mirrors, enabling soliton pulse formation. We obtain 210-W average power at 780-fs pulse duration, 10.96-MHz repetition rate, and 19.2-μJ pulse energy using -16’800 fs2 of GDD (‘This result’ in Fig. 4.1). This result represents the highest output power of any semiconductor saturable absorber mirror (SESAM) modelocked oscillator operated in air. In the previous record of 145 W [46], -346’500 fs2 of round-trip GDD were used. Kerr- lens modelocking (KLM) can require a lower amount of negative GDD for pulse formation (see Fig. 4.1). However, SESAM modelocking is highly ad- vantageous in terms of robust modelocking since pulse formation is decoupled from cavity stability. Our oscillator also delivers more pulse energy than any KLM oscillator to date, where the record is 14 μJ [47], and more than 4 times average power compared to previous lasers involving CQN [57].

Fig. 4.1 Overview of the GDD used in TDLs with respect to their output pulse energy. Our result, due to the use of cascaded χ(2) nonlinearities, overcomes the trade off in GDD versus pulse energy typical of ‘Standard TDL’, lying in a region previously accessible only through expensive vacuum systems. For the non-labeled results, the average output power is below 100 W. Refs: [12, 15, 45-47, 55, 65, 88-91].

Cascaded quadratic nonlinearities

In our laser experiment we use a 100-μm thick, 10-at.% doped Yb:YAG disk contacted on diamond (TRUMPF), mounted in a 36-pass head, and pumped at 940 nm with a 4.4-mm-diameter pump spot. We designed a cavity including three reflections on the disk gain medium. Thus, we could use an output coupler (OC) with a comparatively large TOC = 40% transmission and hence limit the intracavity power. A large OC rate is beneficial in two ways: it reduces the amount of SPM picked up in the intracavity air thus mitigating the requirement of negative GDD, and it decreases the stress on the intracavity components. The folded multi-pass cavity arrangement leads to a lower repetition rate and thus higher pulse energy while keeping a compact footprint (Fig. 4.2). We introduced a thin-film polarizer (TFP) in the cavity to fix the polarization of the laser.

Fig. 4.2 Schematic of the compact laser cavity including multiple bounces on the disk. The photodiode, through a band-pass green filter, measures the green leakage of a HR mirror. The presented beam profile is obtained in modelocked operation at 210 W output power.

In order to modelock the oscillator, we used an in-house grown SESAM as an end mirror, where the beam radius is ≈ 850 μm. The SESAM consists of a distributed AlAs/GaAs Bragg reflector grown at 580 °C and three InGaAs quantum wells as absorber grown at 280 °C in an antiresonant configuration [49, 50]. We measured our SESAM to have a saturation fluence Fsat =

50 µJ/cm2, a modulation depth ∆R = 2.7%, and non-saturable losses ∆Rns = 0.35% [48]. The SESAM was contacted by TRUMPF on a polished copper heatsink (cold radius of curvature >500 m [50]).

Chapter 4

We use only five Gires–Tournois interferometer (GTI) type dispersive mirrors, yielding a total GDD of D = -16’800 fs2 per round trip. Achieving 210-W output power with 780-fs pulses without CQN, would require ≈ 5 times more negative GDD. Thus, the use of CQN critically helps the balance between SPM and GDD. CQN offer a large effective nonlinear refractive index contribution n2,CQN, which depends on the second-order nonlinear coefficient deff and the phase mismatch ∆k = kSH – 2kFW, where SH stands for second harmonic and FW for fundamental wave. This n2,CQN can be tuned in sign and magnitude via ∆k [79]. In this laser experiment, we exploit a negative n2,CQN from a SHG crystal in order to pick up a negative nonlinear phase shift, which counteracts the positive one picked up in air. A potential draw- back of this technique is the loss caused by the SH generated in the cascading processes, since the SH light is not resonant in the laser cavity. The SHG efficiency scales with the peak intensity, hence it represents an inverse saturable loss. On the other hand, if such losses are small compared to the modulation depth of the SESAM ∆R, this property can stabilize the modelocking process [83, 92]. In order to minimize the second-harmonic losses, we operate the crystal near the SHG minima, which correspond to

∆kL ≈ 2πnmin, where L is the length of the crystal and nmin is an integer. Ex- perimentally, we monitor the SHG losses measuring the power of a cavity green leakage (‘Photodiode’, Fig. 4.2) and adjust the crystal’s tilt angle θ through a piezo controlled mount. In this way we can operate the crystal in the SHG minima. To quantify the losses and the phase shift introduced by the CQN device, let us consider a pulse with peak intensity Ipk, progressing through the SHG crystal. We call the phase shift introduced for the peak of the pulse ΒCQN,sp and the efficiency of the SHG process ηCQN,sp:

, / (4.1)

𝐶𝐶𝐶𝐶𝐶𝐶 𝑠𝑠𝑠𝑠 𝑝𝑝𝑝𝑝 , 𝐵𝐵 0.83≈(−𝜉𝜉𝜉𝜉) 𝐼𝐼 /Δ𝑘𝑘 , (4.2) 2 2 𝜂𝜂𝐶𝐶𝐶𝐶𝐶𝐶 𝑠𝑠𝑠𝑠 ≈ 𝜉𝜉 𝛿𝛿𝛿𝛿 𝐼𝐼𝑝𝑝𝑝𝑝 �Δ𝑘𝑘𝜏𝜏𝑝𝑝� where we define a group-velocity mismatch parameter δ = 1/vg,SH – 1/vg,FW, 2 3 2 ξ = 2 [ωFW deff] / [ε0 c (nFW) nSH], and τp is the full-width-at-half-maximum (FWHM) duration of the pulse, assuming a sech2 shape. These equations 52

Cascaded quadratic nonlinearities assume the cascading regime, where the phase mismatch is large and the transfer of energy from the fundamental to the second harmonic is small. The phase shift presented in Eq. (4.1) has a well-known expression in literature [93]. We obtain Eq. (4.2) in the supplementary material assuming a short crystal fulfilling τp > 2δ L, together with a large enough ∆k, and operation in a

SHG minimum (i.e., ∆kL = 2πnmin). In this short-crystal regime, the phase mismatch ∆k(λ) is close to 2πnmin across the whole pulse spectrum, allowing for very low SHG losses for the intracavity pulse. Hence, the ratio between nonlinear phase shift [Eq. (4.1)] and nonlinear losses [Eq. (4.2)] is lower than in the long-crystal limit (τp << δ L) [80]. Additionally, short crystals are beneficial in high-power applications in order to minimize thermal lensing. The free parameters in the design of the CQN device are the crystal length L, the intensity on the crystal Ipk, adjustable through the laser spot size on the SHG crystal, and the phase mismatch ∆k. The goal is to get a large amount of negative phase shift and as little as possible SHG losses, that is to maximize

ΒCQN,sp/ηCQN,sp ~ ∆k/L. Thus, our formulas suggest to use short crystals operated at large phase mismatch angles. We employed an AR-coated type-I LBO crystal (Cristal Laser) with a length L = 5 mm, in a position where the 1/e2 beam radius is ≈ 850 µm. In this way we have a peak intensity on the crystal below 5 GW/cm2. We next consider the balance of the different sources contributing to the cavity SPM. The total phase shift ΒCQN,rt and losses ηCQN,rt per round trip due to the SHG crystal are obtained multiplying the single pass values [Eq. (4.1) and Eq. (4.2)] for (1 + ROC) where ROC = 60% is the reflectivity of the output coupler. A convenient way to express the phase shift is to introduce the SPM coefficient γ = B/Ppk,IC where Ppk,IC is the intracavity peak power immediately before the OC. Regarding the air, we integrate the peak intensity in a cavity round trip to obtain the total SPM, denoted Bair,rt (Supplement in section 4.2) and we obtain γair ≈ 10.6 mrad/MW.

In Fig. 4.3, we plot the expected losses ηCQN,rt and the SPM coefficients γCQN for the CQN device, according to our analytical model (green) and a numerical simulation (blue). For the LBO, we use deff = 0.83 pm/V [94] and n2,LBO

Chapter 4

= 2x10-16 cm2/W for its intrinsic nonlinear refractive index [95]. We obtained the numerical solution by directly solving the pulsed coupled-wave equations for the laser parameters at the maximum output power (τp = 780 fs, Ppk,IC = 54 MW). The analytical model accurately predicts the SHG losses in the minima and the phase shift. The positive contribution to the phase shift from the crystal’s intrinsic n2 leads to a slightly less negative SPM coefficient γCQN in the numerical model compared to the analytical solution since this term is not included in the latter. The other sources of SPM, e.g., the disk, contribute only by few percent and so have been neglected.

Fig. 4.3 Round-trip SHG losses (a) and SPM cancellation (b) due to the CQN device. By operating the crystal in a SHG minimum, few 0.1% losses can be obtained while cancelling most of the SPM from air.

Femtosecond SESAM-modelocked lasers rely on soliton pulse formation. In this regime of SESAM modelocking, pulse duration and intracavity pulse energy EIC = Eout / TOC depend mostly on the GDD versus SPM balance and only marginally on the parameters of the saturable absorber [77]. Their relation is governed by the so-called soliton formula, τp ≈ 1.76 (2|D|) /

(γ avg EIC), where γ avg = ¾ γ takes into account the effective phase shift for a pulse with a Gaussian spatial profile compared to the phase shift for the peak of the pulse [83, 96]. By tuning the phase mismatch ∆k, we can adjust the net

Cascaded quadratic nonlinearities

SPM coefficient γ [Fig. 4.3(b)]. Thanks to the straight-forward tunability of ∆k by adapting the crystal’s tilt during live laser operation, we obtain the shortest pulse duration for several values of the output power (cfr. Fig. 4.4 and Table 4.1). In contrast, a standard TDL, having a fixed amount of GDD and SPM, operates only over a fixed power range and has the shortest pulses only at the maximum output power. In Fig. 4.4 we present the laser output power versus pump power for three phase-matching configurations. The blue and red curves are obtained operating the SHG crystal, respectively in the 4th (∆kL ≈ 8π) and 3rd (∆kL ≈ 6π) SHG minimum. The slope in yellow is obtained starting from the 3rd SHG minimum and gradually decreasing the ∆k as the pump power is increased, in order to reduce the net SPM coefficient γ . Like this, we keep the pulse duration equal to the minimum achievable for our laser, but at increased output power. At the maximum output power (210 W, 780 fs) we measured a SHG efficiency ≈ 1.8 times the one we had in the 3rd SHG minimum. This suggests a shift in ∆kL from the 3rd SHG minimum of ≈-0.2π, that is ∆kL ≈ 5.8π. For this value of ∆kL we have n2,CQN ≈ - 2.1 x 10-15 cm2 /W [93].

Fig. 4.4 Laser slopes: output power (a) and pulse duration (b) as a function of the pump power. Different colors refer to different phase mismatch values ∆k of the SHG crystal.

Chapter 4

Table 4.1 Laser parameters for τp ≈ 800 fs. γsoliton is obtained from the soliton formula, γair = 10.6 mrad/MW, and γCQN is the expected negative SPM coefficient from the CQN device. The last column represents the fraction of SPM from air cancelled by CQN.

nmin ∆ Pout τ γ γ γ γ kL p soliton soliton - air CQN γ CQN (W) (fs) (mrad/MW) γ air ≈ 5.8 π 210 782 2.1 -8.5 -8.6 81% 3 ≈ 6 π 162 805 2.6 -8.0 -8.3 78% 4 ≈ 8 π 112 741 4.2 -6.4 -6.2 59% 5 ≈ 10 π 85 749 5.5 -5.1 -5.0 47% 6 ≈ 12 π 72 782 6.2 -4.4 -4.1 39% 7 ≈ 14 π 61 865 6.6 -4.0 -3.6 33%

Next, in Table 4.1 we quantify the SPM cancellation effect occurring in the laser for several operating points. Except for the point at 210-W output power, we experimentally optimized the crystal’s phase mismatch in order to operate in the SHG minima, i.e. ∆kL ≈ 2πnmin.. For the point at 210-W output power, we slightly detuned the phase mismatch from the 3rd SHG minimum, as described above. The soliton formula together with the measured laser characteristics yields a prediction for the total round-trip SPM coefficient, denoted γsoliton. Two contributing terms to this SPM coefficient are the intracavity air γair, and the CQN crystal γCQN, which we calculate according to

γair = Βair,rt/Ppk,IC and γCQN = ΒCQN,rt/Ppk,IC, respectively. We expect γsoliton =

γair + γCQN. In Table 4.1, we compare γsoliton - γair to γCQN, to show that the laser characteristics are in good agreement with this equation. The last column of the table presents the percentage of the SPM picked up in air cancelled by the CQN device. It ranges from ≈ 30% to ≈ 80% showing the great flexibility of this technique. This, together with the predictive power of the analytical formulas, allows an easy design of a CQN device for SPM cancellation, tai- lored on the experimental needs. In Fig. 4.5 we present the laser diagnostics at the maximum output power, which show a single-pulse stable modelocked operation. We ensure single- pulsed operation by scanning the autocorrelator delay up to 60 ps and acquiring a sampling oscilloscope trace with a 45 GHz photodiode [Fig. 4.5(f)]. We 56

Cascaded quadratic nonlinearities obtain diffraction-limited beam quality (M2 < 1.05) in all configurations. In the presented laser, the output power was limited by the pump intensity on the disk, already close to the safety limit of 5 kW/cm2, and the fluence on the SESAM, which was already operated slightly into the rollover.

Fig. 4.5 Laser diagnostics at the maximum output power (210 W, 780 fs, 19 μJ). (a) Optical spectrum; (b) Intensity autocorrelator; (c-d) RF spectra with 0-dBc marked by 2 black dashed line; (e) M measurement; (f) Sampling oscilloscope trace. RBW: resolution bandwidth. The autocorrelation trace and the optical spectrum are fitted with a sech2 function (red dashed line). The 1/e2 beam width is calculated using the second momentum (D4σ).

In conclusion, we demonstrated a novel concept to cancel the SPM picked up in air in the context of high-power ultrafast oscillators. This allowed us to obtain laser performance in line with best-in-class TDLs using, instead of a complex vacuum system, an inexpensive and easy-to-setup nonlinear crystal. Next to SESAM-modelocked TDL, this technique can be applied to high- power KLM oscillators. Additionally, we prove here that self-defocusing nonlinearities can be used at unprecedented power levels of up to 500 W intracavity power, hence offering a new toolset for high-average-power lasers. Funding. Swiss National Science Foundation (SNSF 200020_172644).

Chapter 4

4.2 Supplementary material: Self-phase modulation cancellation in a high-power ultrafast thin-disk laser oscillator

F. Saltarelli, A. Diebold, I.J. Graumann, C.R. Phillips, and U. Keller Institute for Quantum Electronics, ETH Zurich, 8093 Zurich, Switzerland

In our paper, we deploy a device based on cascaded quadratic nonlinearities (CQN) to cancel the self-phase-modulation (SPM) picked up in air. One main requirement for the design of this device was to quantify the amount of second harmonic (SH) generated and the phase shift for the fundamental wave (FW). CQN processes [79] are well understood within the framework of the pulsed coupled wave equations (CWEs). These equations can be solved nu- merically. Yet, a deeper theoretical understanding and analytical formulas are a powerful tool in order to know which levers to experimentally pull for optimizing the multi-dimensional processes. Analytical solutions for the CWEs for CQN are well known in literature in the limits of very long and very short pulses [79]. The phase shift is usually approximated with Eq. (4.1) of the letter. We found that this equation accurately matches the numerical solution in the regime in which we operate the crystal (see Fig. 4.3 of the letter and related discussion). Regarding the amount of SH generated, i.e. the inverse saturable losses seen by the laser, the cascading regime often refers to a situation where the length of the crystal is long enough such that the minima of the second-harmonic-generation (SHG) process are completely smoothed out. In this regime, the SHG efficiency scales as 1/∆k2. Conversely, for longer pulses or short crystals, a sinc2 tuning curve of SHG efficiency versus crystal angle is recovered, leading to very small SHG losses in the minima of this function. In our case, in order to minimize the SHG losses in the laser, we operate the crystal in a regime where these SHG efficiency minima are still pronounced. This corresponds to a regime of intermediate pulse duration between the limit of very short and long pulses. Since we could not find analytical approximations for the SHG efficiency in this regime, we developed it, see Eq. (4.2) of the letter. Here we present the deri- vation of this formula. 58

Cascaded quadratic nonlinearities

In section 4.2.1 of this document, we introduce the formalism and the efficiency of the SHG process in the well-known case of continuous plane waves. In section 4.2.2, we switch from continuous wave (cw) to pulses and obtain an approximate solution for the losses in the SHG minima. Additionally, we discuss the different regimes and the range of validity of our analytical approximation. In section 4.2.3 we describe in details the cavity design used in the presented laser oscillator and compare it to other possible designs. Lastly, in section 4.2.4, we provide some details on the thermal behavior of the nonlinear crystal during laser operation.

4.2.1 Coupled wave equations We start with the continuous-wave case and use the CWEs in the slowly- varying-envelope approximation (SVEA), including first-order dispersion. We consider the envelopes of the electric field Ei, where the subscript i = 1,2, corresponds, respectively, to the FW and the SH. We define the group-velocity-mismatch (GVM) coefficient δ = 1/vg,2 – 1/vg,1 where vg,i is the group velocity. Additionally, we define the phase mismatch ∆k0 = k(ω2) – 2k(ω1) where ω i is the angular frequency. The other parameters entering the CWEs are the effective nonlinear coefficient for SHG deff and the index of refraction ni.

= (4. 3) 1 1 𝑒𝑒𝑒𝑒𝑒𝑒 ∗ −𝑖𝑖Δ𝑘𝑘0𝑧𝑧 ∂𝐸𝐸 𝜔𝜔 𝑑𝑑 2 1 −𝑖𝑖 1 𝐸𝐸 𝐸𝐸 𝑒𝑒 ∂+𝑧𝑧 =𝑛𝑛 𝑐𝑐 (4.4) 𝜕𝜕𝐸𝐸2 𝜕𝜕𝐸𝐸2 𝜔𝜔1𝑑𝑑𝑒𝑒𝑒𝑒𝑒𝑒 2 𝑖𝑖𝑖𝑖𝑘𝑘0𝑧𝑧 𝛿𝛿 −𝑖𝑖 𝐸𝐸1 𝑒𝑒 For further analysis, it𝜕𝜕 is𝜕𝜕 convenient𝜕𝜕𝜕𝜕 to rewrite𝑛𝑛2𝑐𝑐 the CWEs in terms of a normalized electric field such that its square magnitude is the intensity normalized to the input intensity of the FW, I1,pk. Thus, we define: 𝐸𝐸̄𝑗𝑗 = (4.5)

1 , 𝑗𝑗 𝑗𝑗 𝐸𝐸̄ 𝐸𝐸 �𝑛𝑛1⁄𝑛𝑛𝑗𝑗 𝐸𝐸1 𝑝𝑝𝑝𝑝 This translates to an intensity for the electric field:

= = (4.6) 2 2 , 𝑛𝑛𝑗𝑗𝜀𝜀0𝑐𝑐�𝐸𝐸𝑗𝑗� 2 𝐼𝐼𝑗𝑗 𝐼𝐼1 𝑝𝑝𝑝𝑝�𝐸𝐸̄𝑗𝑗� 59

Chapter 4

Additionally, we define a coefficient Γpk including the properties of the nonlinear medium and the intensity of the FW as:

, = (4.7) 𝜔𝜔1𝑑𝑑𝑒𝑒𝑒𝑒𝑒𝑒𝐸𝐸1 𝑝𝑝𝑝𝑝 𝑝𝑝𝑝𝑝 Γ √𝑛𝑛1𝑛𝑛2𝑐𝑐 In this way, we can rewrite the CWEs in (4.3) and (4.4) as:

+ = (4.8) ∂𝐸𝐸̄2 ∂𝐸𝐸̄2 2 𝑖𝑖Δ𝑘𝑘0𝑧𝑧 𝑝𝑝𝑝𝑝 1 ∂𝑧𝑧 =𝛿𝛿 ∂𝑡𝑡 −𝑖𝑖Γ 𝐸𝐸̄ 𝑒𝑒 (4.9) ∂𝐸𝐸̄1 ∗ −𝑖𝑖Δ𝑘𝑘0𝑧𝑧 ∂𝑧𝑧 𝑝𝑝𝑝𝑝 ̄2 ̄1 In the approximation of low depletion−𝑖𝑖Γ 𝐸𝐸of𝐸𝐸 the𝑒𝑒 fundamental, we solve Eq. (4.9) assuming ( ) = 1. The solution of this equation in a phase-matched condition, i.e., ∆k0 = 0 and for a nonlinear medium of length L is well known. In 𝐸𝐸̄1 𝑧𝑧 particular, the efficiency of the SHG process is:

( ) = = = , (4.10) (0) 2 2 𝐸𝐸̄2 𝐿𝐿 2 𝜔𝜔1𝑑𝑑𝑒𝑒𝑒𝑒𝑒𝑒𝐸𝐸1 𝑝𝑝𝑝𝑝 𝜂𝜂𝑝𝑝𝑝𝑝 � � �Γ𝑝𝑝𝑝𝑝𝐿𝐿� � 𝐿𝐿� ̄1 1 2 4.2.2 Pulsed second𝐸𝐸 harmonic generation√𝑛𝑛 𝑛𝑛 𝑐𝑐 Next, we calculate the efficiency of the SHG process for pulses instead of cw. For this, we switch to the frequency domain, using the Fourier transform and find a propagation equation for the SH. By applying the Fourier transform [ ] = ∞ ( ) ( 2 ) operator ∞ to the left and right hand side of Eq. (4.4), it becomes: 𝐹𝐹𝜈𝜈 𝑔𝑔 ∫− 𝑔𝑔 𝑡𝑡 𝑒𝑒𝑒𝑒𝑒𝑒 − 𝜋𝜋𝜋𝜋𝜋𝜋𝜋𝜋 𝑑𝑑𝑑𝑑

+ (2 ) = [ ] (4.11) ∂𝐸𝐸�2 2 𝑖𝑖Δ𝑘𝑘0𝑧𝑧 𝑖𝑖𝑖𝑖 𝜋𝜋𝜋𝜋 𝐸𝐸�2 −𝑖𝑖Γ𝑝𝑝𝑝𝑝𝐹𝐹𝑣𝑣 𝐸𝐸̄1 𝑒𝑒 Where is the normalized∂𝑧𝑧 electric field in the frequency domain and ν represents the frequency offset relative to the carrier. Without nonlinear ef- 𝐸𝐸�𝑖𝑖 𝐸𝐸̄𝑖𝑖 fects, i.e. deff = 0, the solution of this equation is = ( 2 ), where a is a constant. Thus, it is convenient to search for a solution to the general 𝐸𝐸�2 𝑎𝑎 𝑒𝑒𝑒𝑒𝑒𝑒 − 𝜋𝜋𝜋𝜋𝜋𝜋𝜋𝜋𝜋𝜋 equation with deff ≠ 0 in the form = ( 2 ). In our soliton modelocked TDL, the pulses have a sech shape in both frequency and time �2 ̃2 domain [77], thus we take a sech 𝐸𝐸function𝐴𝐴 𝑒𝑒𝑒𝑒𝑒𝑒 for −the𝜋𝜋 𝜋𝜋𝜋𝜋electric𝜋𝜋𝜋𝜋 field of the

Cascaded quadratic nonlinearities fundamental wave: ( ) = ( / ). By using this expression for the electric field and integrating1 Eq. (4.11) in dz from 0 to L, we again calculate the ratio between the energy𝐸𝐸 𝑡𝑡 in the𝑠𝑠𝑠𝑠𝑠𝑠 ℎSH𝑡𝑡 at𝜏𝜏 the output of the crystal and the initial energy in the FW:

( ) = 2 (4.12) (2 ) 2 𝜂𝜂𝑝𝑝𝑝𝑝 ∞ 𝜋𝜋 𝑣𝑣𝑣𝑣 Δ𝑘𝑘 𝑣𝑣 𝐿𝐿 2 𝜂𝜂𝑝𝑝𝑝𝑝 𝜏𝜏 ∫−∞ �𝑠𝑠𝑠𝑠𝑠𝑠ℎ 𝜋𝜋 𝑣𝑣𝑣𝑣 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 � 2 �� 𝑑𝑑𝑑𝑑 where we defined ∆k(ν) = ∆k0 + (2πν)δ. The efficiency in Eq. (4.12) assumes a spatial plane wave interaction, thus we called it ηpw. In the laser, the beam has a TEM00 spatial mode, that is a Gaussian profile. This corresponds to an electric field distribution of the form ( )~ [ ( / ) ] where w is the beam radius. Hence, we need to calculate the average efficiency2 over this beam profile. The total energy in the 𝐸𝐸FW𝑟𝑟 is 𝑒𝑒𝑒𝑒𝑒𝑒given− by𝑟𝑟 the𝑤𝑤 two-dimensional spatial integral of |E(r)|2. The SH is proportional to the square of the intensity of the fundamental and so the energy included in it is given by the integral of (|E(r)|2)2. By calculating the ratio between these two integrals, we get ½. Thus for a beam with a Gaussian profile, the efficiency of the SHG process

η = ½ ηpw:

( ( ) 2) = . (4.13) ∞ (2 ) 2 ( 2 ( ) /2) 𝜂𝜂 𝜋𝜋 𝑣𝑣𝑣𝑣 𝑠𝑠𝑠𝑠𝑠𝑠 Δ𝑘𝑘 𝑣𝑣 𝐿𝐿⁄ 2 2 𝑝𝑝𝑝𝑝 𝜏𝜏 �−∞ � � 𝑑𝑑𝑑𝑑 We now assume𝜂𝜂 that the bandwidth𝑠𝑠𝑠𝑠𝑠𝑠ℎ 𝜋𝜋 𝑣𝑣𝑣𝑣 of the pulseΔ𝑘𝑘 𝑣𝑣 is𝐿𝐿 narrow enough such that the denominator ∆k(ν)L/2 does not change significantly before the sinh(π2ντ) brings the integrand to zero. Thus, we approximate ∆k(ν) in the denominator with its value at the carrier wavelength, i.e. ∆k0. Additionally, we assume that the center wavelength corresponds to a SHG minimum, i.e. sin(∆k0L/2) = 0. It should be noted that this assumption will reduce our final resulting formula to the case of operation in the SHG minima only. Using the definition of 2 2 ∆k(ν) we have that, in this condition sin (∆k(ν)L/2) = sin [(2πν)δ L/2]. We can thus approximate Eq. (4.13) as:

4 2 = . (4.14) ( ) ∞ (2 ) 2 2 2 𝜂𝜂 𝜏𝜏 𝜋𝜋 𝑣𝑣𝑣𝑣 𝜋𝜋𝜋𝜋𝜋𝜋𝜋𝜋 2 � � 2 � 𝑠𝑠𝑠𝑠𝑠𝑠 � � 𝑑𝑑𝑑𝑑 𝜂𝜂𝑝𝑝𝑝𝑝 Δ𝑘𝑘0𝐿𝐿 −∞ 𝑠𝑠𝑠𝑠𝑠𝑠ℎ 𝜋𝜋 𝑣𝑣𝑣𝑣 61

Chapter 4

This integral can be solved analytically and yields:

2 3 3 = 1 + , (4.15) 3( ) 𝜂𝜂 � − 𝛿𝛿 𝑐𝑐𝑐𝑐𝑐𝑐ℎ�𝛿𝛿�� 2 2 𝑝𝑝𝑝𝑝 0 � � 𝜂𝜂 Δ𝑘𝑘 𝐿𝐿 𝑠𝑠𝑠𝑠𝑠𝑠ℎ�𝛿𝛿� Where = / is the ratio between the temporal walk-off between the FW and the SH in the crystal δ L and the sech-pulse duration parameter τ . For the 𝛿𝛿 𝛿𝛿𝛿𝛿 𝜏𝜏 sake of clarity we want to stress again that Eq. (4.14) and Eq. (4.15) hold only in the SHG minima, that is for ∆k0L = 2πnmin. As a function of the parameter

, the solution of Eq. (4.15) is shown in Fig. 4.6 in units of 2/[3(∆k0L)2] in blue. 𝛿𝛿̄ First we discuss the two limits for , namely = 0 and >> 1. In the limit of large that is a large GVM compared to the pulse duration, as we see in 𝛿𝛿̄ 𝛿𝛿̄ 𝛿𝛿̄ Fig. 4.6 the expression in square brackets in Eq. (4.15) is 1, which implies: 𝛿𝛿̄ 2 = >> 1 (4.16) 3( ) 𝜂𝜂 2 𝑝𝑝𝑝𝑝 0 �𝛿𝛿 � This is a well-known result𝜂𝜂 in the contextΔ𝑘𝑘 𝐿𝐿 of CQN [80, 93]. The opposite limit is = 0, which corresponds to the case of negligible temporal walk off relative to the pulse duration (i.e. narrow bandwidths or short crystals). This results ̄ in 𝛿𝛿no SHG in the SHG minima.

In our experiments we operate with a relatively small value of , in order to minimize the SHG losses. In the time domain this corresponds to a situation ̄ where the temporal walk off between the FW and the SH is a small𝛿𝛿 fraction of the pulse duration. In the frequency domain, this corresponds to a pulse whose spectrum is narrow enough such that ∆k(λ) is close to 2πnmin across the whole pulse spectrum. Thus, we carry out a second-order Taylor expansion of Eq. (4.15) around = 0 obtaining:

𝛿𝛿̄ 4 (4.17) 15 2 𝜂𝜂 𝛿𝛿 ≈ � � 𝜂𝜂𝑝𝑝𝑝𝑝 Δ𝑘𝑘0𝜏𝜏

Cascaded quadratic nonlinearities

This solution corresponds to the red curve in Fig. 4.6 and it differs for less than 10% from the value of Eq. (4.15) for | | < 0.7. In terms of full-width- at-half-maximum (FWHM) pulse duration τp = 1.76τ, | | < 0.7 corresponds 𝛿𝛿̄ to: / < 0.4. For the nonlinear crystal used in this laser experiment, the 𝛿𝛿̄ temporal walk off in the L=5-mm LBO crystal corresponds to 270 fs. Thus 𝛿𝛿𝛿𝛿 𝜏𝜏𝑝𝑝 Eq. (4.17) is correct within 10% if τp > 700 fs. This was indeed the case for our laser experiments.

Fig. 4.6 Calculated value of Eq. (4.15) and second-order Taylor expansion. The variable on the x axis is the ratio between the temporal walk off in the crystal between FW and SH and the sech pulse duration parameter τ . In the area within the vertical dashed lines, the Taylor expansion differs for less than 10% from the exact solution.

By defining a new constant:

= 2 2 (4.18) 2𝜔𝜔1𝑑𝑑𝑒𝑒𝑒𝑒𝑒𝑒 2 3 𝜉𝜉 𝑛𝑛1𝑛𝑛2𝑐𝑐 𝜀𝜀0 we rewrite Eq. (4.17) in the form presented in the letter in Eq. (4.2):

0.83 2 , (4.19) 𝛿𝛿𝛿𝛿 𝜂𝜂 ≈ 𝜉𝜉 � � 𝐼𝐼1 𝑝𝑝𝑝𝑝 Δ𝑘𝑘0𝜏𝜏𝑝𝑝

Chapter 4

4.2.3 Cavity design In this section, we provide additional details on the resonator cavity, which includes three reflections on the disk gain medium. The 1/e2 beam radius as a function of the position inside the cavity is shown in Fig. 4.7 as it is obtained by standard ABCD matrix calculations. The cold disk radius of curvature (ROC) is Rcold = 2.04 m. During laser operation, because of thermal lensing the disk’s curvature changes. Here we estimated a Fdisk = 2/Rlasing – 2/Rcold = -0.035/m [31]. We have the SESAM at position 0 and the output coupler (OC) at the other end of the cavity. In order to have multiple passes on the disk we implemented a relay-imaging active multi-pass architecture [45]. In this way by properly spacing the two concave mirrors (ROC = 2.0 m) and the disk, we obtain the same Gaussian beam radius and curvature for each pass on the disk. This arrangement helps minimize the misalignment sensitivity of our cavity design. This is defined as the displacement of the laser beam on the disk because of an angular misalignment of the disk itself. This plays an important role for thin-disk lasers operated in air since a gas-wedge effect due to the air heating up in front of the disk leads to potential instabilities [31, 43]. Additionally, this configuration allows us to use different spots on the same mirrors in order to increase the number of passes on the disk. In this way, a very small angle of incidence (AOI) (<3 deg) is possible on the disk and on the curved mirrors. This minimizes astigmatism, which is detrimental for modelocked operation. All the mirrors in our cavity are manufactured by Layertec GmbH except for the two high-dispersive (HD) flat mirrors providing -2’000 fs2 of GDD each, which are made by University of Neuchatel. The curved dispersive mirrors provide -550 fs2 of GDD per bounce. The thin film polarizer (TFP), also provided by Layertec GmbH, yields ≈ -550 fs2 of GDD per bounce. The total SPM picked up in air is calculated as the B integral according to the formula:

2 2 , = (4.20) , ( 1/ ) , 𝑙𝑙 ( )/2 𝜋𝜋 𝑇𝑇𝑂𝑂𝑂𝑂 𝑛𝑛2 𝑎𝑎𝑎𝑎𝑎𝑎 𝑎𝑎𝑎𝑎𝑎𝑎 𝑟𝑟𝑟𝑟 𝑝𝑝𝑝𝑝 𝐼𝐼𝐼𝐼 2 𝐵𝐵 𝑂𝑂𝑂𝑂 𝑃𝑃 ��0 𝑑𝑑𝑑𝑑� where λ is the wavelength,𝜆𝜆 𝑙𝑙𝑙𝑙𝑙𝑙 TOC and𝑅𝑅 ROC, respectively,𝜋𝜋𝑤𝑤 𝑧𝑧 the transmission and the reflectivity of the OC, Ppk,IC the intracavity peak power immediately before 64

Cascaded quadratic nonlinearities the OC, l the length of the cavity, w(z) the beam radius inside the laser cavity, and n2,air = 4 x 10-19 cm2 /W [97] the nonlinear refractive index of air. The factor 2TOC/log(1/ROC) takes into account that the peak intensity is not constant in a round trip and assumes an exponential growth [98]. Some TDLs use an alternative approach based on convex mirrors to obtain a design having less intracavity foci [31, 43, 69]. While the reduced number of foci results in a lower amount of SPM picked up in air, such cavities are not compatible with the multi-pass architecture we use here. Therefore, they exhibit increased misalignment sensitivity. These issues motivated our use of the cavity design shown in Fig. 4.7.

4.2.4 Thermal behavior of the nonlinear crystal Using a calibrated thermal camera (FLIR SC640), we measured the temperature of the SHG crystal during laser operation. We record a temperature increase in the steady state of ≈ 10 °C at the highest output power (210 W average output power, with more than 500 W of intracavity power). This implies a low absorption from the crystal since no control over the crystal temperature was in place. Therefore, we expect that this SPM-cancellation technique is suitable for laser operation toward the kW output-power level [99]. The time needed by the nonlinear crystal to reach thermal equilibrium was in the order of a minute. During this transient phase, the laser stayed modelocked.

Chapter 4

Fig. 4.7 Evolution of the 1/e2 beam radius. Vertical dashed lines indicate the position, respectively, of the SESAM, the disk and the output coupler. We report the position of the curved mirrors, the dispersive mirrors, the thin-film polarizer (TFP), and the SHG crystal with circles. Blue circles refer to curved high-reflectivity mirrors, yellow circles to dispersive mirrors providing -550 fs2 GDD, green circles to flat high-dispersive (HD) mirrors providing -2’000 fs2 GDD. The numbers in the Figure refer to the radius of curvature of concave mirrors.

Nonlinear mirror modelocking

5 Nonlinear mirror modelocking

In this chapter, we present our modelocking results using the nonlinear-mirror technique in high-power thin-disk oscillators. We demonstrated the first nonlinear-mirror modelocked TDL in [33] and later on power-scaled it incorporating a SESAM in a nonlinear-mirror modelocked TDL oscillator [34]. This technique is very promising to generate short pulses from thin-disk oscillators while offering a similar flexibility in terms of cavity design as for SESAM modelocking. The details are presented in the two following journal publications: Title: “Modelocking of a thin disk laser with the frequency doubling nonlinear mirror technique”, [33] Journal: Optics Express doi: 10.1364/OE.25.023254

© 2017 Optical Society of America. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modifi- cations of the content of this paper are prohibited.

Chapter 5

Title: “Power-scaling of nonlinear-mirror modelocked thin-disk lasers”, [34] Journal: Optics Express doi: 10.1364/OE.27.037349

© 2019 Optical Society of America. Users may use, reuse, and build upon the article, or use the article for text or data mining, so long as such uses are for non-commercial purposes and appropriate attribution is maintained. All other rights are reserved.

Nonlinear mirror modelocking

5.1 Modelocking of a thin-disk laser with the frequency-doubling nonlinear-mirror technique

F. Saltarelli, A. Diebold, I. J. Graumann, C. R. Phillips, and U. Keller Institute for Quantum Electronics, ETH Zurich, 8093 Zurich, Switzerland

Abstract: We demonstrate a frequency-doubling nonlinear-mirror (NLM) modelocked thin-disk laser. This modelocking technique, composed of an intracavity second harmonic crystal in combination with a dichroic output coupler, offers robust operation decoupled from cavity stability (as in semiconductor saturable absorber mirror (SESAM) modelocking) combined with an ultrafast saturable loss and high modulation depth (as in Kerr-lens modelocking (KLM)). With our NLM diode-pumped Yb:YAG thin-disk laser we achieve 21 W of average power at 323-fs pulse duration, which is an order of magnitude shorter than the previously obtained duration with the same technique in bulk lasers. Using these first results, we present a theoretical model for the NLM technique, which accurately predicts its loss modulation properties and the shortest achievable pulse duration without relying on any fitting parameters. Based on this simulation, we expect that the NLM technique will enable thin-disk lasers with average power of more than 100 W, with potentially sub-200 fs pulses. This could potentially solve the pulse duration limitations with SESAM modelocked Yb:YAG thin-disk lasers without imposing strong cavity stability constraints such as in KLM. © 2017 Optical Society of America

5.1.1 Introduction Femtosecond laser sources with high peak and average power are an indis- pensable tool for many industrial and scientific applications, including laser precision micromachining and cutting [100], frequency metrology and strong-field physics in attosecond science [4]. Laser amplifiers based on the thin-disk, fiber, or Innoslab technology represent the state of the art of high-power ultrafast lasers. They reach kW-level average power with peak powers exceeding the GW level [9, 19, 20]. However, these systems have a substantial level of complexity and, in some cases, non-diffraction-limited

Chapter 5 beam quality. Modelocked thin-disk laser (TDL) oscillators are an attractive alternative to complicated amplifier systems and combine high output and peak power in a compact table-top MHz oscillator with excellent output beam quality. Moreover, these systems drive experiments at MHz repetition rates [28, 101], leading to reduced measurement times, and increased signal-to- noise ratios and photon fluxes [4, 102]. Thin-disk lasers offer the highest performance in terms of average power and excellent beam quality among all ultrafast oscillators. Based on the gain material Yb:YAG and modelocked with semiconductor saturable absorber mirrors (SESAMs), they currently achieve up to 275-W average power with 583-fs pulse duration [12] and 80-µJ pulse energy with 1.07-ps pulses [15]. Using broadband gain materials such as Yb:CALGO, pulse durations down to sub-50 fs were achieved with SESAM modelocking, however, at the expense of the output power, which stayed below 5 W [103, 104]. Because of the limited gain bandwidth of Yb-doped materials suitable for high-power operation (Yb:YAG, Yb:LuO), combining shorter pulse durations (sub-500 fs) and high average powers (>100 W) with SESAM-modelocking is a challenging task. This is mainly due to the SESAM’s non-instantaneous recovery times, mod- erate modulation depths, and thermal effects from unsaturated losses and two-photon absorption [105]. Ongoing efforts to address these issues include improved strain compensation [106], and different bonding techniques to achieve flatter samples with efficient heat removal [50]. Modelocking TDLs with the Kerr-lens technique (KLM) has allowed for shorter pulse durations while maintaining high average power. With the gain material Yb:YAG, this technique resulted in 270 W of average power with 330 fs pulses [47] and 155 W with 140 fs pulses [55]. However, these results were limited to pulse energies <15 µJ. Shorter pulses down to sub-50 fs with average power of around 5 W were reported with Yb:YAG [107] and Yb:LuO [108]. In general, the KLM technique imposes strict constraints on the cavity design that needs to be operated close to its stability edge. This requirement introduces additional challenges in alignment sensitivity and stability, as it directly couples spatial and temporal effects. Recently, TDLs have also been modelocked with the nonlinear polarization rotation (NPR) technique. Using Yb:YAG as gain material and introducing the required intensity-dependent phase shift for NPR via a long and phase-mismatched intracavity second harmonic

Nonlinear mirror modelocking generation (SHG) crystal, these oscillators reached up to 44 W with sub-500 fs pulses [57]. In this work, we investigate and demonstrate modelocking of a TDL with an alternative technique, the frequency-doubling nonlinear mirror (NLM) [51]. In this device, whose operating principles are described in section 5.1.2, the combination of a phase-matched SHG crystal and a dichroic output coupling mirror results in a lower effective output coupling rate for high intensity light, thereby providing a saturable reflectivity and enabling modelocked operation. This approach offers a route to overcome the trade-offs in both SESAM and KLM modelocking of high power oscillators. It offers robust operation decoupled from the cavity stability (as in SESAM modelocking), together with an ultrafast saturable loss (as in KLM), while maintaining power scalability. Compared to the NPR technique, a significantly shorter nonlinear crystal can be used, which should be favorable to avoid thermal lensing in future power scaling experiments (for example we use one 0.5-mm-long BBO crystal in the present work, compared with two ~20-mm-long LBO crystals in [57]). Moreover, the NLM technique offers a large and highly flexible modulation depth that scales with the laser output coupling rate. In Fig. 5.1(a) we present an overview of the performance of solid-state lasers modelocked with the NLM technique [109-113]. Additionally, this technique has also been used to assist the cascaded χ(2) lens modelocking process in order to stabilize it and provide self-starting operation [84]. Solid-state NLM-modelocked lasers achieved multi-ps pulse durations at comparatively high repetition rates (~100 MHz), which results in intracavity peak powers below 50 kW. Consequently, tight focusing is needed in order to reach the required intensities to drive the SHG process. This, in turn, makes spatial walk-off effects significant, which limits the efficiency of the process. Longer SHG crystals can be used, which, however, sets a lower limit for the achievable pulse duration in the few-ps-range due to group velocity mismatch (GVM) between the fundamental and its second harmonic [52]. High-power ultrafast TDLs, on the other hand, are well suited for the NLM process as their high peak powers allow for driving the nonlinear process with short crystals, which results in minimized thermal effects, larger bandwidths, and a corresponding short response time of the saturable reflectivity.

Chapter 5

Additionally, the NLM method is easily power-scalable by increasing the spot size on the SHG crystal. Here we present a first demonstration of a TDL modelocked by the NLM technique, using a Yb:YAG thin disk. We obtain 21 W of average power with 323-fs pulses and, in another configuration, 28 W with 570-fs pulses. Our proof-of-principle laser reaches more than 1 µJ of pulse energy, which results in more than 3 MW of extracavity peak power. Compared to prior results of NLM modelocking in bulk lasers, we decrease the achieved pulse durations by an order of magnitude [Fig. 5.1(a)]. Compared to state-of-the-art TDLs using Yb:YAG as gain medium [Fig. 5.1(b)], this first result reaches pulse durations significantly shorter than those obtained by SESAM-modelocking, and which lie in a range previously only accessible with KLM. In section 5.1.2, we present the operating principles of the NLM technique. In section 5.1.3, we discuss the laser experiment. In section 5.1.4, we describe in detail our numerical model and use it in order to estimate the shortest pulses achievable with our device. We conclude in section 5.1.5 by summariz- ing the obtained results and envisaging the next generation of NLM modelocked thin-disk lasers with average powers in the 100-W level.

Fig. 5.1 (a) Pulse duration and average power of NLM modelocked lasers. (b) Pulse duration and pulse energy of modelocked Yb:YAG TDLs. The symbols specify the modelocking technique: square for SESAM, circle for KLM, cross for NPR and star for NLM. In the presented results, we reduce the pulse durations achieved with the NLM modelocking technique by an order of magnitude, down to sub 350 fs, at output powers approaching 30 W, which is comparable to pulse durations achieved by state- of-the-art thin-disk oscillators.

Nonlinear mirror modelocking

5.1.2 NLM operating principles We show a general schematic of the frequency-doubling NLM technique in Fig. 5.2(a), consisting of a second-order nonlinear crystal (χ(2) crystal) config- ured for SHG, in combination with a dichroic output coupler (OC). In Fig. 5.2(b) we present the evolution of the pulse energy for the fundamental wave (FW) and the second harmonic (SH) inside the χ(2) crystal, based on the simulation discussed in Sec. 5.1.4. The NLM device can be described in three stages:

(i) Intracavity laser light [Pi in Fig. 5.2(a)] is directed through an intracavity SHG crystal, where some of this FW light is converted to its SH [in Fig. 5.2(b) solid red and green curves, refer, respectively, to FW and SH]. The SHG crystal is tilted in order to fulfill the phase match-

ing condition (∆k = kSH – 2kFW = 0) for the SHG process. (ii) Both wavelengths travel through a variable length of air [“air space” in Fig. 5.2(a)] and are reflected from a dichroic OC, which is highly reflective (HR) for the SH and partially reflective for the FW. The transmitted power [Pt in Fig. 5.2(a)] of the FW defines the transmission of the NLM device.

(iii) The beams then pass back through the χ(2) crystal [dashed curves in Fig. 5.2(b)]. The relative phases of the FW and SH are adjusted via the air space in such a way that the reverse process of SHG (i.e., optical parametric amplification, OPA) occurs optimally (∆φ = -π), thereby converting the SH light back to the FW. Essentially, the NLM modelocking device acts as an OC with intensity-dependent reflectivity and transmission. At higher input intensities, more light is converted to the SH in stage (i). This implies a reduced output coupling rate for the FW, and more total power (FW + SH) being reflected by the OC in stage (ii). Then, by converting the reflected SH back to the FW in stage (iii), there is a higher overall reflectivity for the FW. To quantify the behavior of the device, we consider the average power of the FW at different positions: Pi, Pt, and Pr refer to the initial intracavity power, the transmitted extracavity power, and the final reflected intracavity power, 73

Chapter 5 respectively. We also introduce the corresponding FWHM (full-width at half- maximum) pulse durations, denoted τi, τt, and τr. We then define the following parameters [114-116]:

, = / (5.1)

𝑅𝑅𝑛𝑛𝑛𝑛�𝐼𝐼𝑝𝑝𝑝𝑝, 𝜏𝜏𝑖𝑖� = 𝑃𝑃𝑟𝑟/𝑃𝑃𝑖𝑖 (5.2) 𝑇𝑇𝑛𝑛𝑛𝑛�𝐼𝐼𝑝𝑝𝑝𝑝, 𝜏𝜏𝑖𝑖�= 𝑃𝑃/𝑡𝑡 𝑃𝑃.𝑖𝑖 (5.3)

𝑝𝑝𝑝𝑝 𝑖𝑖 𝑟𝑟 𝑖𝑖 The parameter Rnl indicates the𝜅𝜅�𝐼𝐼 nonlinear𝜏𝜏 � 𝜏𝜏 reflectivity𝜏𝜏 of the device, Tnl the ratio between the intracavity power and the output power of the laser, while κ indicates the pulse-shortening factor, which is related to the modulation bandwidth of the device. The variable Ipk is the peak intensity of the incoming (2) beam on the χ crystal, Ipk = max(Ii(r, t)).

Fig. 5.2 (a) Schematic representation of the nonlinear-mirror modelocking (NLM) technique. (b) Evolution of the pulse energy inside the χ(2) crystal. Solid and dashed lines refer, respectively, to the forward and backward pass in the crystal. (OC – output coupler, SHG – second harmonic generation, FW – fundamental wave, SH – second harmonic).

5.1.3 Experiment In this section, we present the laser cavity used in the presented experiment and the results we obtain with it. Then, we discuss how the output pulse parameters depend on the NLM modelocking device configuration. Experimental setup The laser experiment we present here uses a 230-µm thick, 5-at.% doped Yb:YAG disk, contacted on a CuW heatsink by Dausinger + Giesen GmbH,

Nonlinear mirror modelocking and mounted in a 24-pass thin-disk pump head with a 2.1-mm diameter pump spot. The disk has a wedge of ~0.1 deg between the front and back surface and a non-astigmatic cold radius of curvature of -5.3 m. The disk is diode-pumped up to 160 W at a center wavelength of 936 nm. In Fig. 5.3(a) we present a schematic of the laser cavity and in Fig. 5.3(b) the evolution of the 1/e2 laser mode radius within the oscillator. We designed our cavity to have a double-reflection on the thin disk in order to increase the available gain per roundtrip. The cavity includes a 2.5-mm undoped YAG Brewster plate (BP), which fixes the polarization in the plane of the optical table and provides δ = 6.37 mrad/MW of self-phase modulation (SPM). In a first step, we operate the cavity without the χ(2) crystal, but with the dichroic OC, and we achieve up to 30 W of output power with 33% optical-to-optical efficiency in contin- 2 uous-wave (cw) single-mode operation (M <1.1). The dichroic OC used for the NLM configuration has 19.7% transmission (RFW = 80.3%) at the FW (1030 nm) and high reflectivity (RSH = 99.9%) at the SH (515 nm). For modelocking, we insert a 500-µm-thick type-1 BBO crystal close to the cavity focus on the OC mirror (beam waist radius of 185 μm), as shown in the inset [Fig. 5.3(c)]. The crystal is cut for phase matching at 1030 nm with both faces anti-reflection coated for 1030 nm and 515 nm. We achieve correct phase matching for the SHG process by optimizing the tilt of the BBO crystal while looking at the small green leakage from the OC. For a correct phase offset ∆φ between FW and SH for high-efficiency OPA we tune the spacing between the nonlinear crystal and the OC in a range between 5 mm and 8 mm in order to minimize the non-back-converted SH. The modelocking process is initiated by lightly tapping the mounting post of the focusing mirror before the BBO crystal.

Chapter 5

Fig. 5.3 (a) Schematic representation of the laser cavity. (b) Evolution of the 1/e2 mode radius. Vertical dashed lines indicate the position of crystals, OC, and end mirror. Labels indicate the curvature of concave mirrors. Inset (c): zoom of mode radius near the OC. (GTIs – dispersive mirrors, BP – Brewster plate).

Flat dispersion-compensating mirrors providing negative group delay dispersion (GDD) are used in the cavity to balance the SPM accumulated in air, the BBO crystal, the BP, and the disk. Modelocking results In our optimization of the modelocked operation, we focused on the one hand on reaching the shortest pulse duration, and on the other hand on max- imizing the output power. We always optimize the distance between BBO crystal and OC in order to have the maximum back-conversion of the SH during the second pass in the BBO crystal. However, by adjusting the SHG phase matching, we adapt the reflectivity saturation and thus obtain the following two configurations:

- Short pulse (SP) configuration: the BBO tilt is tuned such that the green leakage through the OC (in cw operation) is maximized, i.e., ∆k = 0. This maximize the reflectivity modulation of the NLM device, allowing for the shortest pulses.

- High power (HP) configuration: we slightly phase mismatch the SHG process by reducing the transmitted green light through the OC to ~85% of the maximum value (in cw operation). This reduction of the SHG efficiency corresponds to a phase mismatch |∆k·L| ~ 0.3π [117]. This results in a higher OC rate and lower FW reflectivity, which, in turn, allows for higher output power.

Nonlinear mirror modelocking

Using an intracavity GDD from the GTI mirrors of -5900 fs2 per roundtrip, we obtain 323-fs pulses at 21 W of output power in the SP configuration, at a repetition rate of 17.8 MHz. This corresponds to a pulse energy of 1.2 µJ and to more than 3 MW of extracavity peak power. The pulses are supported by an optical spectrum with a FWHM of 4.23 nm [see Fig. 5.4(a)], which corresponds to a transform-limited duration of 263 fs. The chirp in the pulses could be due to the SHG process, and will be investigated in future work.

Fig. 5.4 Diagnostics for the configuration with the highest peak power (SP configuration, total GDD from the mirrors 5900 fs2 yielding 323 fs pulse duration and 21 W average power). We acquire the diagnostics on the output beam of the laser. (a) optical 2 spectrum, (b) autocorrelation trace, (c) M measure, (d) radio frequency (RF) trace showing the RF comb, (e) RF trace showing the peak at the repetition rate, (f) sampling scope trace, in the inset a zoom on a single pulse with a different span. The ripple in 2 2 the sampling oscilloscope trace is due to the detector. The 1/e beam radius in the M measurement is calculated using the second momentum width (D4σ). The autocorrelation trace and the optical spectrum are fitted with a sech2 function (red dashed line). (RBW – Resolution bandwidth)

Chapter 5

In the HP configuration, we could increase the output power up to 28 W at 150 W of pump power, however with substantially longer pulses of 570 fs. In this case, the intracavity GDD is increased to -7000 fs2 per roundtrip. We ensured clean modelocking in all configurations by obtaining the optical spectrum, the autocorrelation trace and radio frequency spectra. Moreover, by scanning the autocorrelator delay up to 60 ps and acquiring a sampling oscilloscope trace with a 45 GHz bandwidth photodiode we prove single-pulsed operation. The beam quality is assessed by measuring the M2 of the output beam using a commercially available scanning-slit automatized beam profiler. In all configurations, we obtain a nearly-diffraction-limited beam with an average M2 = [(M2x) + (M2y)]/2 below 1.10. In Fig. 5.4 we present the diagnostics for the 323 fs pulse, corresponding to the highest peak power. Stable modelocking was observed for several hours in daily operation without any breakdown of modelocking. The maximum achievable output power in this proof-of-principle experiment is currently limited by the comparatively small pump-spot size on our disk. We chose a maximum pump intensity safety limit of ~5 kW/cm2, which re- stricted the maximum pump power on our disk to 160 W. Additionally, the non-optimal center wavelength of the pump diodes led to our comparatively low optical-to-optical efficiency of 33 % in continuous wave single-mode operation and ~19 % in modelocked operation. Experimental investigation of the NLM-modelocking regime In Fig. 5.5(a) and Fig. 5.5(b) we show the pulse duration and output power versus pump power for three different experimental conditions: two short pulse (SP) configurations with different values of GDD, and one high-power (HP) configuration. In the NLM modelocking technique, the effective OC rate of the cavity varies with the peak intensity in the χ(2) crystal. For a given configuration, increasing the pump power results in a decrease of the effective transmission, which yields a nonlinear relation between output power and pump power as we can see in Fig. 5.5(b).

In order to accurately determine the intensity-dependent OC rate Tnl, we employed a photodiode to measure a small FW leakage through an intracavity mirror in order to infer the intracavity power in modelocked operation. We

Nonlinear mirror modelocking calibrated the ratio between photodiode voltage and intracavity power in cw operation, since in this case the OC rate is equal to the linear transmission of the OC at the laser wavelength. Using the beam waist on the BBO crystal calculated from the cavity design [Fig. 5.3(b)] and the pulse duration retrieved from the autocorrelation trace (assuming a sech2 pulse), we can estimate the peak intensity on the BBO crystal. The fluctuations in the effective OC transmission from different measurements are within 10%. In Fig. 5.5(a) each data point is labelled with the corresponding OC rate for comparison to Fig. 5.5(c), where we show the effective OC rate versus the peak intensity on the BBO crystal. The solid points in Fig. 5.5(c) represent the same data points presented in Fig. 5.5(a) and Fig. 5.5(b) while the dashed points are additional measurements shown only in Fig. 5.5(c). For clarity of presentation, these additional points are not shown in Fig. 5.5(a) and Fig. 5.5(b). The solid purple line in Fig. 5.5(c) is the prediction of our numerical model, which we describe in section 5.1.4. The model accurately predicts the behavior of the device. The configurations optimized for high power gener- ally present an effective OC rate slightly higher than the ones optimized for short pulses, and higher than the model (which assumes ∆k=0). This trend is consistent with the fact that in the high-power configuration, the SHG process efficiency is slightly sub-optimal, leading to a less pronounced effect of the NLM of reducing the effective OC transmission. Additionally, our model does not take into account the reflection losses on the BBO, which are <0.5%. These losses will have the effect of slightly reducing the effective OC transmission. Next, we also investigate the influence of the NLM device on the pulse shaping. For that we compare in Fig. 5.5(a) the pulse duration achieved in the short-pulse and high-power configuration with the same amount of intracavity GDD (-5900 fs2). The difference between these two configurations clearly indicate that the phase matching substantially influences the pulse duration. Moreover, we compare the pulse durations achieved in the SP configuration for different values of intracavity GDD [in Fig. 5.5(b) we show -4800 fs2 and -5900 fs2]. The change in GDD only slightly influences the shortest achievable pulse duration. This observation suggests that the leading process in pulse formation is the NLM, rather than the soliton shaping effect.

Chapter 5

To further test this hypothesis, we fit the experimental data with an exponen- α tial function, τt = cEp- , where Ep is the intracavity pulse energy. We find for α values between 0.5 and 0.8. A conventional soliton shaping mechanism, arising from GDD and SPM, would have α ~ 1 [77]. This deviation from pure soliton shaping suggests that the NLM device dynamics strongly contribute to the pulse formation process. In the HP configuration, the slightly phase mismatched SHG process leads to a non-negligible SPM, with its sign depending on the sign of the phase mismatch ∆k. This could potentially influence the pulse formation mechanism. However, in these experiments we did not observe any significant change in the modelocking behavior for different signs of the phase mismatch.

Fig. 5.5 Characterization of pulse duration (a) and output power (b) versus the pump power. Circles correspond to configurations optimized for short pulses (SP), i.e., ∆k = 0; squares to configurations optimized for high power (HP), i.e., the SHG process is slightly detuned from perfect phase matching. (c) Saturable loss effect of the nonlinear mirror. The solid line is the prediction of our model. Solid points: same data shown in in (a) and (b); dashed points: additional data points for the same laser configuration. (GDD – Group delay dispersion).

Nonlinear mirror modelocking

5.1.4 Numerical model of the NLM device In this section, we present a model for the NLM technique, demonstrate that it stands in excellent agreement with our experimental results presented in section 5.1.3, and predict the next steps needed for scaling the output power and pulse duration of NLM modelocked TDLs. Description of the model We base our model on coupled-wave equations which describe the two-stage process, namely SHG on the first pass through the χ(2) crystal, followed by the reverse process of OPA on the return pass. Because of the high intracavity pulse energy involved (>1 µJ), we can use a loose focus (beam waist radius of 185 µm) on a thin BBO crystal (length L = 500 µm), and hence spatial effects such as diffraction and Poynting vector walk-off are negligible. On the other hand, temporal effects (mainly the group velocity mismatch (GVM)) play an important role in limiting the bandwidth of the device [52, 113]. Indeed the GVM delays the SH pulse with respect to the FW, which leads to a reduced back conversion of the SH to the FW during the second pass in the χ(2) crystal. In our configuration the GVM parameter in the χ(2) crystal corresponds to

δ1,2 = 1/vgSH - 1/vgFW = 93 fs/mm [118]. For two passes in a 500-µm thick BBO crystal, the total delay sums up to ~100 fs and becomes comparable to the pulse duration, thus it has to be included in our model. By neglecting the spatial effects but including temporal effects to first and second order, we obtain a simplified coupled-wave equations model:

( , ) = 2 2 ∂𝐸𝐸𝐹𝐹𝐹𝐹 𝑡𝑡 𝑧𝑧 𝛽𝛽𝐹𝐹𝐹𝐹 ∂ 𝐸𝐸𝐹𝐹𝐹𝐹 − 𝑖𝑖 2 ∂𝑧𝑧 ( , ) ( , ∂)𝑡𝑡 ( ) 𝑑𝑑𝑒𝑒𝑒𝑒𝑒𝑒𝜔𝜔𝐹𝐹𝐹𝐹 ∗ 𝐹𝐹𝐹𝐹 𝑆𝑆𝑆𝑆 (5.4) −𝑖𝑖 𝐹𝐹𝐹𝐹 𝐸𝐸 𝑡𝑡 𝑧𝑧 𝐸𝐸 𝑡𝑡 𝑧𝑧 𝑒𝑒𝑒𝑒𝑒𝑒 −𝑖𝑖Δ𝑘𝑘𝑘𝑘 ( , ) 𝑐𝑐𝑛𝑛 1 1 ( , ) + = ( ) ( ) 2 2 ∂𝐸𝐸𝑆𝑆𝑆𝑆 𝑡𝑡 𝑧𝑧 ∂𝐸𝐸𝑆𝑆𝑆𝑆 𝑡𝑡 𝑧𝑧 𝛽𝛽𝑆𝑆𝑆𝑆 ∂ 𝐸𝐸𝑆𝑆𝑆𝑆 � − � − 𝑖𝑖 2 ∂𝑧𝑧 𝑣𝑣𝑔𝑔 𝜔𝜔𝑆𝑆𝑆𝑆 𝑣𝑣𝑔𝑔 𝜔𝜔𝐹𝐹𝐹𝐹( , ) ∂(𝑡𝑡 ) ∂𝑡𝑡 𝑒𝑒𝑒𝑒𝑒𝑒 𝐹𝐹𝐹𝐹 2 𝑑𝑑 𝜔𝜔 𝐹𝐹𝐹𝐹 −𝑖𝑖 𝑆𝑆𝑆𝑆 𝐸𝐸 𝑡𝑡 𝑧𝑧 𝑒𝑒𝑒𝑒𝑒𝑒 𝑖𝑖Δ𝑘𝑘𝑘𝑘 We use the following variables:𝑐𝑐𝑛𝑛 Ej: electric field envelope (j = FW or j = SH); nj refractive index; ωj: center frequency; vg: group velocity; deff: effective 81

Chapter 5

nonlinear coefficient of the material [119]; βj: group velocity dispersion parameter; ∆k phase mismatch for wavevectors kj = ωj nj /c ; z : longitudinal position in the crystal; t : delay, in the moving coordinate system relative to the group velocity of the FW. We use Eqs. (5.4) to model stages (i) and (iii) of the NLM device, as described in section 5.1.2. For stage (i), the SHG process, we solve Eqs. (5.4) using as initial conditions a pulse with a temporal sech profile for EFW(t, 0), and set

ESH(t, 0) = 0. We assume perfect phase-matching and therefore set ∆k to zero. For stage (ii), we take the output envelopes EFW(t, L) and ESH(t, L), where L is the length of the BBO crystal, and apply the linear reflectivity of the OC (i.e., power reflectivities of RFW = 80.3% for the FW and RSH = 99.9% for the SH). Additionally, we add a phase shift ∆φ = -π to the SH. The combination of ∆φ = -π and ∆k = 0 corresponds to the optimal condition for the back-conversion of the SH to the FW. The resulting envelopes are then used as the input conditions to Eqs. (5.4) to model the returning pass (iii), i.e., the OPA process. By performing a series of simulations for different peak intensities on the χ(2) crystal of the incoming pulse (Ipk), we retrieve the behavior of the NLM device for a pulse with a Gaussian intensity profile in space. It is worth noting that this model does not rely on any fitting parameters. Results of the model: bandwidth considerations

We show the nonlinear reflectivity Rnl(Ipk, τi) as a function of the peak intensity on the BBO crystal Ipk for different output pulse durations τt in Fig. 5.6(a). The reflectivity modulation is given by the difference between the RFW = 80.3% line (i.e., the linear reflectivity of the OC at 1030 nm) and the Rnl curve, defined as in Eq. (5.1). The nonlinear reflectivity is significantly reduced for shorter pulse durations, because GVM leads to a reduced temporal overlap between the FW and SH in the second pass through the crystal. This effect results in increased losses of the device. The degradation in performance for shorter pulses corresponds to a limited bandwidth for which this device is able to provide optimal performance. We refer to this limit as modulation bandwidth. It is worthwhile to mention that the phase-matching bandwidth of each one of the single χ(2) processes (namely SHG and OPA) is significantly larger than the bandwidth 82

Nonlinear mirror modelocking of the two processes combined together, because the delay between the FW and SH pulses accumulates through the two processes.

In Fig. 5.5(c), we showed the corresponding transmission of the NLM Tnl, as defined in Eq. (5.2), as a purple solid line. The nonlinear transmission

Tnl(Ipk, τi) depends strongly on the pulse peak intensity on the BBO crystal Ipk. In contrast to the behavior of Rnl, Tnl is unaffected by the output pulse duration τt in the considered range (i.e., for pulses longer than 200 fs). This independence of Tnl from τt is due to the fact that it involves only one pass in the χ(2) crystal and that the bandwidth of the SHG process alone is sufficient for efficient conversion. Thus, in Fig. 5.5(c) we show only one curve, calculated for a pulse duration of 1 ps, to compare with the experimental values. The good agreement between experiment and theory confirms the validity of our model. The limitations in the modulation bandwidth of the NLM does not only consist in a reduced nonlinear reflectivity, but translates also into a pulse lengthening effect. Fig. 5.6(b) shows the pulse-shortening parameter, κ, defined as in Eq. (5.3), as a function of the pulse duration transmitted by the NLM. Below a certain pulse duration, the NLM stops acting as a pulse short- ener on each round-trip of the cavity. As is clearly visible, this effect is only weakly dependent on the pulse peak intensity on the BBO crystal Ipk. Moreo- ver, this threshold point scales with the crystal length. For pulse durations below 300 fs in our experimental configuration, Fig. 5.6(b) predicts that the NLM causes a pulse lengthening on each round trip. Thus, this transition to κ > 1 likely explains why 300 fs pulse duration was the shortest we could obtain in this experiment, since the NLM (in the configuration used here) acts to lengthen pulses shorter than this.

Chapter 5

Fig. 5.6 Analysis of the performance of the NLM as a function of the output pulse duration τt and of the peak intensity on the BBO crystal Ipk. (a) Saturable reflectivity behaviour: effective reflectivity as a function of Ipk for different τt, (b) pulse shortening factor κ = τr/τi as a function of τt for different Ipk.

Our model succeeded in predicting both the expected OC rate of the cavity and the shortest achievable pulse duration. Thus, we can use it in the design of the next generation NLM lasers with shorter pulses and higher powers. For example, increasing the nominal transmission of the OC for the FW to 40% instead of 20% would, at the same intensity and BBO crystal length, yield κ = 1 (i.e. the transition between pulse-shortening and pulse-lengthening) at a pulse duration of ~200 fs, together with an effective OC rate of ~25%. Yb:YAG thin-disk lasers with a similar or even much higher OC rate have already been demonstrated [15, 46]. Use of a slightly shorter BBO crystal (~300 µm thick) and slightly higher intensity ~90 GW/cm2 would yield a further reduction in the NLM-limited pulse duration, towards <150 fs pulses. This intensity is still below the BBO crystal damage threshold, based on other demonstrated systems. For instance in [120] a BBO crystal is used in an optical parametric amplifier with peak intensities up to 300 GW/cm2 (~500-fs pulses at 515 nm). Additionally, the pulse duration supported by the NLM can be reduced even further by GVM compensation techniques. These techniques have already been proposed [121] and demonstrated [113] to increase the modulation bandwidth of the NLM modelocking technique.

Nonlinear mirror modelocking

As well as offering more favorable pulse shortening, a higher OC rate also reduces the intracavity power demands for a given output power, which is highly favorable for power scaling. Moreover, with the NLM technique, the available modulation depth is approximately proportional to the nominal transmission of the OC for the FW. Thus, going to higher OC rates also increases the modulation depth accordingly, which is beneficial for obtaining short pulses. By scaling the pump spot size on the disk, and the laser spot size on the disk and BBO crystal, we expect that >100 W output powers are well within reach. We expect that the BBO crystal will be able to handle the increased thermal load based on other demonstrated systems, where such crystals are operated with kW-level average power [20].

5.1.5 Conclusion and outlook We demonstrated the first NLM modelocked TDL, achieving 323-fs pulses at 21 W output power, which corresponds to pulses with >1 µJ pulse energy and >3 MW peak power. A key factor in obtaining this performance was the use of a thin-disk instead of a bulk laser geometry. Indeed the NLM, based on ultrafast nonlinear processes, benefits from high intracavity peak power that is typical of high-power short-pulsed thin disk lasers. Additionally the NLM process is well suited for high-power short-pulsed TDL operation as it provides an easily scalable modulation depth, offers an ultrafast response of the saturable loss (as in KLM), and can be operated in the center of the cavity stability region (as in SESAM modelocking). We also presented a simple model for the NLM technique that, without any fitting parameters, succeeded in both predicting the effective OC rate and the shortest achievable pulse duration in the presented configuration. Based on our current laser performance and our simulations, we expect this first result to enable a new way towards high-power short-pulsed modelocked thin-disk oscillators in the near future. Increasing the spot size on the disk and simultaneously on the BBO crystal will allow for pumping harder and thus scaling up the average power to the 100-W regime. Employing a shorter crystal and an OC with a higher nominal transmission seems a promising way toward shorter pulses. Additionally, applying broadband gain materials (e.g., Yb:LuO, Yb:CALGO), even shorter pulses could be achieved. By simple adjustment of the χ(2) crystal parameters or material, the technique also holds great

Chapter 5 promise for long-wavelength TDLs using new thin-disk gain media such as Ho:YAG [122]. Funding Swiss National Science Foundation (SNSF) project grant numbers 200020_172644. Acknowledgements We would like to thank Prof. Clara J. Saraceno from the Ruhr-Universität Bochum for helpful discussions of thin-disk laser technologies.

Nonlinear mirror modelocking

5.2 Power-scaling of nonlinear-mirror modelocked thin-disk lasers

I. J. Graumann,1 F. Saltarelli,1 L. Lang,1 V. J. Wittwer,2 T. Südmeyer,2 C. R. Phillips,1 and U. Keller1 1Institute for Quantum Electronics, ETH Zurich, 8093 Zurich, Switzerland 2Laboratoire Temps-Fréquence, Université de Neuchâtel 2000 Neuchâtel, Switzerland

Abstract: We present a first power-scaled nonlinear-mirror (NLM) modelocked thin-disk laser based on an Yb-doped gain material. The laser oscillator delivers average output powers up to 87 W and peak powers up to 14.7 MW with sub-600-femtosecond pulses at ≈9-MHz repetition rate. We demonstrate a threefold improvement in average output power and sixfold improvement in pulse energy compared to previous NLM-modelocking results. We obtain peak powers in excess of 10 MW for the first time from an NLM-modelocked laser oscillator. In our laser, the NLM is assisted by a semiconductor saturable absorber mirror (SESAM) to reliably initiate pulsed operation. We validate the high-power suitability of the NLM modelocking technique using low-absorption χ(2) crystals and optimized dichroic-mirror coating designs. Furthermore, we discuss stability against Q-switching and study how the tuning of the nonlinear mirror affects the laser performance. © 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

5.2.1 Introduction Ultrafast laser sources are key technological devices to a variety of applications both in industry and scientific research. For example, the combination of high peak power and ultrashort pulse duration has enabled industrial micro-ma- chining, nonlinear biomedical imaging, and frequency conversion to extreme wavelengths such as the extreme ultraviolet (XUV) and THz [4, 5, 58, 123]. The development of Yb-based systems, with low-cost direct diode-pumping schemes, further facilitated the deployment of these sources and provided the technology for combining high-power and ultrafast laser operation. Today, the leading technologies for high-power ultrafast laser amplifier systems,

Chapter 5 namely fiber, slab and thin-disk, are based on a geometry that optimizes the surface-to-volume ratio for efficient heat removal, enabling kW-level average powers [7, 9, 20, 62]. These benchmark performances are achieved in amplifier systems which consist of a low-power seed oscillator followed by pulse shaping stages, several amplification stages and compression. Besides the overall large footprint of these multiple stages, high-power amplifiers gener- ally have various trade-offs in terms of beam quality, nonlinearity management, repetition rate scaling, spectral bandwidth, pulse quality, and pulse contrast. Alternatively, high-power ultrafast laser operation can be achieved from a single modelocked laser oscillator combining diffraction-limited beam quality, transform-limited pulses, megahertz repetition rates, and low noise [23]. The thin-disk geometry is well-suited for this purpose, with the thin gain medium providing excellent heat removal capabilities, low nonlinearity and power-scalability [24]. Based on the high quality and technological maturity of Yb:YAG as gain material, thin-disk laser (TDL) oscillators have demonstrated continuous-wave (cw) operation up to 10 kW 2 (M ≈10) from a single disk [124] and ultrafast operation up to 350 W [21]. Ultrafast laser operation in TDL oscillators is achieved via passive modelocking and requires an intracavity saturable loss to initiate and stabilize the pulse formation with soliton modelocking [77, 125]. The record performance of 350 W [21] was achieved using a semiconductor saturable absorber mirror (SESAM) [26] (Fig. 5.7(a)). The SESAM consists of semiconductor layers forming a distributed Bragg-reflector topped by InGaAs quantum wells acting as saturable absorbers and a top coating for a high damage threshold [26, 49, 50]. The epitaxially-grown SESAM structure can be contacted onto a heatsink and directly placed inside the laser resonator to initiate and stabilize soliton modelocking [77]. This flexibility is reflected in the numerous results achieved with very diverse laser configurations and gain materials [23]. However, for targeting shorter pulses, a trade-off between gain bandwidth and average power has been observed for Yb-doped thin-disk gain media when using alternative host materials with broader bandwidths than YAG (see Fig. 3 in [23]). This trade-off is attributed to a combination of less favorable material properties and crystal quality for high-power laser operation, and the slow saturable absorber behavior of the SESAM. Alternatively Kerr-lens modelocked (KLM) thin disk lasers have demonstrated high output powers

Nonlinear mirror modelocking up to 270 W with 330-fs pulses [47] and 155 W with 140-fs pulses [55] (Fig. 5.7(a)). Relying on Kerr-lensing combined with soft- and hard-aperture effects, this modelocking scheme provides a fast absorption-free loss modulation. For a given gain material, KLM has enabled shorter pulse durations due to its fast saturable loss mechanism, which enables a larger fraction of the available gain bandwidth to be utilized. However, this comes at the cost of an increased complexity in the resonator design, which couples resonator stability and pulse formation. This reduces the flexibility of KLM and makes initiating pulse formation more challenging. An attractive alternative providing a fast loss modulation is for example the frequency-doubling nonlinear-mirror (NLM) modelocking technique [51]. In this technique, the output coupler (OC) of the laser cavity is replaced with a new device: an intracavity χ(2) crystal cut for type-1 second-harmonic generation (SHG), combined with a dichroic output coupler (OC) fully reflecting the second harmonic (SH) but only partially reflecting the fundamental wave (FW) [51]. The incident intracavity FW light is partly converted to the SH in the χ(2) crystal, experiences losses at the dichroic OC, and is partially replenished by the fully reflected SH in the return pass through the χ(2) crystal (described in Section 5.2.2 and Fig. 5.8). Since SHG is a nonlinear process, higher reflectivities are obtained at higher intensities, yielding a saturable loss mechanism [51]. The resulting NLM promises to combine the advantages of SESAM modelocking and KLM by providing a large, ultrafast, and absorption-free loss modulation that is decoupled from the oscillator geometry. These features make NLM modelocking ideally suited to generate ultrashort pulses at high average powers. NLM modelocking was mainly investigated with low-power, high repetition rate bulk oscillators. Due to the low available intracavity power, this required the use of few-millimeter-long χ(2) crystals, which severely limited the lowest achievable pulse duration to >5 ps [112, 113, 126] (Fig. 5.7(b)) due to group- velocity mismatch (GVM) between the FW and SH in the χ(2) crystal. The higher intracavity peak power available from thin-disk laser oscillators allows for the use of much thinner crystals (≈1 mm), thereby enabling significantly shorter pulses. In our recent first demonstration of an NLM-modelocked thin-disk laser, we used a 0.5-mm-thick BBO crystal and obtained pulses as 89

Chapter 5 short as 323 fs at an average power of 21 W, reaching 3.2 MW of peak power [33] (Fig. 5.7(b)). It is worth noting that the achieved pulse duration is comparable to typical pulse durations obtained with KLM (Fig. 5.7(a)), and is the first sub-picosecond pulse duration reported for NLM-modelocking, to the best of our knowledge (Fig. 5.7(b)).

Fig. 5.7 (a) Overview of passively modelocked thin-disk laser results obtained with the gain material Yb:YAG and different modelocking techniques. Refs. [12, 15, 21, 33, 45- 47, 53, 55, 63, 88-91, 127, 128]. NPR: nonlinear polarization rotation [57]. The dashed lines indicate constant pulse energy values. The average power of state-of-the art results is indicated on the graph and the presented results are highlighted by the green circle. (b) Average output power and pulse duration of NLM-modelocked oscillators in the thin-disk and bulk geometries. Refs. [109, 110, 112, 113, 126, 129-131]. The peak power of state-of-the-art results is indicated on the graph and the presented results are encircled in green.

Here we demonstrate significant improvements in NLM-modelocked thin- disk lasers towards the state-of-the-art demonstrated with other modelocking techniques. We combine the fast loss modulation of the NLM with a SESAM to obtain a reliable initiation of pulsed operation and optimize the NLM- modelocking process in terms of Q-switching instabilities that arise in this new regime of laser operation (femtosecond NLM). We demonstrate an NLM-modelocked thin-disk laser delivering 66 W in 426-fs pulses at 9.3 MHz in a first configuration, and up to 87 W with 586-fs pulses at 8.8 MHz in a second configuration. The ultrafast oscillator produces pulses with energies up to 9.8 µJ and peak powers up to 14.7 MW (Fig. 5.7). In particular, we demonstrate peak powers in excess of 10 MW for the first time with an NLM- modelocked oscillator, while the average power is three times higher than previously demonstrated with this modelocking technique, to the best of our knowledge. Moreover, as illustrated in Fig. 5.7, the pulse duration is 90

Nonlinear mirror modelocking significantly shorter than typically achieved by high-power SESAM- modelocked Yb:YAG thin disk lasers. In the following, we first present our modelocking results (section 5.2.2) and comment on our approach to mitigate Q-switching instabilities (section 5.2.3). In the final part we present our investigation of the NLM-modelocking regime (section 5.2.4) and conclude with prospects for further power scaling.

5.2.2 High-power NLM-modelocked oscillator In this section we present our high-power NLM-modelocked thin-disk laser. We took several key steps compared to our earlier result [33] to enable the improved performance: (1) We used a state-of-the-art Yb-doped thin-disk module from TRUMPF. (2) We implemented an active-multipass cavity geometry to optimize the oscillator for high-power operation and simultaneously lower the repetition rate compared to previous results. (3) We improved the thermal and damage properties of the NLM device by using a low-absorption LBO crystal as the χ(2) medium, and optimized dichroic output coupler (OC) coatings leading to a higher damage threshold. (4) We included an intracavity SESAM to assist the optimization of the NLM device during modelocking and reliably initiate pulsed operation. (5) We carefully characterized the NLM operating regime, allowing us to define guidelines to avoid Q-switching instabilities and tune the pulse duration during modelocked operation. We first present the operating principles of the NLM device and introduce its tuning parameters, then describe the thin-disk oscillator and finally present the modelocking results.

Chapter 5

NLM operating principle Here we describe the three-stage operating principle of the frequency-doubling NLM and introduce the key parameters used to tune the NLM device, as illustrated in Fig. 5.8:

(1) An incident FW with a power generates a SH with an efficiency inc depending on the phase-mismatch ∆k = kSH – 2kFW (Fig. 5.8(b), solid 𝑃𝑃FW lines). (2) The FW and SH co-propagate to the OC where a part of the FW is transmitted. The reflected FW and SH co-propagate backout to the χ(2) 𝑃𝑃FW crystal. The waves accumulate a relative phase offset due to dispersion in the air gap and different reflection phases in the dichroic OC coating layers. (3) The SH is converted back to the FW via optical-parametric amplification (OPA) (Fig. 5.8(b), dashed lines), resulting in a reflected power at the FW and a residual power loss in the SH. The efficiency ref loss ofFW the back-conversion process is determinedSH by the relative phase offset𝑃𝑃 introduced by the difference in the𝑃𝑃 refractive index of air for the FW and SH, and can be adjusted experimentally via the air gap.

As emerges from this description, for a given beam size on the χ(2) crystal, the operation of the NLM is mainly determined by two parameters: the phase- mismatch ∆k, given by the angle of incidence of the intracavity beam on the χ(2) crystal, and the air gap between the χ(2) crystal and the dichroic OC. The operation of the NLM can be characterized experimentally by carefully measuring and via leakages of intracavity mirrors in addition to . The inc loss out effectiveFW nonlinearSH reflectivity, effective nonlinear transmission and SHFW losses of the𝑃𝑃 NLM are𝑃𝑃 then calculated as follows: 𝑃𝑃

= 1 ( + )/ (5.5) out loss inc 𝑅𝑅eff − =𝑃𝑃FW 𝑃𝑃SH 𝑃𝑃FW (5.6) out inc 𝑇𝑇eff = 𝑃𝑃FW ⁄/𝑃𝑃FW (5.7) loss inc 𝑆𝑆𝑆𝑆 SH FW 𝐿𝐿 𝑃𝑃 𝑃𝑃

Nonlinear mirror modelocking

Fig. 5.8 Nonlinear mirror (NLM): (a) Operating principle of the NLM device: the incident fundamental wave (FW) at 1030 nm is partially converted to the second harmonic (SH) in the χ(2) crystal, then experiences higher losses than the SH upon reflection on the dichroic output coupler (OC), and is finally replenished by the OPA process during the second propagation through the χ(2) crystal. The phase-mismatch ∆k and the air gap deter-mine the efficiency of the second harmonic generation (SHG) process and the back-conversion, respectively. (b) Evolution of the power in the FW and SH during the first pass through the χ(2) crystal leading to the genera-tion of the SH (solid lines) and during the second pass through the crystal converting the energy back to the FW (dashed lines). TFW: transmission of the dichroic OC for the FW.

Thin-disk laser oscillator The thin-disk laser oscillator used in our experiments is depicted in Fig. 5.9(a) and is based on an Yb-doped thin-disk module from TRUMPF Lasers GmbH. In our experiments, we used a pump laser with a central wavelength of 940 nm and up to 400 W of power with a beam diameter of 4.4 mm on the disk. Under these conditions, the diopter change due to thermal lensing of the disk is <0.1 m-1 which we measured with an interferometer. In order to optimize the laser resonator for high output power, we increase the available roundtrip-gain by increasing the number of passes of the intracavity laser beam through the disk via a re-imaging scheme [45]. With three reflections on the disk, our cavity supports laser operation with an OC transmission >40% (Fig. 5.9 (c)). The multipass arrangement also significantly increases the cavity length, leading to repetition rates around 9 MHz. The cavity layout is shown in Fig. 5.9(a). In addition to the multipass arrangement, it includes a telescope extension at one end of the cavity to adjust the beam size on the NLM device from ≈290 µm to ≈400 µm (Fig. 5.9 (b)).

Chapter 5

We first characterized the performance of the laser in cw operation, i.e. without the χ(2) crystal and the SESAM inside the cavity. As we expect the overall cavity losses to decrease during modelocked operation, we operated the laser at two different values of the OC transmission. We achieved up to 160 W of average output power with a linear 25% OC, and 99 W with a linear 45% OC, at a pump power of 355 W (Fig. 5.9 (c)). This corresponds to an optical-to- optical efficiency of 45% and 28% respectively. We also characterized the 2 beam quality in both cases and measured an M <1.15, confirming that the beam is close to diffraction-limited. For the modelocking experiments we choose to use a large linear OC transmission around 40% to minimize the intracavity power. The power slope with a 25% OC confirms that the cavity behaves well for lower cavity losses and higher intracavity powers. Modelocking experiments Femtosecond thin-disk lasers are usually modelocked in the soliton modelocking regime and therefore rely on the balance of intracavity self-phase modulation (SPM) and dispersion for pulse shaping, and a saturable absorber to initiate and stabilize pulsed operation [77]. The re-imaging scheme implemented to increase the number of laser passes on the disk results in numerous intracavity foci (Fig. 5.9(b)), leading to a large SPM contribution from the intracavity air. We compensate this nonlinear phase with Gires-Tournois-In- terferometer (GTI)-type dispersive mirrors inserted in the multipass arrangement (Fig. 5.9(a)). Accounting for the dispersion of the intracavity thin-film polarizer (TFP) introduced for polarization selection, and the op- tional addition of a -5000 fs2 GTI mirror to the cavity, the total cavity dispersion amounts to either ≈-31,600 fs2 or ≈-41,600 fs2 per roundtrip. In order to facilitate the optimization of the NLM device and achieve reliable initiation of the modelocked operation, we introduce a SESAM at one end of the cavity. Using the approach of Ref. [48], we characterized the SESAM nonlinear reflectivity as a function of the incident pulse fluence and retrieved a saturation fluence of 35 µJ/cm2, a modulation depth of 2.7%, nonsaturable losses of 0.35% and a rollover parameter of 0.5 J/cm2 (for a pulse duration of 170 fs). The 1/e2 intracavity beam radius on the SESAM is ≈950 µm.

Nonlinear mirror modelocking

Fig. 5.9 SESAM-assisted NLM-modelocked thin-disk laser oscillator: (a) Cavity layout. The mirrors indicated with a blue color are Gires-Tournois-Interferometer (GTI)- type mirrors and introduce negative group delay dispersion (GDD). The multipass arrangement is extended on one end towards the SESAM and on the other end towards the NLM device. A thin-film polarizer (TFP) is introduced for polarization control. The multipass arrangement also includes most of the intracavity dispersion. (b) Evo- lution of the 1/e2 cavity mode radius. The re-imaging scheme on the disk leads to numerous foci. (c) Output power slopes in cw operation for two different OCs. The insets show the corresponding beam profiles at the highest power.

For our first modelocking experiments, we used a 0.5-mm-thick BBO crystal and a 45% dichroic OC for the NLM device. The 1/e2 intracavity beam radius on the BBO crystal was ≈290 µm. We operated the NLM at a non-zero SHG phase-mismatch ∆k in order to mitigate Q-switching instabilities (see section 5.2.3). With an intracity dispersion of ≈-31,600 fs2, we achieved up to 66 W of average output power with pulses as short as 426 fs full-width at half maximum (FWHM), at a repetition rate of 9.3 MHz (Fig. 5.10(a) - Fig. 5.10(c)). This corresponds to a pulse energy of 7.1 µJ and a peak power of 14.7 MW. Using a leakage through one of the intracavity mirrors, we estimate the intracavity average power to be ≈180 W, corresponding to an effective transmission of the NLM device of ≈36.7% (Eq. (5.6)). We also measured the

Chapter 5 maximum temperature of the BBO crystal with a thermal camera and found that it exceeds 80 °C, which would ultimately limit power scaling [132]. The heat load on the crystal is likely due to linear absorption at the laser or second- harmonic wavelength. The linear absorption is specified by the manufacturer (EKSMA) as <1000 ppm/cm at 1030 nm. Additionally, the dichroic OC was very susceptible to damage when initiating modelocking. To target higher powers, we therefore improved the thermal and damage properties of the NLM device. We replaced the BBO crystal by a low-absorption LBO crystal (<20 ppm/cm at 1030 nm, Cristal Laser) and designed an optimized dichroic coating for the OC mirror with high-damage threshold (see section 5.2.3). Furthermore, we increased the beam size on the LBO crystal to ≈400 µm, in order to saturate the NLM device at higher peak powers. Using a 1-mm-thick LBO and a 40% dichroic OC, and with ≈-41,600 fs2 of intracavity dispersion, we achieved modelocking up to 87 W with a pulse duration of 586 fs and a repetition rate of 8.9 MHz (Fig. 5.10(d) - Fig. 5.10(f)), corresponding to a pulse energy of 9.8 µJ and a peak power of 14.7 MW. In this configuration, no damage of the dichroic OC occurred and the LBO crystal stayed at a temperature <25 °C, for an intracavity power of ≈240 W. The effective transmission of the NLM device in that case was ≈36.3%. For both results, we verified that no double-pulse was present by scanning the autocorrelation delay over a range of ≈60 ps. Additionally, we measured the pulse train with a fast (45 GHz) photodiode and a sampling oscilloscope. The results presented in this section show the power-scalability of the NLM modelocking technique towards the 100-W level. We improved the average power by a factor ≈3 over previous results while keeping femtosecond pulse durations and demonstrated peak powers close to 15 MW. Optimizing our oscillator also provided us with new insights into the mitigation of Q-switching instabilities and the influence of the NLM device on the pulse formation, which we present in the following section.

Nonlinear mirror modelocking

Fig. 5.10 High-power NLM-modelocked thin-disk laser oscillator: (a) Autocorrelation trace of the 426-fs pulses obtained at 66 W. (b) Optical spectrum of the 426-fs pulses, with a time-bandwidth product (TBP) of 1.34 x 0.315 (a transform-limited sech2-pulse has 0.315). (c) Microwave spectrum analyzer (MSA) trace showing the repetition rate of 9.3 MHz. (d) Autocorrelation trace of the 586-fs pulses obtained at 87 W. (b) Optical spectrum of the 586-fs pulses, with a TBP of 1.21 x 0.315. (c) MSA trace showing the repetition rate of 8.9 MHz. The inset shows a sampling scope measurement with a 45-GHz fast photodiode. No side-pulse is apparent over the roundtrip time of 112.4 ns.

5.2.3 Study of the nonlinear-mirror modelocking regime Here we describe the results of our investigation of the NLM-modelocking regime. In particular, we focus on avoiding Q-switching instabilities, which requires operation of the NLM device with a finite phase-mismatch ∆k. We carefully characterize the operation of the NLM in these conditions and show its influence on the shaping of the intracavity pulse. Q-switching instabilities The NLM provides a saturable nonlinear reflectivity for initiating and stabi- lizing pulsed operation [77]. However, unlike SESAM and KLM modelocking schemes, the NLM effectively saturates the reflectivity of the OC, i.e. the main contribution to the total cavity losses. On one hand, this enables a 97

Chapter 5 straightforward scaling of the available modulation depth by changing the OC transmission. On the other hand, however, this implies that the saturation of the NLM device strongly affects the Q-factor of the laser cavity (e.g. by potentially halving the cavity losses). As a result, NLM-modelocked lasers are susceptible to Q-switched modelocking instabilities with a strongly modulated amplitude of the pulse train. The modulation depth provided by the NLM is maximized when operating the χ(2) crystal at phase-matching ∆k = 0, and adjusting the phase offset between the electric field of the SH and the electric field squared of the FW on the return pass to π (mod 2π) for optimal back-conversion (Fig. 5.11(a), blue curve) [33]. For short pulse durations, the group-velocity mismatch (GVM) between the FW and SH in the χ(2) crystal leads to a reduction of the modulation depth, however this effect is small for the pulse durations considered here (>400 fs). In our experiments, we initially attempted to operate the NLM for optimal efficiency (∆k = 0 and optimal back-conversion), however we systematically damaged the dichroic OC due to Q-switching instabilities (Fig. 5.11(b)); the OC in this case was obtained commercially. In the aftermath of these damage events, we fabricated a custom OC using ion-beam sputtering (IBS), designed to minimize the interaction of the SH with the coating layers. We designed this dichroic mirror to optimize the reflection of the SH within the first layers (see the green line in Fig. 5.11(c)) and adjusted the underlying layers for a flat 40% transmission of the FW and flat and nearly zero-dispersion for the FW and SH (Fig. 5.11(d)). We used SiO2 as low- and Ta2O5 as high-index material. Since Ta2O5 has a bandgap of ~4.2 eV [133], two photon processes of the SH (about 2.4 eV) could ultimately limit further power scaling. Therefore we kept the field intensity of the SH (green line in Fig. 5.11(c)) low in the Ta2O5 layers. This resulted in a significantly improved damage threshold as no damage was observed with this mirror, despite continued Q-switched operation. If nonlinear effects or damage were a limiting factor for further power scaling, we could use HfO2 (bandgap ~5.7 eV [134]) as a high-index material.

Nonlinear mirror modelocking

Fig. 5.11 Optimization of the NLM: (a) Simulated effective nonlinear reflectivity of the NLM device as a function of the incident pulse peak intensity for a 1-mm-long LBO and a 40% dichroic OC. The 1/e2 beam radius on the LBO is 300 µm and the pulse duration is set to 500 fs; the simulation assumes a Gaussian beam profile and a sech2 pulse profile. The nonlinear reflectivity curve is plotted for different values of the phase mismatch ∆k. For each case we adjust the phase offset between FW and SH to obtain an optimal back-conversion. (b) Microscope images of the OC mirror used in our first modelocking experiments at phase-matching ∆k = 0, showing several damaged spots. (c) Custom-made dichroic OC using ion-beam sputtering (IBS). Layers and standing-wave pattern of the coating developed for increasing the damage-threshold of the dichroic OC. (d) Transmission and GDD of the produced dichroic mirror, shown for the FW and SH wavelengths.

In order to mitigate Q-switching instabilities, we introduce a rollover in the nonlinear reflectivity curve of the NLM. The onset of rollover effects gener- ally determine the transition between Q-switched modelocking and cw modelocking [92]. We detune the NLM from its optimal operation regime by rotating the χ(2) crystal and changing the angle of incidence compared to phase-matching, and therefore operating at a finite phase-mismatch 0. This induces a rollover in the nonlinear reflectivity of the NLM that can be understood as follows: for a phase-matched cw interaction, the singleΔ𝑘𝑘-pass ≠ SHG process of the NLM does not exhibit back-conversion to the FW; however, with a finite phase-mismatch, back-conversion occurs after a certain distance through the SHG crystal, and the maximum SHG efficiency is 99

Chapter 5 reduced. Moreover, this distance decreases with input intensity and phase- mismatch [117]. In the context of an NLM device, these effects lead to a reduced maximum reflectivity and a rollover of the reflectivity at high intensities. Hence, the crystal phase mismatch can be used to limit both the available modulation depth and to reduce the intensity at which maximal reflectivity is obtained (Fig. 5.11(a), yellow and green curves).

By operating the NLM with a finite phase mismatch ∆k, we suppressed Q- switching instabilities and achieved stable cw modelocking. Both results presented in section 5.2.2 were achieved in this regime, with a phase-mismatch ∆k <0. We further characterized the operation of the NLM in this regime, in particular its influence on pulse shaping. Operation at non-zero phase-mismatch In order to characterize the operation of the NLM, we carefully measure the output power at 1030 nm directly with a power meter, as well as the out incident power at 1030 nm FW and the SH loss power from the NLM 𝑃𝑃 inc 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 via leakages of intracavity mirrors.FW The experimentally deduced𝑆𝑆𝑆𝑆 effective nonlinear reflectivity and SH losses𝑃𝑃 of the NLM are then 𝑃𝑃calculated using Eq. (5.5) and Eq. (5.6). Furthermore, we estimate the nonlinear phase contribution of the NLM under the assumption of soliton modelocking [77]. The total roundtrip nonlinear phase contributing to the soliton pulse formation can be estimated using soliton theory [135]:

= 1.76 , (5.8) 2 𝜑𝜑sol −� ⁄𝜏𝜏p� 𝐷𝐷rt where τp is the full-width at half-maximum (FWHM) pulse duration and Drt is the total roundtrip dispersion. The two main sources of nonlinear phase- shifts contributing to the roundtrip B-integral Brt are the NLM and the intracavity air. Brt is the accumulated nonlinear phase for the peak of the pulse in space and time, and for free-space propagation the soliton phase ϕsol is related to Brt via [96]: 3 3 = = ( + ) = + , (5.9) 4 4 𝜑𝜑sol 𝐵𝐵rt 𝐵𝐵NLM 𝐵𝐵air 𝜑𝜑NLM 𝜑𝜑air 100

Nonlinear mirror modelocking

where ϕNLM and ϕair are the effective roundtrip nonlinear phase contributions to the soliton pulse formation, accumulated in the NLM and the intracavity air respectively. The effective nonlinear phase contribution from the intracavity air can be calculated using: 3 3 2 = = , (5.10) 4 4 air pk( ) air air 𝜋𝜋 2 2 𝑃𝑃 𝜑𝜑 𝐵𝐵 ∙ 𝑛𝑛 � 𝜋𝜋 2 𝑑𝑑𝑑𝑑 𝜆𝜆 𝑤𝑤 𝑧𝑧 where λ is the central wavelength of the pulse, n2air is the nonlinear refractive index of air, w(z) is the 1/e2 intracavity beam radius, and Ppk is the pulse peak power. We deduce the nonlinear phase contribution from the NLM, under the assumption of soliton modelocking, by calculating: = . We further define the SPM coefficients = and = 𝜑𝜑NLM 𝜑𝜑sol − 𝜑𝜑air / . 𝛾𝛾NLM 𝜑𝜑NLM⁄𝑃𝑃pk 𝛾𝛾air For𝜑𝜑air our𝑃𝑃𝑝𝑝𝑝𝑝 study, we use a 1-mm LBO and a 40% OC for the NLM. In cw operation, we initially align the LBO to obtain phase-matched SHG. The SH power generated in cw is of order 100 nW - 1 µW and can be measured with a calibrated photodiode in order to optimize phase-matching. We then detune the angle of incidence by ≈20.7 mrad, corresponding to a phase-mismatch ∆kL = -0.61 π, similar to the detuning used in our modelocking experiments (L = 1 mm is the length of the LBO). Next, we optimize the air gap in cw operation to obtain optimal back-conversion of the SH to the FW. We then initiate modelocking by gently knocking the OC and tune the air gap in pulsed operation by moving the LBO to study the influence of the phase offset on the laser performance. In Fig. 5.12(a), we show the evolution of the output power and the pulse duration as a function of the air gap. The first point of the scan (air gap ≈83 mm) corresponds to the optimal air gap for back-conversion in cw, with modelocked operation initiated at this point. We then translate the LBO away from the OC to increase the air gap. As observed on Fig. 5.12(a), the output power is ≈70 W and varies by less than 5% over the scan range. However, the pulse duration varies significantly over the same range, from ≈790 fs down to ≈490 fs, hinting towards a large change of the roundtrip nonlinear phase as a function of the air gap. Since the intracavity beam size on the LBO

101

Chapter 5

(predicted from ray transfer matrix calculations) stays virtually constant (310 ± 2 µm) across the scan range, the change in nonlinear phase can be attributed to the change of the NLM parameters, in this case the phase offset. Under the assumption of soliton shaping, we calculated the SPM coefficients air, NLM for the intracavity air and for the NLM device and show the results in Fig. 5.12(c). The intracavity peak power was evaluated using = 𝛾𝛾 𝛾𝛾 0.88 , where frep is the pulse repetition rate and τp,FTL is the , 𝑃𝑃pk transforminc -limited pulse duration deduced from the measured spectrum of the �𝑃𝑃FW�𝑓𝑓rep��𝜏𝜏p FTL output beam. As expected, the SPM coefficient for air is almost constant at ≈8 mrad/MW, as most of the SPM from air originates from the multipass part of the cavity, which essentially stays unaffected by the changing NLM air gap. The inferred SPM coefficient of the NLM device, however, varies significantly from ≈3.2 mrad/MW to ≈8.9 mrad/MW, becoming comparable to the SPM coefficient of the intracavity air for large air gaps. We conclude that the nonlinear phase introduced by the NLM is strongly dependent on the phase offset between the FW and SH on the return pass, and that this dependence leads to the tuning of the pulse duration we observe in Fig. 5.12(a). We have recently demonstrated compensation of positive SPM contributions with an intracavity phase-mismatched second-harmonic-generation crystal in a high-power thin-disk laser [32], which could be implemented to compensate or add to the nonlinear phase from the NLM device when targeting short pulses at higher powers and keep the laser operated in air. We also calculated the experimental effective reflectivity and SH losses of the NLM device as a function of the air gap and plotted the results in Fig. 5.12(b). Interestingly, we initiated modelocking in a regime for which the effective reflectivity of the NLM is lower than the linear reflectivity of the OC, clearly indicating that the NLM device is not operating optimally. This indicates that the experimental conditions for optimal back-conversion in cw operation are different than those for pulsed operation, which could be due to a combination of intensity and temperature dependent phase-shifts in the LBO crystal. This difference also justifies the presence of the SESAM in the cavity for initiating modelocking. We can differentiate two regimes of operation:

- Modelocking initiation: At the optimal air gap found in cw operation, we initiate modelocked operation. The SESAM losses are saturated,

102

Nonlinear mirror modelocking

providing a modulation depth of ≈2%, but the NLM losses increase (Reff < Rlin) by ≈1%, resulting in a net ≈1% saturable loss in the cavity. - Modelocking optimization: As we increase the air gap, the SESAM losses stay saturated, but the effective reflectivity of the NLM increases and eventually provides a net positive loss modulation (i.e. when Reff > Rlin = 60%) of ≈2%, resulting in a net 4% saturable loss in the cavity.

Fig. 5.12 Experimental characterization of the NLM-modelocking regime at a phase- mismatch ∆kL = -0.61π. The NLM device combines a 1-mm LBO with a 40% dichroic OC. We tune the air gap in pulsed operation by moving the χ(2) crystal relative to the OC. We show the evolution of: (a) the output power and pulse duration, (b) the experimentally deduced effective reflectivity and SH losses, the dashed line represents the linear reflectivity of 60%, (c) the deduced SPM coefficients for the intracavity air and the NLM device as a function of the air gap.

The fast loss modulation provided by the NLM supports the shorter pulses generated at larger air gaps. This improvement of the NLM operating regime when increasing the air gap is also reflected in the decreasing SH losses. It is worth noting that pulse durations <700 fs are usually not supported by SESAM-modelocked thin-disk lasers based on Yb:YAG [23, 96], which

103

Chapter 5 further confirms the additional pulse reduction due to the fast saturable-absorber effect of the NLM device. To summarize: we characterized the operation of the NLM device at a fixed phase-mismatch and variable air gap between the LBO crystal and the OC. By adjusting the air gap, we change the efficiency of the back-conversion process and hence the strength of the NLM. This tuning also yielded shorter pulses at the output of the oscillator. Based on the assumption of soliton pulse shaping, i.e. that the reduced pulse duration corresponds to a change in intracavity nonlinearity, we deduce a strong dependence of the nonlinear phase contribution of the NLM on the phase offset set by the air gap. Power scaling prospects The underlying mechanism of the NLM is readily scalable by the beam size on the device. However, at some power level the thermal load on the crystal due to absorption at the FW or SH will become significant and lead to thermo-optic distortions. While thermal lensing effects are well-known in the context of power scaling, for an NLM there is the additional, related effect of thermal dephasing of the nonlinear interaction. Therefore, in this section we consider the sensitivity of the NLM process to changes in the phase mismatch, as would occur in the presence of excessive absorption in the crystal. We evaluate the case of an NLM consisting of a 1-mm-thick LBO crystal and a 40% dichroic OC, operating at a phase-mismatch . = 0.36 , for which the optimal peak intensity lies around 100 GW/cm2 (Fig. 5.11(a), yellow). For Δ𝑘𝑘 𝐿𝐿 − 𝜋𝜋 a phase-mismatch . = 0.52 , the optimal peak intensity is reduced by a factor of two (Fig. 5.11(a), green). Using the temperature sensitivity of the phase mismatch ofΔ 𝑘𝑘 𝐿𝐿 − = 0𝜋𝜋.09 , calculated from the Sellmeier relations [136], we can evaluate the temperature−1 difference leading to such a dephasing for a 1-mm𝑑𝑑Δ LBO𝑘𝑘⁄𝑑𝑑𝑑𝑑 crystal and𝑚𝑚𝑚𝑚 find⁄ 𝐾𝐾a value of ≈5.6°C. Power scaling could most readily be achieved by finding a suitable crystal and beam geometry to keep the on-axis temperature increase (arising due to absorption at the FW and SH) below these levels. Given the multi-100-W SHG results achieved in recent years [32, 62, 99], we are optimistic about further power scaling of the NLM approach.

104

Nonlinear mirror modelocking

Additionally, shorter pulse durations could be generated by using GVM compensation techniques [113]. This could allow for the generation of sub-200 fs pulses from a multi-100 W NLM-modelocked TDL.

5.2.4 Conclusion and outlook We presented a first power-scaled NLM-modelocked thin-disk laser oscillator delivering close to 15 MW of peak power in 426-fs or 586-fs pulses, representing a promising alternative to KLM for generating peak powers >10 MW at sub-500-fs pulse durations. We designed our laser resonator using a re- imaging scheme on the disk allowing us to couple out >40% of the intracavity power and operate at reduced repetition rates <10 MHz. We further used a SESAM to facilitate the optimization of the NLM device and enable reliable modelocked operation. During our first modelocking attempts, we identified Q-switching instabilities as the main obstacle for stable cw modelocking because the NLM can saturate a large fraction of the cavity losses. We designed a new dichroic OC coating with a minimized interaction of the second harmonic wave and the coating layers, which led to significant improvements in terms of damage threshold. Furthermore, we mitigated Q-switching instabilities by operating the NLM device at a finite phase-mismatch, thus introducing a rollover in the nonlinear reflectivity of the device. Using a BBO crystal, we demonstrated modelocking up to 66 W with 426-fs pulses at a repetition rate of 9.3 MHz. The crystal however suffered from a high absorption leading to a significant temperature increase during laser operation. For our next modelocking experiments, we replaced the BBO with a low-absorption LBO crystal and achieved up to 87 W of average power with a pulse duration of 586 fs and a repetition rate of 8.9 MHz. This is to the best of our knowledge the highest power demonstrated with the NLM-technique (≈3 times more than the previous record [112]). The corresponding pulse energy is 9.8 µJ and the peak power is 14.7 MW. We characterized the operation of the NLM device at a fixed phase-mismatch and in particular the influence of the phase offset on the laser performance. We tuned this parameter by adjusting the air gap between the χ(2) crystal and the OC, which effectively adjusts the efficiency of the back-conversion

105

Chapter 5 process. This is confirmed by our experiments, showing an increase of the NLM reflectivity and a simultaneous decrease of the SH losses when tuning the air gap. However, this tuning also significantly impacts the pulse formation process, likely due to a phase-offset-dependent nonlinear phase-shift provided by the NLM device. In our experiments, we could tune the pulse duration by a factor of almost two, from 790 fs down to 490 fs at almost constant output power. Based on this change and the other sources of nonlinear phase inside the cavity, we infer a change in the SPM coefficient introduced by the NLM device by one order of magnitude. Our experiments validate the compatibility of the NLM for high-power modelocking. We expect that modelocking at multi-100s-W is achievable with the combination of low-absorption nonlinear crystals and optimized dichroic OC coating used in this work. Additionally, we identified a strong dependence of the NLM nonlinear phase on the tuning of the air gap, which can be ex- ploited to tune the output pulse duration or calls for a strong intracavity source of SPM to decouple pulse shaping from NLM optimization. Finally, new NLM designs with a reduced loss modulation could allow for high-power NLM-modelocking at phase-matching without Q-switching instabilities. Funding Swiss National Science Foundation (SNSF 200020_172644). Acknowledgments The authors acknowledge the support of the technology and cleanroom facility FIRST of ETH Zurich for advanced micro- and nanotechnology, Dr. Matthias Golling for the SESAM fabrication and Dr. Olga Razskazovskaya (Université de Neuchâtel, Switzerland) for her contribution in the fabrication and characterization of optical coatings. The University of Neuchatel group acknowledges the financial support from the Swiss National Science Founda- tion (R’EQUIP 144970 and 170772) for an ion-beam sputtering (IBS) machine used to produce the optimized dichroic OC.

106

Nonlinear mirror modelocking

Disclosures The ETH Zurich authors signed an NDA with TRUMPF with regards to the thin-disk module and head.

107

Power scaling results

6 Power scaling results

In this chapter, we present the highest-power thin-disk laser oscillators developed during this thesis. We improved the long-standing 275-W average output power record for a modelocked laser demonstrating first a 350-W modelocked thin-disk laser and later improving it to 430 W. In particular, the 430-W average output power laser delivered 68-µJ, 769-fs pulses at 6.29 MHz repetition rate resulting in 78-MW of peak power. To the best of our knowledge, this oscillator sets a new benchmark for both the average power and the peak power achieved from any modelocked ultrafast laser. These results leverage many of the solutions and learnings discussed in the previous chapters of this thesis. The key points have been the use of cavities with large output coupling rates, allowed by an imaging scheme for multiple reflections on the disk, operating the laser in a low-pressure environment, and a careful engineering of the cavity to minimize the angle of incidences on the optics and hence astigmatic effects. The subsequent improvement to 430-W average power hinges on a SESAM optimized for heat management, further refinements to the cavity design, and a system to monitor the disk fluorescence to simplify the alignment of the laser cavity and operate as a safety interlock in case of failures. We discuss in detail the 350-W average output power laser oscillator in the journal article presented in section 6.1 and we present the improvements which led to the 430-W average power oscillator in section 6.2.

109

Chapter 6

Title: “Power scaling of ultrafast oscillators: 350-W average-power sub-picosecond thin-disk laser”, [21] Journal: Optics Express doi: 10.1364/OE.27.031465

110

Power scaling results

6.1 Power scaling of ultrafast oscillators: 350-W average-power sub-picosecond thin-disk laser

F. Saltarelli,1 I.J. Graumann,1 L. Lang,1 D. Bauer,2 C.R. Phillips,1 and U. Keller1 1Institute for Quantum Electronics, ETH Zurich, 8093 Zurich, Switzerland 2TRUMPF Laser GmbH, Aichhalder Straße 39, 78713 Schramberg, Germany

Abstract: We report a semiconductor saturable absorber mirror (SESAM)- modelocked thin-disk laser oscillator delivering a record 350-W average output power with 940-fs, 39-μJ pulses at 8.88-MHz repetition rate and 37-MW peak power. This oscillator is based on the Yb:YAG gain material and has a large pump spot on the disk. The cavity design includes an imaging scheme, which results in multiple reflections on the disk gain medium to enable a larger output coupling rate compared to those used in thin-disk oscillators with a single reflection on the disk. This reduces the intracavity power for a given output power, thus decreasing the stress on the intracavity components. We operate the laser in a low-pressure environment in order to limit the disk’s thermal lensing and drastically reduce the nonlinearity picked up in the intracavity air medium. The combination of the imaging scheme and low- pressure operation paves the way to further power scaling of ultrafast thin- disk oscillators toward the kW milestone. © 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

6.1.1 Introduction Many industrial and scientific applications greatly benefit from ultrafast laser sources with megahertz repetition rate and multi-100-W average output power [4, 6]. The current state of the art in terms of average power is achieved with diode-pumped laser amplifier systems based on fiber [7], slab [9], and thin-disk [62, 137] technologies, each of which leverages a high surface-to- volume ratio for efficient heat removal. These systems can achieve more than 1 kW of average output power. By coherently combining multiple fiber amplifiers, up to 3.5 kW of average power have been demonstrated [7].

111

Chapter 6

In this paper, we focus on the thin-disk laser (TDL) technology [24]. In TDLs, the gain medium is shaped as a disk, with a typical thickness of around 100 µm and is used in reflection inside the laser cavity. The pump and laser beams have a diameter of a few millimeters on the disk. The heat is extracted through the backside of the disk. This results in a quasi-1D heat flow which ensures optimal heat management and thus enables straightforward power scaling by increasing simultaneously the pump spot and the laser spot size on the disk. Amplifier systems based on the TDL technology achieved up to 2-kW average output power with 6.7-mJ pulses in a multi-pass configuration [62, 137] and 1-kW average output power with 200-mJ 1.1-ps pulses in a regenerative amplifier configuration [20]. The reduced thickness and high-gain per unit length of the thin-disk gain medium make this technology ideal for the development of high-power ultrafast oscillators. In fact, the short interaction length between the pulses and the gain medium results in a sufficiently small amount of nonlinearity that modelocked pulse formation is not hindered. Hence, thin disks allow for the generation of high-power laser pulses directly from a high-power modelocked oscillator, bypassing the complexity of multi-stage ultrafast amplifier systems. Additionally, the timing jitter and limited repetition rate of regenerative amplifiers is avoided, as well as amplified spontaneous emission added by amplifier chains [138]. Moreover, TDLs offer by far the highest average power and pulse energy of any ultrafast oscillator technology [23]. They deliver a low-noise output [28], megahertz repetition rates, and diffraction- limited beam quality from a single-box, diode-pumped laser source. These features enabled applications such as high-harmonic generation to the extreme ultraviolet [28] and optical rectification to the THz [139] directly from a laser oscillator. Additionally, the high intracavity power in TDL oscillators can be leveraged to drive intracavity nonlinear-optics experiments [27]. Fi- nally, the recent demonstrations of multi-pass cell compression at 375-W average output power to 170 fs [22] and at 60 W to 16 fs pulses [140], show the possibility to compress the high-power output of these oscillators in order to get the optimal peak power for many nonlinear optics applications. Over the last twenty years, the performance of modelocked TDLs has been continuously improved. We present in Fig. 6.1 an overview of how the

112

Power scaling results average power was scaled over time focusing on Yb:YAG thin disks, which is the current leading gain material for high power. The first ultrafast TDL oscillator was demonstrated in the year 2000 using an Yb:YAG disk, and a semiconductor saturable absorber mirror (SESAM) for modelocking. It delivered 16-W average output power [63]. This result was later scaled to 80-W average output power due to improvements in the disk’s quality and mitigation of the thermal effects [53]. These first ultrafast TDL oscillators were operated in air and based on short cavities encompassing a single reflection on the disk gain medium. Because of the limited gain from the disk, low output coupling rates of around 10% were used, resulting in very high intracavity average and peak powers. In fact, once few-μJ pulse energies and sub-ps pulse durations were achieved, the peak power became sufficient to induce strong self-phase modulation (SPM) from the nonlinear refractive index of the intracavity air [89]. This SPM (of order 1 rad or more) would need to be balanced with group delay dispersion (GDD) (of order 104 – 105 fs2) for soliton pulse formation. The large negative GDD could be obtained through dispersive mirrors, which however have worse thermal behavior compared to standard dielectric mirrors and cause thermo-optic distortions at high intracavity powers [23]. In order to tackle the simultaneous challenges of having enough negative GDD and limiting the intracavity power, different ap- proaches have been suggested in literature. One approach consists in designing a cavity encompassing multiple reflections on the disk gain medium in order to increase the round-trip gain, allowing the laser to be operated with a large output coupling rate. This approach led to the demonstration of a TDL oscillator with 11 reflections on the disk, delivering 145-W average output power with 41-μJ pulses [46]. Another approach consists in operating the laser in a low-pressure environment (few mbar of air) or in a helium atmosphere in order to decrease the amount of SPM accumulated in the intracavity atmosphere and thereby reduce the required GDD by an order of magnitude or more [89]. This is the approach which led to the previous record: a 275-W average power SESAM-modelocked TDL oscillator with 17-μJ pulses demonstrated in 2012 [12]. Additionally, this approach led to the demonstration of the thin-disk oscillator delivering the highest pulse energy to date, that is 80 μJ at 242-W average output power [15].

113

Chapter 6

Kerr-lens modelocking (KLM) has also been employed in order to modelock TDL oscillators. In its first demonstration in 2011, 45-W average output power was achieved [127], and shortly thereafter, a KLM TDL matched the performance of SESAM-modelocked TDLs with 270-W average output power at 14-μJ pulse energy [47]. Both results have been achieved in an air environment and delivered shorter pulses at higher repetition rate compared to the presented high-power SESAM-modelocked Yb:YAG thin-disk oscillators [12, 15, 46]. Recently, a KLM Yb:YAG thin-disk oscillator designed with an active multi-pass configuration and delivering 140-W average power at 13-μJ pulse energy has been demonstrated [56]. Power scaling of thin-disk lasers requires increasing the spot size on the disk in order to avoid damaging the gain material. For example, without laser operation we have observed damage when operating at 5.4-kW/cm2 pump intensity and 8-mm-diameter pump spot on an Yb:YAG thin disk. In the discussed ultrafast TDL oscillators [12, 15, 46, 47, 53, 56, 63, 89, 127], the pump spot was at most 4.7-mm in diameter, which limits the pump power to ≈1 kW when keeping within a safe intensity regime. However, scaling the beam size on the disk and on other optical components comes at the cost of an increased sensitivity to the thermal lensing of those components [37]. This increased sensitivity renders it hard to operate thin-disk oscillators in fundamental-spatial mode with large pump spots and, combined with the pre-existing challenges, hindered further power scaling of these results until now. Here we present a TDL oscillator (Fig. 6.2) with a large 6-mm-diameter pump spot on the disk. In order to overcome the mentioned challenges associated with the large pump spot and keep the intracavity power low to reduce the stress on the intracavity components, we combined an imaging scheme for multiple reflections on the disk with low-pressure operation. Additionally, we carefully arranged the mirrors in the cavity in order to keep the angle of incidence on the curved mirrors small and hence avoid astigmatism. We obtained 350-W average output power with 940-fs, 39-μJ pulses at 8.88-MHz repetition rate and 37-MW peak power. To the best of our knowledge, this is the highest average power obtained at the output of any modelocked laser oscillator. Ad- ditionally, we demonstrate modelocked operation with a pump spot size

114

Power scaling results compatible with pumping at 1.5 kW and hence more than 500-W average output power. We detail the cavity design in Section 6.1.2 and analyze the performance of the laser in continuous-wave (cw) and modelocked operation in Section 6.1.3. We conclude in Section 6.1.4 by presenting an outlook on the scaling prospects of ultrafast thin-disk oscillators.

Fig. 6.1 Average output power from Yb:YAG SESAM-modelocked and KLM oscillators, which represented a new record at the time of publication. The labels indicate the output pulse energy. References are provided in the text. In this result we combine a cavity design including multiple reflections on the disk gain medium with operation in a low-pressure environment.

6.1.2 Cavity design Power scaling thin-disk oscillators involves simultaneously increasing the pump and laser spot size on the disk. This approach has been extremely successful, in fact cw thin-disk oscillators delivering up to 10 kW in multi-mode operation have been demonstrated [35]. Modelocked operation imposes additional requirements: the cavity needs to be operated in fundamental transverse mode, must incorporate a saturable- loss device, and nonlinearity needs to be managed [23, 32]. The larger laser spot on the disk leads, to a larger spot throughout the cavity and hence on the intracavity components. This makes the cavity more susceptible to static and thermo-optical wavefront distortions on many intracavity components such as the disk, the dispersive mirrors, and the SESAM, especially for cavities including multiple reflections on the disk. The width of the stability zone [Fig. 115

Chapter 6

6.3(b)] with respect to disk’s thermal lensing scales inversely with the square of the laser-spot size on the disk, for a fixed number of intracavity passes over the gain medium [37]. Thus, achieving fundamental mode operation over an extended power range becomes more challenging for increased laser-spot sizes. To modelock high-power oscillators, the SESAM is particularly well suited since pulse formation is decoupled from cavity stability, hence disentangling fundamental spatial-mode operation and modelocking. Additionally, the thin structure of the SESAM compared to the beam size ensures an efficient heat extraction analogous to the gain disk and its parameters can be adjusted via semiconductor engineering. To obtain sub-ps pulses in SESAM-modelocked lasers despite the presence of a slow saturable loss, we rely on soliton pulse shaping effects [77]. This process is based on a balance between intracavity GDD typically obtained through Gires-Tournois interferometer (GTI)-type dispersive mirrors, and SPM. The dispersive mirrors, because of their resonant structure, have worse thermal behavior compared to high-reflective dielectric mirrors based on distributed Bragg reflection (DBR) structures [23]. The SESAM also has some thermal lensing determined by its small non-saturable losses, which are typically of order 0.1% in state-of-the-art SESAMs [50]. Operating these components at kW-level intracavity average power results in thermo-optic distortions, which ultimately hinder pulse formation, limiting the achievable output power. In order to mitigate these thermal effects, a compelling approach is to reduce the intracavity power by designing an imaging scheme in the laser cavity encompassing multiple reflections on the disk gain medium and, hence, allowing a larger output coupling rate [32, 46, 56]. However, such an imaging scheme further increases the sensitivity to the disk’s thermal lensing. In fact, the width of the stability zone scales as the reciprocal of the number of passes on the disk. Hence this approach was avoided for the previous power-scaling result [12]. We recently developed a better understanding of the sources of thermal lensing in thin-disk lasers, and, particularly, discovered that a substantial contribution to the disk’s thermal lensing originates in the heated air in front of the disk [31]. We removed this contribution by operating the laser in a low- pressure environment and optimized the laser cavity accounting for the

116

Power scaling results change in thermal lens between air operation (during alignment) and low- pressure operation (during modelocking). In this way, we also drastically reduced the amount of SPM picked up in the intracavity air, hence reducing the amount of GDD needed for soliton pulse formation by an order of magnitude. In our oscillator, we employed a 100-μm thick, 10-at.% doped Yb:YAG disk, contacted on a concave diamond with a cold radius of curvature Rcold = 3.80 m (TRUMPF GmbH). We pumped the disk with a 6.0-mm-diameter pump spot through a 44-pass thin-disk head using free-space-coupled diodes able to deliver up to 3 kW at 938 nm. We limited the pump power to 1.4 kW corresponding to 5.0 kW/cm2 of pump intensity in order to avoid damaging the disk. At this power the diodes emit at 930 nm. We designed an imaging scheme with two 2-m concave dispersive mirrors encompassing three reflections on the disk to support a comparatively large TOC = 25% transmission output coupler [Fig. 6.2(a) and Fig. 6.3(a)]. A larger output coupling rate (for example of 40% as in [32]) would have been possible, however we found that larger output coupling rates resulted in a reduced optical-to-optical efficiency and hence additional thermal load on the disk. Each bounce on the 2-m dispersive mirrors inside the active multi-pass cell results in -550 fs2 of GDD. Hence, we obtain -6’600 fs2 of round-trip GDD directly from the active multi- pass cell, i.e., 2-m concave mirrors, disk, and 45° high-reflective flat mirrors. On the SESAM arm of the cavity we implemented a telescope using a 300-mm concave mirror and a 3-m concave mirror in order to have the optimal spot size with respect to the saturation property of our SESAM. This results in a designed 1/e2 laser spot radius on the SESAM wSESAM ≈1.35 mm. Fundamental spatial-mode operation in thin-disk oscillators is achieved by optimizing the laser spot to pump spot ratio. Empirically, the optimal ratio is known to be ≈75%. This ensures that higher order modes, due to their larger transverse size, are disfavored and thus fundamental spatial mode operation is achieved. Thermal lensing on the disk results in a change of the disk’s radius of curvature R, quantified by the change in focusing power: ∆Fdisk = 2/Rcold

– 2/R(T), where T is the temperature of the disk. We measured the ∆Fdisk with an interferometer and the disk’s temperature T with a thermal camera (FLIR) without laser operation. Hence, by measuring T during laser operation and

117

Chapter 6 taking into account the difference in focusing power between air and low- pressure operation, we can infer ∆Fdisk, as described in [31]. We have ∆Fdisk

≈-0.007 m-1 for laser operation just above threshold and ∆Fdisk ≈-0.020 m-1 at 350-W output power in modelocked operation. We thus optimized the cavity design in order to have the center of the stability zone at -0.014 m-1, in order to minimize the change in laser beam radius on the disk over an extended power range (Fig. 6.3).

Fig. 6.2 (a) Schematic of the cavity design, including three reflections on the disk gain medium. TFP: thin-film polarizer; (b) beam profile at 350-W output power in cw operation, i.e., with the SESAM replaced by a HR mirror; (c) beam profile at 350 W in modelocked operation. The beam profiles are acquired by imaging the leakage of a mirror in a position ≈0.85 m from the SESAM. The horizontal and vertical cuts of the beam through the center of mass are presented together with gaussian fits (in red).

In addition to the challenges due to thermal lensing, the finite angle of incidence on the curved mirrors leads to a difference in the effective curvature of these mirrors in the vertical and horizontal direction. This results in cavity astigmatism and a shift in the stability zone. This effect is particularly relevant on the 2-m concave mirrors employed in the active multi-pass cell because of the large spot size on these mirrors [they are located before and after the disk, see Fig. 6.3(a)]. In order to avoid any significant astigmatism problems we employed two Newport Suprema Clear Edge 2” mirror mounts to place the 2-m concave mirrors almost in touch with each other and hence limit the angle of incidence on the disk to < 2.5° and on these mirrors to < 1.5°. The angles of incidence on the other curved mirrors in the cavity was < 2° by folding the cavity. By following these measures of precaution, the astigmatic

118

Power scaling results effects are negligible and proper operation of the laser over the full range of output powers has become possible.

Fig. 6.3 (a) Evolution of the 1/e2 mode radius as a function of the position inside the laser cavity. ∆Fdisk = 0 corresponds to the cold disk. The green line assumes the disk’s focusing power at lasing threshold and the orange line at the middle of the stability zone; (b) stability zone: calculated beam radius at the position of the disk (black line) and the SESAM (light blue line) as a function of the disk’s focusing power change ∆Fdisk. The vertical green and orange dashed lines represent the disk’s focusing power values used for Fig. 6.3(a); the red dashed line the focusing power at the maximum output power. We optimized the cavity such that going from low to high power, we move around the center of the stability zone.

6.1.3 Laser performance in continuous wave and modelocked operation For stable SESAM modelocking the cavity should operate in fundamental spatial mode. Hence, we first characterized the oscillator without the SESAM and with only the –6’600 fs2 of round-trip GDD coming from the dispersive mirrors in the active multi-pass cell. In this configuration we obtained up to 570 W output power at 1.4 kW of pump power, corresponding to 41% optical-to-optical efficiency [red squares in Fig. 6.4(a)]. The beam quality stays diffraction limited over the whole range of power with an M2 < 1.05. The next step was to introduce the dispersion required for soliton pulse formation, we replaced four flat DBR mirrors with GTI-type dispersive mirrors, two of them introducing -500 fs2 of GDD per bounce (Layertec GmbH) and two of them introducing -2’000 fs2 of GDD per bounce (University of Neu- chatel). In this way we have a total of -16’600 fs2 of round-trip GDD from the mirrors. Additionally, we introduced a thin-film polarizer (TFP) in the

119

Chapter 6 laser cavity in order to fix the polarization of the laser. We again tested this cavity in cw operation obtaining fundamental mode operation (M2 < 1.10) at up to 350 W output power with 1.1 kW of pump power, corresponding to 31% optical-to-optical efficiency [blue squares in Fig. 6.4(a) and beam profile in Fig. 6.2(b)]. There is a ≈10% loss in optical-to-optical efficiency compared to the same laser cavity without the additional dispersive mirrors and the TFP. This is most likely due to the additional losses introduced by the TFP and the thermal effects in the dispersive mirrors which alter the cavity mode and introduce non-spherical aberrations. Additionally, the lower optical-to-optical efficiency translates into a larger thermal load on the disk due to the reduced heat extraction through lasing and hence additional thermal lensing. Lastly, we replaced the end mirror with a SESAM designed for high-power operation [49]. The SESAM was grown and contacted to a copper mount in the ETH Zurich FIRST cleanroom facility. It consists of a DBR and three InGaAs quantum wells as absorber in an anti-resonant configuration. It has a saturation fluence of 120 μJ/cm2, a modulation depth of 1.1%, non-saturable losses of ≈0.1%, and a two-photon absorption (TPA) coefficient F2 = 650 mJ/cm2 for 130-fs pulses [48].

We operated the laser in a 30-mbar N2 atmosphere resulting in a SPM coefficient of ≈0.3 mrad/MW per cavity roundtrip, defined as the ratio between the B-integral and the intracavity peak power. Additionally, we estimate a contribution of ≈0.3 mrad/MW of SPM from the coatings of the dispersive mirrors based on the measured pulse duration and assuming soliton pulse formation [32, 96]. The SPM accumulated in the thin-disk and in the SESAM is negligible. The laser shows stable modelocking from 220-W output power with 1.14-ps pulses up to 350-W output power with 940-fs pulses at 1.2 kW of pump power [green symbols in Fig. 6.4(a) and beam profile in Fig. 6.2(c)] (power meter: Coherent PM LM-5000). This corresponds to an optical-to- optical efficiency of 29%. We note that this is only 2% lower compared to the efficiency in cw operation in the same laser configuration, confirming the very low non-saturable losses of the employed SESAM. We monitored the beam profile of the laser imaging the leakage of a mirror in a position ≈0.85 m from the SESAM. The expected 1/e2 beam radius from ABCD matrix calculation, at that position in the cavity, is ≈1.4 mm [Fig. 120

Power scaling results

6.3(a)]. For comparison, we took cuts along the horizontal and vertical axes of the measured beam profiles in cw and modelocked operation. The cuts are shown in Fig. 6.2(b) and Fig. 6.2(c) together with Gaussian fits, showing close agreement. Regarding the 1/e2 mode radius, we find in cw a slightly astigmatic beam with an average beam radius of 1.35 mm and in modelocked operation a symmetric beam with an average mode radius of 1.6 mm. These values are within 15% of the expected beam size. The slightly larger beam radius in modelocked operation may be due to the different thermal load on the disk because of the slightly lower optical-to-optical efficiency and the thermal lensing of the SESAM. The modelocking dynamics of femtosecond solid- state lasers with a slow saturable absorber is often approximated by soliton pulse shaping [77]. A signature of this modelocking regime is that the pulse duration decreases with increasing pulse energy, which we also find in our oscillator [Fig. 6.4(a)]. In the soliton-modelocking regime the saturable absorber starts and stabilizes the modelocking process while the pulses are shaped by the balance between GDD and SPM. This results in sech2-shaped pulses. Hence, we fitted the laser diagnostics assuming this pulse shape and extracted the spectrum full-width-half-maximum (FWHM) and the pulse duration from the fits. At 220-W average output power, we have 1.14-ps pulses and a spectrum FWHM of 1.27 nm (time-bandwidth product, TBP = 1.30 x 0.315), at the maximum output power of 350 W (Fig. 6.5) we have 940-fs pulses and a spectrum FWHM of 1.63 nm (TBP = 1.36 x 0.315). We notice that the pulses are longer than the transform-limited duration, suggesting that they could be chirped. Further investigation will be necessary in order to understand the causes. The diagnostics in Fig. 6.5 at the maximum output power (350 W) shows stable modelocking. We acquired large span microwave spectrum analyzer (Hewlett Packard 8562E) traces and, additionally, scanned a long-range (200 ps) autocorrelator (Femtochrome FR-103XL) to confirm single-pulse operation. In this experiment, we decided to not increase the power further to prevent the disk from overheating in case laser operation was interrupted due to misalignment or SESAM damage. A planned safety interlock to switch off the pump in case of non-lasing conditions will allow safe operation at even higher powers in the future. Furthermore, we calculated the nonlinear reflectivity curve of the employed SESAM, taking into account soliton pulse shaping [105] [Fig. 6.4(b)]. The

121

Chapter 6

TPA coefficient F2, characterizing the strength of the inverse saturable absorption, scales linearly with the pulse duration. We therefore take our experimental modelocking point at 39 µJ, 940 fs as a reference and calculate the expected pulse duration τp at any given pulse energy Ep according to soliton pulse shaping τp ~ 1/Ep. The spatially-averaged incident fluence on the

SESAM is calculated according to SESAM = /( SESAM) 8[]4 . At the 2 maximum output power in modelocked operation we have FSESAM = 𝐹𝐹 𝐸𝐸𝑝𝑝 𝜋𝜋 𝑇𝑇𝑂𝑂𝑂𝑂 𝑤𝑤 2.7 mJ/cm2 [Fig. 6.4(b), vertical dashed line]. This lies close to the maximum of the SESAM reflectivity curve. Operation slightly further into the rollover is possible but at the expenses of additional losses and hence thermal load on the SESAM [105].

Fig. 6.4 Power slopes: (a) average output power and pulse duration versus pump power. Red squares refer to cw laser operation with -6’600 fs2 of round-trip GDD. Blue and green squares refer to a laser configuration with -16’600 fs2 of GDD and including a TFP, in cw and modelocked operation, respectively; (c) saturation properties of the SESAM: reflectivity for a Gaussian beam versus spatially-averaged fluence on the SESAM (black line). For this calculation we assume that the pulse duration scales inversely to the pulse energy (orange line), as in soliton pulse shaping. The operating point at 350-W average output power, 940-fs pulse duration is marked with a vertical dashed line.

122

Power scaling results

Fig. 6.5 Laser diagnostics at 350-W output power. (a) Optical spectrum; (b) intensity autocorrelator; microwave spectrum (c) centered on the peak at the repetition rate with 300 Hz resolution bandwidth and noise floor around -42 dBc and (d) showing the harmonics with 10 kHz resolution bandwidth and noise floor around -50 dBc. Red dashed lines in (a) and (b) are fits assuming sech2-shaped pulses, the resulting FWHM of the optical spectrum and the pulse duration from the fits are reported in the corresponding figures.

6.1.4 Conclusion and outlook In conclusion, we demonstrated an ultrafast laser oscillator based on the thin- disk technology delivering 350-W average output power with 940-fs pulses at 8.88-MHz repetition rate. This represents, to the best of our knowledge, the highest average power achieved from any modelocked ultrafast oscillator. We obtained this record result by using a thin-disk head with a large pump spot on the disk and tackling the resulting cavity stability challenges through an imaging scheme encompassing multiple reflections on the disk gain medium and low-pressure operation. A roadmap for further power scaling of this laser architecture beyond 500-W output power consists in designing an active multi-pass cell encompassing five rather than three reflections on the disk and hence increasing the output coupling rate to 40% from the current 25%. Thin-disk oscillators based on the Yb:YAG gain material and operating with even larger output-coupling rates

123

Chapter 6 have already been demonstrated [32, 46, 56]. For this purpose, 2”-diameter mirrors inside the multi-pass cell can be used to accommodate the multiple reflections. The same intracavity power we use here would then yield 550 W output power, while keeping the spot size on the SESAM similar to the current configuration and thus avoiding additional thermal effects or aberrations from this component. A further step in power scaling toward the kW level could be done by actively compensating the thermal lensing of the intracavity components via a deformable mirror, which has already been demonstrated in cw at kW-level output power [66] and the development of large-area SES- AMs with improved thermal characteristics [50]. This result shows the possibility to develop sources combining multi-100-W average output power with the simplicity and high repetition rates of oscillators. Additionally, its output pulse energy of 39 μJ makes it a compelling source for high-field physics experiments such as high-repetition-rate high- harmonic generation and for industrial applications such as laser micromachining. Funding Swiss National Science Foundation (SNSF 200020_172644). Acknowledgments The authors acknowledge support of the technology and cleanroom facility FIRST of ETH Zurich for advanced micro- and nanotechnology. Addition- ally, we thank Dr. Valentin Wittwer, Dr. Olga Razskazovskaya, and Prof. Dr. Thomas Südmeyer (University of Neuchatel) for providing some of the dispersive mirrors. Disclosures The authors declare no conflicts of interest.

124

Power scaling results

6.2 Further power scaling to 430-W average power In this section, we present a further development of the oscillator discussed in Section 6.1. The key improvements were in the three following areas:

- we designed a cavity with five reflections on the disk instead of three to increase the round-trip gain. - we employed a lapped SESAM contacted on copper in collaboration with TRUMPF GmbH to improve the flatness and the heat management of the SESAM. - we set up a real-time imaging scheme for the disk’s saturation to optimize the laser cavity alignment and operate as a safety interlock to prevent the disk from overheating. We extensively discussed in this thesis that the high intracavity power in thin- disk laser oscillators represents one of the main challenges to overcome in power scaling these lasers. To tackle this challenge, the laser presented in section 6.1 employed a cavity design with three reflections on the disk gain medium. This increases the gain per round trip, which, in turn, allows us to use a larger output coupling rate while keeping the optical-to-optical efficiency high. Here we pushed that approach one step further and increased the number of reflections on the disk from three to five. This allowed us to increase the output-coupling rate of the cavity from 25% to 40%. Increasing the number of reflections of the intracavity beam on the disk results in a longer cavity: the repetition rate of the oscillator went down from 8.88 MHz for the cavity with three reflections on the disk to 6.29 MHz for the cavity with five reflections. This, in turn, results in a higher pulse energy for a given output power and hence increases the fluence on the SESAM. Increasing the fluence pushes the operating point of the SESAM further in the rollover and hence increases its losses and the heat deposited on it. One way to counteract this effect would be to further increase the laser spot size on the SESAM, this however would result in an increase in the sensitivity to the SESAM’s thermal lensing. The approach we pursued here is to improve the thermal properties of the saturable absorber by lapping its GaAs sub- strates from the original 600 µm to ≈200 µm. According to our FEM simulations for the thermal properties of the SESAM, this leads to a reduction

125

Chapter 6 of its temperature increase by a factor of ≈2 for a given absorbed power. Additionally, we collaborated with our industrial partner TRUMPF GmbH for contacting the SESAM on copper. Their industrially developed contacting technique results in a flat and homogenous bonding between the SESAM and the copper with a cold radius of curvature >500 m. Another important challenge in power scaling thin-disk oscillators is the high pump intensity on the disk: if the thermal load is too high, damage to the disk can occur. During laser operation the gain is depleted by the laser action, reducing the fraction of pump power that goes into fluorescence emission and heat. On the other hand, when there is no laser action, the entirety of the absorbed pump power goes into fluorescence and heat. The latter is the cause of the disk’s damage. Hence, a higher pump intensity is possible during laser operation compared to when there is no laser operation. In particular, we observed disk damage at 5.4 kW/cm2 pump intensity without laser operation when the pump-spot diameter was 8.0 mm [21]. In order to further power scale the 350-W average power result presented in Section 6.1, we required a higher pump intensity. This required intensity was very close to the mentioned value at which we had previously observed damage on the same type of disk. While such pump intensities are well below the damage threshold during laser operation, they may damage the disk if laser operation is abruptly interrupted. An abrupt interruption of the laser operation can happen due to damage to an optical component or cavity misalignment due to thermal expansion of, e.g., a mirror mount. Hence, we implemented a safety interlock to monitor the fluorescence light emitted by the disk, which is a proxy for the heat deposited on the disk, and shut down the pump diodes when the intensity of the fluorescence light goes above a given threshold. Practically, for a given pump power we set the threshold 10% above the fluorescence light that we have during normal laser operation. This interlock was triggered a few times during the project, probably preventing the disk from being damaged. The device we implemented to monitor the disk’s fluorescence had also another relevant function. We realized that monitoring and minimizing the disk’s fluorescence represents a very effective way to optimize the laser alignment. In particular, the disk’s fluorescence provided a way to probe in real 126

Power scaling results time the alignment of the laser. The standard approach to optimize the output power becomes cumbersome at high power due to the slow thermalization time of kilowatt-level power meters of some seconds. Leveraging these improvements, we were able to develop a thin-disk oscillator delivering 430-W average power with 68-µJ, 769-fs pulses at 6.29-MHz repetition rate. These parameters correspond to 78-MW of peak power. To the best of our knowledge, this oscillator sets a new benchmark for the average power and the peak power achieved from any modelocked laser (Fig. 6.6). We provide a description of the laser cavity in Section 6.2.1, discuss the laser performance in Section 6.2.2 and conclude in Section 6.2.3.

Fig. 6.6 Overview of SESAM-modelocked and KLM thin-disk laser oscillators. (a) Average output power over the years of those oscillators which represented a new record at the time of publication; (b) peak power versus pulse duration of cutting-edge oscillators. Dashed lines indicate pulse energy for a transform-limited sech2 pulse. Our result represents the highest output power and peak power ever achieved from any ultrafast oscillator. Labels report the pulse energy when >10 µJ. Refs: [12, 15, 21, 46, 47, 53, 63, 127].

6.2.1 Cavity design The laser cavity used in this oscillator is based on a Yb-doped thin disk (TRUMPF GmbH) and has a very similar design to the cavity we extensively discussed in Section 6.1.2. It differs only in the number of reflections on the disk which has been increased from three to five. We realigned the active multi-pass cell and shifted the pick-up mirror [small mirror after the concave 127

Chapter 6

2-m mirror in Fig. 6.2(a)] such that the spacing between the beams on the 2-m mirrors is reduced and hence we can support additional reflections on the disk. In this way the angles of incidence on the disk and on the concave mirrors can be kept small to minimize astigmatic effects, as described Section 6.1.2. We extensively studied the laser performance as a function of the number of reflections on the disk and the output coupler rate in order to optimize the efficiency of the laser. For a cavity with one reflection on the disk, the optimal output-coupling rate to maximize efficiency is, for our oscillator, ≈8%. Thus, increasing the output coupling rate to 25% with three reflections on the disk and 40% with five reflections lead to the same optical-to-optical and slope efficiency (Fig. 6.7).

Fig. 6.7 Power slopes in cw operation. Output power (a), and intracavity power (b) vs pump power. Increasing the number of reflections on the disk (nrefl) and the output coupling rate correspondingly results in a high optical-to-optical efficiency combined with a lower intracavity power.

Increasing the number of reflections on the disk shrinks the stability zone with respect to the disk thermal lensing (cfr. Fig. 6.3(b) and Fig. 6.8(b)). In the present configuration with five reflections on the disk, the cavity travels the full stability zone increasing the power from threshold to the maximum power. The stability zone can be shifted to smaller or larger ∆Fdisk values by adjusting the cavity lengths. Shifting it to more negative ∆Fdisk values, leads to a worse beam quality at low power but improves the beam quality at high power (i.e., larger thermal lensing in absolute value). While this approach works for cw thin-disk lasers, it is more complicated for modelocked laser where a poor beam quality would probably prevent the laser from being 128

Power scaling results modelocked. Without the use of active optics to compensate for the thermal lensing, going above five reflections on the disk seems arduous.

Fig. 6.8 (a) Evolution of the 1/e2 mode radius as a function of the position inside the laser cavity. ∆Fdisk = 0 corresponds to the cold disk; (b) stability zone: calculated beam radius at the position of the disk (black line) and the SESAM (light blue line) as a function of the disk’s focusing power change ∆Fdisk. The values of ∆Fdisk used are the same of Fig. 6.3 for comparison. Note the reduction of the stability zone width due to the increased number of passes on the disk.

6.2.2 Modelocking and laser performance For modelocking, we employed a different SESAM compared to the one of the 350-W average power oscillator. We used a dielectrically top-coated SESAM with 1.6% modulation depth and 42 µJ/cm2 saturation fluence. We lapped the SESAM substrate from wafer thickness (600 µm) down to 200 µm. For a given thermal load and spot size on the SESAM, this yields a two-fold reduction in temperature increase, based on heat flow simulations (COM- SOL). Hence we expect a reduction of the thermal lensing by the same amount [50]. We operated our oscillator in a low-pressure environment in order to reduce the overall disk’s thermal lensing (removing the gas-lens effect) and limit the nonlinearities from air during modelocking. We fixed the laser polarization through a thin-film polarizer and introduced -27’000 fs2 of round-trip GDD through dispersive mirrors (Layertec GmbH and University of Neuchatel). Compared to the -16’600 fs2 of round-trip GDD we had in the 350-W oscillator, we obtained the additional GDD through the additional four reflections

129

Chapter 6 on the 2-m concave dispersive mirrors and extra flat dispersive mirrors. The additional GDD ensures a stronger soliton pulse shaping and together with the slightly larger SESAM’s modulation depth (1.6% vs 1.1%) allows us to modelock the laser despite the larger output coupling rate. The laser shows stable modelocking starting from 254 W output power with 1.1 ps pulses [beam profile in Fig. 6.9(b)], up to 430-W output power with 769-fs pulses [Fig. 6.9(c)] and 1.67-nm spectral bandwidth (time-bandwidth product 1.15x0.315). We observe the typical shortening of pulse duration with pulse energy as expected for soliton pulse shaping [Fig. 6.9(a)]. We ensure soliton-pulse formation balancing the intracavity GDD with ≈0.7 mrad/MW of SPM obtained from the residual 47-mbar air pressure. We measured the M2 and obtained 1.1 at low power and 1.5 at the maximum power [Fig. 6.10(f)]. In Fig. 6.10 we present the laser diagnostics at 430-W average power showing stable modelocking: optical spectrum and second-harmonic autocorrelation trace fitted assuming sech2-shaped pulses, radio-frequency (RF) spectrum at the repetition rate, and RF spectrum with a large span showing the harmonics up to 100 MHz. Additionally, we checked single-pulse operation scanning the long-range (200 ps) autocorrelator and measuring the pulses with a fast 45-GHz photodiode and a sampling oscilloscope [Fig. 6.10(e)].

Fig. 6.9 (a) Laser power slopes and pulse duration in cw (without SESAM) and modelocking; beam profile at (b) 254-W and (c) 430-W average power in modelocked operation.

130

Power scaling results

Fig. 6.10 (a) Laser diagnostics at 430-W output power showing a stable modelocking regime (a) optical spectrum; (b) second-harmonic autocorrelation trace; (c) radio-frequency (RF) spectrum at the repetition rate with 300 Hz resolution bandwidth (RBW); (d) large-span RF trace showing harmonics up to 100 MHz with constant intensity, RBW = 3 kHz; (e) sampling oscilloscope trace and, in the inset, a zoom on the pulse 2 showing the ripples typical of the impulse response of the photodiode; (f) M measurements, the 1/e2 beam width is calculated using the second momentum width (D4σ). Red dashed lines in (a) and (b) are fits assuming sech2-shaped pulses.

We notice that compared to the 350-W laser we obtain here shorter pulses (pulse duration 769 fs vs 940 fs) and a lower TBP (1.15x0.315 vs 1.30x0.315). This is probably due to the larger amount of negative GDD and the larger SESAM’s modulation depth. Regarding the beam quality at high power and 2 the comparatively large M value of 1.50, this is probably due to the operation at the edge of the stability zone [Fig. 6.8(b)] at a |∆Fdisk| > 0.020 m-1. We infer the ∆Fdisk extrapolating our thermal lensing measurements at lower 2 power. In cw, at the same pump power, we achieved an M = 1.20 with the same cavity using the same amount of GDD and with the SESAM replaced by an high-reflective mirror [blue point at the highest power in Fig. 6.9(a)]. The average output power was, in that case, 510 W instead of the 430 W in modelocked operation. Consequently, the disk’s thermal lensing (|∆Fdisk|) 131

Chapter 6 was lower due to the reduced thermal load on the disk. Additionally, in modelocked operation, the thermal lensing of the SESAM is also likely to play a role in degrading the beam quality. Further optimization of the cavity design to shift the position of the stability zone can lead to an improved beam quality at high power.

6.2.3 Conclusion and outlook In conclusion, we demonstrated a thin-disk laser oscillator delivering 430-W average output power at 78-MW peak power. The laser parameters reached here, especially if combined with a pulse-compression stage, are compelling for a variety of nonlinear-optics experiments such as high-harmonic generation. In the current configuration, the power is limited by the onset of the rollover in the SESAM, which leads to additional losses and hence clamps the output power. By designing a different SESAM’s top coating we can push the onset of the rollover to higher fluences. Hence, we are confident that we will be able to exceed the 500-W milestone in the near future. Additionally, by ex- tending the laser cavity, pulse energies above 100 µJ and peak powers above 100 MW are within reach.

132

Conclusion and outlook

7 Conclusion and outlook

During this thesis, we conducted a thorough investigation of the factors limiting the maximum achievable output power in thin-disk laser oscillators. We developed ways to overcome these limitations and, as a result, were able to demonstrate a new record for the highest average output power of any ultrafast oscillator. We identified the air in front of the thin-disk gain medium as a substantial source of thermal lensing for state-of-the-art thin-disk lasers operating in the multi-hundreds of watts regime [31]. We showed that by operating the laser in vacuum or in a helium atmosphere, this contribution to the thermal lensing can be removed. This resulted, in our experiments, in a twofold extension of the power range over which optimal beam quality (M2 < 1.10) is achieved in vacuum compared to air. In particular, we were able to operate a thin-disk laser at 800-W average output power in cw with an M2 < 1.10. We investigated the use of quadratic nonlinearities in high-power oscillators. In particular, we demonstrated how a second-harmonic generation crystal can be used to obtain a negative phase shift that cancels the SPM picked up in femtosecond-modelocked thin-disk oscillators through the process of cascaded quadratic nonlinearities. The large amount of SPM picked up in air represents a major challenge especially in SESAM-modelocked high-power thin-disk oscillators. This challenge is often overcome by removing the air and operating the laser in vacuum. We demonstrated a SESAM-modelocked thin- disk oscillator operated in air, delivering 210-W average output power [32]. We achieved this result by cancelling 80% of the SPM picked up in air through 133

Chapter 7 cascaded nonlinearities. Such a level of average power has been previously achieved with SESAM modelocking only by removing the air through expensive vacuum systems. This result paves the way to the use of cascaded quadratic nonlinearities for high-power lasers. Additionally, we employed quadratic nonlinearities to directly modelock a thin-disk laser oscillator through the nonlinear mirror technique. In our first demonstration, we obtained 21-W average output power, with 323-fs pulses [33]. This result demonstrated, for the first time, the possibility to obtain sub-picosecond pulses using the NLM technique. This technique is of great interest for high-power modelocking as the modulation does not come from an absorption process, hence limiting thermal effects. Additionally, the NLM does not couple the spatial and temporal properties of the cavity. Thus, the laser cavity can be designed for single-spatial-mode operation in cw and only after the NLM can be added to obtain modelocked operation. This technique offers the best of KLM, i.e., a fast absorption-free modulation together with the flexibility of SESAM modelocking. After our first result with the NLM modelocking technique, we pursued investigation into the use of this technique to modelock lasers with output powers in the 100-W range. Two of the main challenges we faced during this work were: the linear absorption of the intracavity nonlinear crystal needed and the complexity of the NLM modelocking dynamics in the sub-picosecond regime, regarding which little investigation was done. To overcome the linear absorption issue, we explored different crystals materials and lengths. To overcome the modelocking-dynamics challenge, we combined the NLM with a SESAM. In this way we obtained modelocked laser operation at 66-W average output power, with 426-fs pulses at 9.3-MHz repetition rate and 87 W with 586-fs pulses [33]. Additionally, we defined a set of guidelines regarding which nonlinear crystal to use to minimize linear absorption and how to avoid q-switching. The NLM modelocking represents a new option to modelock high-power lasers delivering shorter pulses compared to SESAM modelocking. Leveraging the findings discussed so far and employing a cavity design with an imaging scheme that results in multiple reflections on the disk gain medium, we were able to improve the long-standing 275-W average power 134

Conclusion and outlook record for ultrafast oscillators [12]. We first obtained 350 W, with 940-fs pulses at 8.88-MHz repetition rate [21]. In the next phase of the project, we obtained 430 W, with 769-fs pulses at 6.29-MHz repetition rate, corresponding to 68-µJ pulse energy. The use of the mentioned imaging scheme allows us to have a large output coupling rate, which results in a low intracavity power for a given output power. The 430-W average power results represents an improvement in terms of average power of more than 50% compared to the prior 275-W record. Additionally, our oscillator delivers 78-MW peak power, which is, to the best of our knowledge, the highest peak power ever recorded at the output of a modelocked oscillator. On the laser device side, with the aim of achieving even higher average output power from ultrafast TDL oscillators, we foresee the possibility to use SES- AMs with improved thermal properties together with active optics. In particular, by completely removing the SESAM’s GaAs substrate, better thermal performance can be achieved. The techniques presented in [50] confirm the exceptional thermal property achievable and we are confident that by optimizing the processing, SESAMs with a large usable are will be produced. Additionally, the use of an active optic as a deformable mirror can compensate for the residual thermal lensing effects. In particular, a deformable mirror able to compensate for the spherical part of the disk’s thermal lensing in kilowatt-level cw lasers has already been demonstrated [66]. We are confident that this combination will allow the development of ultrafast laser oscillators with output power towards the kilowatt regime. Another appealing property of oscillator is the possibility to increase the pulse energy by making the laser cavity longer. In particular, using a passive Herriot-type cell as in [15] to increase the cavity length of our 430-W average output power oscillator would result in an oscillator delivering substantially more than 100-µJ pulse energy. Lastly, the use of CQN for nonlinearity management, offers an opportunity to improve the performance of TDL oscillators operated in air. In this way expensive vacuum systems would not be required anymore, hence making an important step in the direction of a more widespread use of high-power thin- disk oscillators in research and industry. Additionally, we see the nonlinear mirror modelocking as a concrete option to obtain shorter pulses directly at the output of the laser oscillator.

135

Chapter 7

On the applications side, the lasers built during this thesis are attractive sources for many nonlinear optics applications as XUV and terahertz generation. These applications are already performed using ultrafast thin-disk laser oscillators [29, 30] and would benefit from the higher average power of the oscillators developed in this thesis. Additionally, pairing our oscillators with a compression scheme to obtain sub-50 fs pulses would pave the way to laser sources operating at megahertz repetition rate and delivering hundreds of megawatts peak power. The recently demonstrated compression scheme based on a multi-pass cell architecture [22, 140] offers a feasible way to achieve this goal. In particular, a multi-pass cell has been recently used to compress a laser source to 30-fs pulse duration at 530-W average power with a very good beam quality (M2 < 1.2) [141].

136

Author contributions

My contributions to the journal publications listed in the Publications chapter: Power-scaling of nonlinear-mirror modelocked thin-disk lasers I. J. Graumann, F. Saltarelli, L. Lang, V. J. Wittwer, T. Südmeyer, C. R. Phillips, and U. Keller Opt. Express 27, 37349-37363 (2019) - Designed the multi-pass arrangement in the thin-disk oscillator. - Performed some preliminary experiments to power scale our first nonlinear-mirror modelocked thin-disk oscillator. These experiments highlighted the issues related to the absorption of the nonlinear crystal and guided us to select the crystals used in the final version of the laser. - Supported the experimental work. - Participated in the writing of the manuscript. Power scaling of ultrafast oscillators: 350-W average-power sub-picosecond thin-disk laser F. Saltarelli, I. J. Graumann, L. Lang, D. Bauer, C. R. Phillips, and U. Keller Opt. Express 27, 31465-31474 (2019) - Led the project. - Design and developed the thin-disk laser oscillator. - Performed the measurements to characterize the laser in the laboratory and analyzed the data. - Wrote the manuscript and incorporated the feedback from the authors.

137

Author contributions

Regarding the second stage of the project, resulting in the further power scaling to 430-W average output power, presented in section 6.2, my contributions are: - Led the project. - Optimized the laser oscillator to achieve the new record in power. - Developed the electronics for the interlock system. - Designed and lapped the SESAM. Additionally, coordinated the development of the SESAM and its contacting with the industrial partner TRUMPF GmbH. Self-phase modulation cancellation in a high-power ultra-fast thin- disk laser oscillator F. Saltarelli, A. Diebold, I. J. Graumann, C. R. Phillips, and U. Keller Optica 5, 1603-1606 (2018) - Led the project. - Design and developed the thin-disk laser oscillator. - Participated in the development of the numerical model and used it to define the requirements on the crystal for self-phase modulation cancellation. - Characterized the laser and analyzed the data. - Wrote the manuscript and incorporated the feedback from the authors. Gas-lens effect in kW-class thin-disk lasers A. Diebold*, F. Saltarelli*, I. J. Graumann, C. J. Saraceno, C. R. Phillips, and U. Keller *These authors contributed equally to this work Opt. Express 26, 12648-12659 (2018) - Performed preliminary measurements showing the impact of the gas environment on the disk’s thermal lensing. - Took the set of thermal-lensing measurements on the high-power laser together with A. Diebold. - Analyzed the data together with A. Diebold. - Wrote the manuscript together with A. Diebold.

138

Author contributions

Modelocking of a thin-disk laser with the frequency-doubling nonlinear-mirror technique F. Saltarelli, A. Diebold, I. J. Graumann, C. R. Phillips, and U. Keller Opt. Express 25, 23254-23266 (2017) - Led the project. - Designed and developed the thin-disk laser oscillator. - Performed the measurements to characterize the laser in the laboratory and analyzed the data. - Contributed to the development of the numerical model and used the model to define the best components for nonlinear mirror modelocking. - Wrote the manuscript and incorporated the feedback from the authors.

139

Bibliography

[1] T. H. Maiman, "Stimulated Optical Radiation in Ruby," Nature 187, 493-494 (1960). [2] A. Einstein, "Zur Quantentheorie der Strahlung," Physik. Zeitschrift XVIII, 121-128 (1917). [3] A. H. Zewail, "Femtochemistry: atomic-scale dynamics of chemical bond," J. Phys. Chem. A 104, 5660-5694 (2000). [4] T. Südmeyer, S. V. Marchese, S. Hashimoto, C. R. E. Baer, G. Gingras, B. Witzel, and U. Keller, "Femtosecond laser oscillators for high-field science," Nat. Photonics 2, 599-604 (2008). [5] C. J. Saraceno, "Mode-locked thin-disk lasers and their potential application for high-power terahertz generation," J. Opt. 20, 044010 (2018). [6] S. Nolte, F. Schrempel, and F. Dausinger, "Ultrashort Pulse Laser Technology," in Springer Series in Optical Sciences, (Springer International Publishing, 2016). [7] M. Müller, A. Klenke, A. Steinkopff, H. Stark, A. Tünnermann, and J. Limpert, "3.5 kW coherently combined ultrafast fiber laser," Opt. Lett. 43, 6037-6040 (2018). [8] T. Dietz, M. Jenne, D. Bauer, M. Scharun, D. Sutter, and A. Killi, "Ultrafast thin-disk multi-pass amplifier system providing 1.9 kW of average output power and pulse energies in the 10 mJ range at 1 ps of pulse duration for glass-cleaving applications," Opt. Express. 28, 11415-11423 (2020). [9] P. Russbueldt, T. Mans, J. Weitenberg, H. D. Hoffmann, and R. Poprawe, "Compact diode-pumped 1.1 kW Yb:YAG Innoslab femtosecond amplifier," Opt. Lett. 34, 4169-4171 (2010). [10] P. Russbueldt, T. Mans, G. Rotarius, J. Weitenberg, H. D. Hoffmann, and R. Poprawe, "400 W Yb:YAG Innoslab fs-Amplifier," Opt. Express 17, 12230- 12245 (2009). [11] T. Eidam, S. Hanf, E. Seise, T. V. Andersen, T. Gabler, C. Wirth, T. Schreiber, J. Limpert, and A. Tunnermann, "Femtosecond fiber CPA system emitting 830 W average output power," Opt. Lett. 35, 94-96 (2010).

141

Bibliography

[12] C. J. Saraceno, F. Emaury, O. H. Heckl, C. R. E. Baer, M. Hoffmann, C. Schriber, M. Golling, T. Südmeyer, and U. Keller, "275 W average output power from a femtosecond thin disk oscillator operated in a vacuum environment," Opt. Express 20, 23535-23541 (2012). [13] C. Teisset, M. Schultze, R. Bessing, M. Haefner, S. Prinz, D. Sutter, and T. Metzger, "300 W Picosecond Thin-Disk Regenerative Amplifier at 10 kHz Repetition Rate," in Advanced Solid-State Lasers Congress Postdeadline, G. Huber, and P. Moulton, (Optical Society of America, Paris, 2013), paper JTh5A.1. [14] A. Klenke, S. Hädrich, T. Eidam, J. Rothhardt, M. Kienel, S. Demmler, T. Gottschall, J. Limpert, and A. Tünnermann, "22 GW peak-power fiber chirped-pulse amplification system," Opt. Lett. 39, 6875-6878 (2014). [15] C. J. Saraceno, F. Emaury, C. Schriber, M. Hoffmann, M. Golling, T. Südmeyer, and U. Keller, "Ultrafast thin-disk laser with 80 µJ pulse energy and 242 W of average power," Opt. Lett. 39, 9-12 (2014). [16] Z. Zhao, and Y. Kobayashi, "Ytterbium fiber-based, 270 fs, 100 W chirped pulse amplification laser system with 1MHz repetition rate," Appl. Phys. Express 9 (2016). [17] M. Schultze, S. Klingebiel, C. Wandt, C. Y. Teisset, R. Bessing, M. Haefner, S. Prinz, K. Michel, and T. Metzger, "500 W - 10 mJ - Picosecond Thin-Disk Regenerative Amplifier," Europhoton Conference 2016, SSL-5.4. [18] M. Kienel, M. Müller, A. Klenke, J. Limpert, and A. Tünnermann, "12 mJ kW-class ultrafast fiber laser system using multidimensional coherent pulse addition," Opt. Lett. 41, 3343-3346 (2016). [19] M. Müller, M. Kienel, A. Klenke, T. Gottschall, E. Shestaev, M. Plötner, J. Limpert, and A. Tünnermann, "1 kW 1 mJ eight-channel ultrafast fiber laser," Opt. Lett. 41, 3439-3442 (2016). [20] T. Nubbemeyer, M. Kaumanns, M. Ueffing, M. Gorjan, A. Alismail, H. Fattahi, J. Brons, O. Pronin, H. G. Barros, Z. Major, T. Metzger, D. Sutter, and F. Krausz, "1 kW, 200 mJ picosecond thin-disk laser system," Opt. Lett. 42, 1381-1384 (2017). [21] F. Saltarelli, I. J. Graumann, L. Lang, D. Bauer, C. R. Phillips, and U. Keller, "Power scaling of ultrafast oscillators: 350-W average-power sub-picosecond thin-disk laser," Opt. Express. 27, 31465-31474 (2019). [22] J. Schulte, T. Sartorius, J. Weitenberg, A. Vernaleken, and P. Russbueldt, "Nonlinear pulse compression in a multi-pass cell," Opt. Lett. 41, 4511-4514 (2016). [23] C. J. Saraceno, F. Emaury, C. Schriber, A. Diebold, M. Hoffmann, M. Golling, T. Südmeyer, and U. Keller, "Toward millijoule-level high-power ultrafast thin-disk oscillators," IEEE J. Sel. Top. Quantum Electron. 21 (2015). [24] A. Giesen, H. Hügel, A. Voss, K. Wittig, U. Brauch, and H. Opower, "Scalable Concept for Diode-Pumped High-Power Solid-State Lasers," Appl. Phys. B 58, 365-372 (1994).

142

Bibliography

[25] U. Keller, D. A. B. Miller, G. D. Boyd, T. H. Chiu, J. F. Ferguson, and M. T. Asom, "Solid-state low-loss intracavity saturable absorber for Nd:YLF lasers: an antiresonant semiconductor Fabry-Perot saturable absorber," Opt. Lett. 17, 505-507 (1992). [26] U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. Aus der Au, "Semiconductor saturable absorber mirrors (SESAMs) for femtosecond to nanosecond pulse generation in solid-state lasers," IEEE J. Sel. Top. Quantum Electron. 2, 435- 453 (1996). [27] F. Labaye, M. Gaponenko, V. J. Wittwer, A. Diebold, C. Paradis, N. Modsching, L. Merceron, F. Emaury, I. J. Graumann, C. R. Phillips, C. J. Saraceno, C. Kränkel, U. Keller, and T. Südmeyer, "Extreme ultraviolet light source at a megahertz repetition rate based on high-harmonic generation inside a mode-locked thin-disk laser oscillator," Opt. Lett. 42, 5170-5173 (2017). [28] F. Emaury, A. Diebold, C. J. Saraceno, and U. Keller, "Compact extreme ultraviolet source at megahertz pulse repetition rate with a low-noise ultrafast thin-disk laser oscillator," Optica 2, 980-984 (2015). [29] F. Meyer, N. Hekmat, T. Vogel, A. Omar, S. Mansourzadeh, F. Fobbe, M. Hoffmann, Y. Wang, and C. J. Saraceno, "Milliwatt-class broadband THz source driven by a 112 W, sub-100 fs thin-disk laser," Opt. Express. 27, 30340-30349 (2019). [30] J. Drs, N. Modsching, C. Paradis, C. Kränkel, V. J. Wittwer, O. Razskazovskaya, and T. Südmeyer, "Optical rectification of ultrafast Yb lasers: pushing power and bandwidth of terahertz generation in GaP," Journal of the Optical Society of America B 36, 3039-3045 (2019). [31] A. Diebold, F. Saltarelli, I. J. Graumann, C. J. Saraceno, C. R. Phillips, and U. Keller, "Gas-lens effect in kW-class thin-disk lasers," Opt. Express. 26, 12648-12659 (2018). [32] F. Saltarelli, A. Diebold, I. J. Graumann, C. R. Phillips, and U. Keller, "Self- phase modulation cancellation in a high-power ultrafast thin-disk laser oscillator," Optica 5, 1603-1606 (2018). [33] F. Saltarelli, A. Diebold, I. J. Graumann, C. R. Phillips, and U. Keller, "Modelocking of a thin-disk laser with the frequency-doubling nonlinear- mirror technique," Opt. Express. 25, 23254-23266 (2017). [34] I. J. Graumann, F. Saltarelli, L. Lang, V. Wittwer, T. Südmeyer, C. R. Phillips, and U. Keller, "Power-scaling of nonlinear-mirror modelocked thin-disk lasers," Opt. Express 27, 37349--37363 (2019). [35] S.-S. Schad, T. Gottwald, V. Kuhn, M. Ackermann, D. Bauer, M. Scharun, and A. Killi, "Recent development of disk lasers at TRUMPF," Proc. of SPIE 972615 (2016).

143

Bibliography

[36] V. Kuhn, T. Gottwald, C. Stolzenburg, S.-S. Schad, A. Killi, and T. Ryba, "Latest advances in high brightness disk lasers," Proc. of SPIE 93420 (2015). [37] V. Magni, "Multielement stable resonators containing a variable lens," J. Opt. Soc. Am. A 4, 1962-1969 (1987). [38] A. Giesen, and J. Speiser, "Fifteen Years of Work on Thin-Disk Lasers: Results and Scaling Laws," IEEE J. Sel. Top. Quantum Electron. 13, 598-609 (2007). [39] J. Perchermeier, and U. Wittrock, "Precise measurements of the thermo- optical aberrations of an Yb:YAG thin-disk laser," Opt. Lett. 38, 2422-2424 (2013). [40] G. Zhu, Y. Qiu, Z. Wang, X. Zhu, and C. Zhu, "Analytical model of optical field distribution of thin disk laser with thermal-optical aberration gain medium," Optics & Laser Technology 82, 134-138 (2016). [41] P. Wittmuess, S. Piehler, T. Dietrich, M. A. Ahmed, T. Graf, and O. Sawodny, "Numerical modeling of multimode laser resonators," Journal of the Optical Society of America B 33, 2278-2287 (2016). [42] B. Weichelt, D. Blazquez-Sanchez, A. Austerschulte, A. Voss, T. Graf, and A. Killi, "Improving the brightness of a multi-kW thin disk laser with a single disk by an aspherical phase-front correction," Proc. of SPIE 7721 (2010). [43] T. Dietrich, S. Piehler, C. Roecker, M. Rumpel, M. A. Ahmed, and T. Graf, "Passive compensation of the misalignment instability caused by air convection in thin-disk lasers," Opt. Lett. 42, 3263-3266 (2017). [44] J.-P. Negel, A. Voss, M. A. Ahmed, D. Bauer, D. Sutter, A. Killi, and T. Graf, "1.1 kW average output power from a thin-disk multipass amplifier for ultrashort laser pulses," Opt. Lett. 38, 5442-5445 (2013). [45] J. Neuhaus, J. Kleinbauer, A. Killi, S. Weiler, D. Sutter, and T. Dekorsy, "Passively mode-locked Yb:YAG thin-disk laser with pulse energies exceeding 13 μJ by use of an active multipass geometry," Opt. Lett. 33, 726- 728 (2008). [46] D. Bauer, I. Zawischa, D. H. Sutter, A. Killi, and T. Dekorsy, "Mode-locked Yb:YAG thin-disk oscillator with 41 µJ pulse energy at 145 W average infrared power and high power frequency conversion," Opt. Express 20, 9698-9704 (2012). [47] J. Brons, V. Pervak, E. Fedulova, D. Bauer, D. Sutter, V. Kalashnikov, A. Apolonskiy, O. Pronin, and F. Krausz, "Energy scaling of Kerr-lens modelocked thin-disk oscillators," Opt. Lett. 39, 6442-6445 (2014). [48] D. J. H. C. Maas, B. Rudin, A.-R. Bellancourt, D. Iwaniuk, S. V. Marchese, T. Südmeyer, and U. Keller, "High precision optical characterization of semiconductor saturable absorber mirrors," Opt. Express 16, 7571-7579 (2008). [49] C. J. Saraceno, C. Schriber, M. Mangold, M. Hoffmann, O. H. Heckl, C. R. E. Baer, M. Golling, T. Südmeyer, and U. Keller, "SESAMs for high-power

144

Bibliography

oscillators: design guidelines and damage thresholds," IEEE J. Sel. Top. Quan. Electron. 18, 29-41 (2012). [50] A. Diebold, T. Zengerle, C. G. E. Alfieri, C. Schriber, F. Emaury, M. Mangold, M. Hoffmann, C. J. Saraceno, M. Golling, D. Follman, G. D. Cole, M. Aspelmeyer, T. Südmeyer, and U. Keller, "Optimized SESAMs for kilowatt- level ultrafast lasers," Opt. Express 24, 10512-10526 (2016). [51] K. A. Stankov, and J. Jethwa, "A new mode-locking technique using a nonlinear mirror," Opt. Commun. 66, 41-46 (1988). [52] K. A. Stankov, V. P. Tzolov, and M. G. Mirkov, "Frequency-doubling mode locker: the influence of group-velocity mismatch," Opt. Lett. 16, 1119-1121 (1991). [53] F. Brunner, E. Innerhofer, S. V. Marchese, T. Südmeyer, R. Paschotta, T. Usami, H. Ito, S. Kurimura, K. Kitamura, G. Arisholm, and U. Keller, "Powerful red-green-blue laser source pumped with a mode-locked thin disk laser," Opt. Lett. 29, 1921-1923 (2004). [54] D. Bauer, F. Schättiger, J. Kleinbauer, D. Sutter, A. Killi, and T. Dekorsy, "Energies above 30 μJ and average power beyond 100 W directly from a mode‐locked thin‐disk oscillator," presented at the Advanced Solid-State Photonics Istanbul, Turkey, 2011. [55] J. Brons, V. Pervak, D. Bauer, D. Sutter, O. Pronin, and F. Krausz, "Powerful 100-fs-scale Kerr-lens mode-locked thin-disk oscillator," Opt. Lett. 41, 3567- 3570 (2016). [56] M. Poetzlberger, J. Zhang, S. Gröbmeyer, D. Bauer, D. Sutter, J. Brons, and O. Pronin, "Kerr-lens mode-locked thin-disk oscillator with 50% output coupling rate," Opt. Lett. 44, 4227-4230 (2019). [57] B. Borchers, C. Schaefer, C. Fries, M. Larionov, and R. Knappe, "Nonlinear Polarization Rotation Mode-locking via Phase-mismatched Type I SHG of a Thin Disk Femtosecond Laser," in ASSL, (OSA, Berlin, 2015), paper ATh4A.9. [58] U. Keller, "Recent developments in compact ultrafast lasers," Nature 424, 831-838 (2003). [59] K. Sugioka, and Y. Cheng, "Ultrafast lasers - reliable tools for advanced materials processing," Light Sci. Appl. 3, 149 (2014). [60] M. N. Zervas, and D. A. Codemard, "High Power Fiber Lasers: A Review," IEEE J. Sel. Top. Quan. Electron. 20, 0904123 (2014). [61] P. Russbueldt, D. Hoffmann, M. Hoefer, J. Loehring, J. Luttmann, A. Meissner, J. Weitenberg, M. Traub, T. Sartorius, D. Esser, R. Wester, P. Loosen, and R. Poprawe, "Innoslab Amplifiers," IEEE J. Sel. Top. Quan. Electron. 21, 3100117 (2015). [62] J.-P. Negel, A. Loescher, A. Voss, D. Bauer, D. Sutter, A. Killi, M. A. Ahmed, and T. Graf, "Ultrafast thin-disk multipass laser amplifier delivering 1.4 kW

145

Bibliography

(4.7 mJ, 1030 nm) average power converted to 820 W at 515 nm and 234 W at 343 nm," Opt. Express 23, 21064-21077 (2015). [63] J. Aus der Au, G. J. Spühler, T. Südmeyer, R. Paschotta, R. Hövel, M. Moser, S. Erhard, M. Karszewski, A. Giesen, and U. Keller, "16.2 W average power from a diode-pumped femtosecond Yb:YAG thin disk laser," Opt. Lett. 25, 859-861 (2000). [64] F. Emaury, A. Diebold, A. Klenner, C. J. Saraceno, S. Schilt, T. Südmeyer, and U. Keller, "Frequency comb offset dynamics of SESAM modelocked thin disk lasers," Opt. Express 23, 21836-21856 (2015). [65] S. V. Marchese, C. R. E. Baer, A. G. Engqvist, S. Hashimoto, D. J. H. C. Maas, M. Golling, T. Südmeyer, and U. Keller, "Femtosecond thin disk laser oscillator with pulse energy beyond the 10-microjoule level," Opt. Express 16, 6397-6407 (2008). [66] S. Piehler, T. Dietrich, P. Wittmuess, O. Sawodny, M. A. Ahmed, and T. Graf, "Deformable mirrors for intra-cavity use in high-power thin-disk lasers," Opt. Express 25, 4254-4267 (2017). [67] B. Weichelt, A. Voss, M. A. Ahmed, and T. Graf, "Enhanced performance of thin-disk lasers by pumping into the zero-phonon line," Opt. Lett. 37, 3045- 3047 (2012). [68] G. Zhu, X. Zhu, M. Wang, Y. Feng, and C. Zhu, "Analytical model of thermal effect and optical path difference in end-pumped Yb:YAG thin disk laser," Appl. Opt. 53, 6756-6764 (2014). [69] K. Schuhmann, K. Kirch, and A. Antognini, "Multi-pass oscillator layout for high-energy mode-locked thin-disk lasers," ArXiv, 1603.00404v00402 (2016). [70] K. Schuhmann, K. Kirch, F. Nez, R. Pohl, and A. Antognini, "Thin-disk laser scaling limit due to thermal lens induced misalignment instability," Appl. Opt. 55, 9022-9032 (2016). [71] C. R. E. Baer, O. H. Heckl, C. J. Saraceno, C. Schriber, C. Kränkel, T. Südmeyer, and U. Keller, "Frontiers in passively mode-locked high-power thin disk laser oscillators," Opt. Express 20, 7054-7065 (2012). [72] S. Chenais, F. Balembois, F. Druon, G. Lucas-Leclin, and P. Georges, "Thermal lensing in diode-pumped ytterbium lasers - Part I: Theoretical analysis and wavefront measurements," IEEE J. Quant. Electron. 40, 1217- 1234 (2004). [73] J. Shang, X. Zhu, and G. Zhu, "Analytical approach to thermal lensing in end- pumped Yb:YAG thin-disk laser," Applied Optics 50, 6103 - 6120 (2011). [74] R. Penndorf, "Tables of the Refractive Index for Standard Air and the Rayleigh Scattering Coefficient for the Spectral Region between 0.2 and 20.0 μ and Their Application to Atmospheric Optics," J. Opt. Soc. Am. 47, 176- 182 (1957). [75] J. A. Stone, and A. Stejskal, "Using helium as a standard of refractive index: correcting errors in a gas refractometer," Metrologia 41, 189-197 (2004).

146

Bibliography

[76] E. R. Peck, and B. N. Khanna, "Dispersion of Nitrogen," J. Opt. Soc. Am. 56, 1059-1063 (1966). [77] F. X. Kärtner, I. D. Jung, and U. Keller, "Soliton Mode-Locking with Saturable Absorbers," IEEE J. Sel. Top. Quant. 2, 540-556 (1996). [78] O. Razskazovskaya, T. T. Luu, M. Trubetskov, E. Goulielmakis, and V. Pervak, "Nonlinear absorbance in dielectric multilayers," Optica 2, 803-811 (2015). [79] F. Wise, L. Qian, and X. Liu, "Applications of cascaded quadratic nonlinearities to femtosecond pulse generation," Journal of Nonlinear Optical Physics & Materials 11, 317-338 (2002). [80] C. R. Phillips, A. S. Mayer, A. Klenner, and U. Keller, "SESAM modelocked Yb:CaGdAlO4 laser in the soliton modelocking regime with positive intracavity dispersion," Opt. Express. 22, 6060-6077 (2014). [81] L. J. Qian, X. Liu, and F. W. Wise, "Femtosecond Kerr-lens mode locking with negative nonlinear phase shifts," Opt. Lett. 24, 166-168 (1999). [82] G. Cerullo, S. De Silvestri, A. Monguzzi, D. Segala, and V. Magni, "Self- starting mode locking of a cw Nd:YAG laser using cascaded second-order nonlinearities," Opt. Lett. 20, 746-748 (1995). [83] A. S. Mayer, C. R. Phillips, and U. Keller, "Watt-level 10-gigahertz solid-state laser enabled by self-defocusing nonlinearities in an aperiodically poled crystal," Nature Communications 8, 1673 (2017). [84] H. Iliev, D. Chuchumishev, I. Buchvarov, and V. Petrov, "Passive modelocking of a diode-pumped Nd:YVO4 laser by intracavity SHG in PPKTP," Opt. Express. 18, 5754-5762 (2010). [85] A. L. Viotti, R. Lindberg, A. Zukauskas, R. Budriunas, D. Kucinskas, T. Stanislauskas, F. Laurell, and V. Pasiskevicius, "Supercontinuum generation and soliton self-compression in χ(2)-structured KTiOPO4," Optica 5, 711-717 (2018). [86] M. Bache, O. Bang, W. Krolikowski, J. Moses, and F. W. Wise, "Limits to compression with cascaded quadratic soliton compressors," Opt. Express. 16, 3273-3287 (2008). [87] C. Dorrer, R. G. Roides, J. Bromage, and J. D. Zuegel, "Self-phase modulation compensation in a regenerative amplifier using cascaded second-order nonlinearities," Opt. Lett. 39, 4466-4469 (2014). [88] J. Zhang, J. Brons, N. Lilienfei, E. Fedulova, V. Pervak, D. Bauer, D. Sutter, Z. Wei, A. Apolonski, O. Pronin, and F. Krausz, "260-megahertz, megawatt- level thin-disk oscillator," Opt. Lett. 40, 1627-1630 (2015). [89] S. V. Marchese, T. Südmeyer, M. Golling, R. Grange, and U. Keller, "Pulse energy scaling to 5 μJ from a femtosecond thin disk laser," Opt. Lett. 31, 2728- 2730 (2006).

147

Bibliography

[90] E. Innerhofer, T. Südmeyer, F. Brunner, R. Häring, A. Aschwanden, R. Paschotta, U. Keller, C. Hönninger, and M. Kumkar, "60 W average power in 810-fs pulses from a thin-disk Yb:YAG laser," Opt. Lett. 28, 367-369 (2003). [91] J. Neuhaus, D. Bauer, J. Zhang, A. Killi, J. Kleinbauer, M. Kumkar, S. Weiler, M. Guina, D. H. Sutter, and T. Dekorsy, "Subpicosecond thin-disk laser oscillator with pulse energies of up to 25.9 microjoules by use of an active multipass geometry," Opt. Express 16, 20530-20539 (2008). [92] T. R. Schibli, E. R. Thoen, F. X. Kärtner, and E. P. Ippen, "Suppression of Q-switched mode locking and break-up into multiple pulses by inverse saturable absorption," Appl. Phys. B 70, S41-S49 (2000). [93] G. I. Stegeman, D. J. Hagan, and L. Torner, "χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons," Optical and Quantum Electronics 28, 1691-1740 (1996). [94] S. P. Velsko, M. Webb, L. Davis, and C. Huang, "Phase-matched harmonic generation in lithium triborate (LBO)," IEEE J. Quant. Electron. 27, 2182- 2192 (1991). [95] H. P. Li, C. H. Kam, Y. L. Lam, and W. Ji, "Femtosecond Z-scan measurements of nonlinear refraction in nonlinear optical crystals," Optical Materials 15, 237-242 (2001). [96] J. Herrmann, "Theory of Kerr-lens mode locking: role of self-focusing and radially varying gain," J. Opt. Soc. Am. B 11, 498-512 (1994). [97] E. T. J. Nibbering, G. Grillon, M. A. Franco, B. S. Prade, and A. Mysyrowicz, "Determination of the inertial contribution to the nonlinear refractive index of air, N2, and O2 by use of unfocused high-intensity femtosecond laser pulses," J. Opt. Soc. Am. B 14, 650-660 (1997). [98] J. Neuhaus, D. Bauer, J. Kleinbauer, A. Killi, D. H. Sutter, and T. Dekorsy, "Numerical analysis of a sub-picosecond thin-disk laser oscillator with active multipass geometry showing a variation of pulse duration within one round trip," Journal of the Optical Society of America B 27, 65-71 (2010). [99] T. Dietrich, S. Piehler, M. Rumpel, P. Villeval, D. Lupinski, M. Abdou- Ahmed, and T. Graf, "Highly-efficient continuous-wave intra-cavity frequency-doubled Yb:LuAG thin-disk laser with 1 kW of output power," Opt. Express. 25, 4917-4925 (2017). [100] A. Ancona, S. Doring, C. Jauregui, F. Roser, J. Limpert, S. Nolte, and A. Tünnermann, "Femtosecond and picosecond laser drilling of metals at high repetition rates and average powers," Opt. Lett. 34, 3304-3306 (2009). [101] M. Gaponenko, F. Labaye, V. Wittwer, C. Paradis, N. Modsching, L. Merceron, A. Diebold, F. Emaury, I. Graumann, C. Phillips, C. J. Saraceno, C. Kränkel, U. Keller, and T. Südmeyer, "Compact Megahertz Coherent XUV Generation by HHG inside an Ultrafast Thin Disk Laser," in Nonlinear Optics, (Optical Society of America, Waikoloa, Hawaii, 2017), paper NTh3A.1.

148

Bibliography

[102] S. Hädrich, M. Krebs, A. Hoffmann, A. Klenke, J. Rothhardt, J. Limpert, and A. Tünnermann, "Exploring new avenues in high repetition rate table-top coherent extreme ultraviolet sources," Light Sci Appl 4 (2015). [103] A. Diebold, F. Emaury, C. J. Saraceno, C. Schriber, M. Golling, T. Südmeyer, and U. Keller, "SESAM mode-locked Yb:CaGdAlO4 thin disk laser with 62 fs pulse generation," Opt. Lett. 38, 3842-3845 (2013). [104] C. Schriber, L. Merceron, A. Diebold, F. Emaury, M. Golling, K. Beil, C. Kränkel, C. J. Saraceno, T. Südmeyer, and U. Keller, "Pushing SESAM modelocked thin-disk lasers to shortest pulse durations," in Advanced Solid State Lasers, (Optical Society of America, Shanghai, 2014), paper AF1A.4. [105] I. J. Graumann, A. Diebold, C. G. E. Alfieri, F. Emaury, B. Deppe, M. Golling, D. Bauer, D. Sutter, C. Kränkel, C. J. Saraceno, C. R. Phillips, and U. Keller, "Peak-power scaling of femtosecond Yb:Lu2O3 thin-disk lasers," Opt. Express. 25, 22519-22536 (2017). [106] C. G. E. Alfieri, A. Diebold, F. Emaury, E. Gini, C. J. Saraceno, and U. Keller, "Improved SESAMs for femtosecond pulse generation approaching the kW average power regime," Opt. Express. 24, 27587-27599 (2016). [107] J. Zhang, J. Brons, M. Seidel, D. Bauer, D. Sutter, V. Pervak, V. Kalashnikov, Z. Wei, A. Apolonski, F. Krausz, and O. Pronin, "Generation of 49-fs pulses directly from distributed Kerr-lens mode-locked Yb:YAG thin-disk oscillator," in Advanced Solid State Lasers, (Optical Society of America, Berlin, 2015), paper ATh4A.7. [108] C. Paradis, N. Modsching, V. J. Wittwer, B. Deppe, C. Kränkel, and T. Südmeyer, "Generation of 35-fs pulses from a Kerr lens mode-locked Yb:Lu2O3 thin-disk laser," Opt. Express. 25, 14918-14925 (2017). [109] G. M. Thomas, T. Omatsu, and M. J. Damzen, "High-power neodymium- doped mixed vanadate bounce geometry laser, mode locked with nonlinear mirror," Appl. Phys. B 108, 125-128 (2012). [110] G. Cerullo, M. B. Danailov, S. D. Silvestri, P. Laporta, V. Magni, D. Segala, and S. Taccheo, "A diode‐pumped nonlinear mirror mode‐locked Nd:YAG laser," Appl. Phys. Lett. 65, 2392-2394 (1994). [111] K. A. Stankov, "25 ps pulses from a Nd:YAG laser mode locked by a frequency doubling β‐BaB2O4 crystal," Appl. Phys. Lett. 58, 2203-2204 (1991). [112] G. M. Thomas, and M. J. Damzen, "30 W Nd:GdVO4 oscillator modelocked with nonlinear mirror," in 2011 Conference on Lasers and Electro-Optics Europe and 12th European Quantum Electronics Conference (CLEO EUROPE/EQEC), (2011), paper 1-1. [113] G. Cerullo, V. Magni, and A. Monguzzi, "Group-velocity mismatch compensation in continuous-wave lasers mode locked by second-order nonlinearities," Opt. Lett. 20, 1785-1787 (1995).

149

Bibliography

[114] I. Buchvarov, G. Christov, and S. Saltiel, "Transient behaviour of frequency doubling mode-locker. Numerical analysis," Optics Communications 107, 281-286 (1994). [115] O. V. Chekhlov, and V. A. Zaporozhchenko, "Mapping of the second- harmonic nonlinear mirror characteristics for laser mode locking and pulse shortening," J. Opt. Soc. Am. B 15, 210-215 (1998). [116] A. A. Mani, D. Lis, Y. Caudano, P. A. Thiry, and A. Peremans, "Optimal performances of a mode-locking technique: Theoretical and experimental investigations of the frequency-doubling nonlinear mirror," Opt. Commun. 284, 398-404 (2011). [117] R. Eckardt, and J. Reintjes, "Phase matching limitations of high efficiency second harmonic generation," IEEE J. Quantum Elect. 20, 1178-1187 (1984). [118] K. Kato, "Second-harmonic generation to 2048 Å in b-BaB2O4," IEEE J. Quantum Elect. 22, 1013-1014 (1986). [119] R. C. Eckardt, H. Masuda, Y. X. Fan, and R. L. Byer, "Absolute and relative nonlinear optical coefficients of KDP, KD*P, BaB2O4, LiIO3, MgO:LiNbO3, and KTP measured by phase-matched second-harmonic generation," IEEE J. Quantum Elect. 26, 922-933 (1990). [120] J. Rothhardt, S. Demmler, S. Hadrich, J. Limpert, and A. Tünnermann, "Octave-spanning OPCPA system delivering CEP-stable few-cycle pulses and 22 W of average power at 1 MHz repetition rate," Opt. Express 20, 10870-10878 (2012). [121] K. A. Stankov, V. P. Tzolov, and M. G. Mirkov, "Compensation of group- velocity mismatch in the frequency-doubling modelocker," Appl. Phys. B 54, 303-306 (1992). [122] J. Zhang, K. F. Mak, S. Gröbmeyer, D. Bauer, D. Sutter, V. Pervak, F. Krausz, and O. Pronin, "Generation of 220 fs, 20 W pulses at 2 µm from Kerr-lens mode-locked Ho:YAG thin-disk oscillator," in Conference on Lasers and Electro- Optics, (Optical Society of America, San Jose, California, 2017), paper SM1I.6. [123] W. Sibbett, A. A. Lagatsky, and C. T. A. Brown, "The development and application of femtosecond laser systems," Opt. Express 20, 6989–7001 (2012). [124] T. Gottwald, C. Stolzenburg, D. Bauer, J. Kleinbauer, V. Kuhn, T. Metzger, S. Schad, D. Sutter, and A. Killi, Recent disk laser development at Trumpf (SPIE, 2012). [125] F. X. Kärtner, J. A. d. Au, and U. Keller, "Mode-locking with slow and fast saturable absorbers-what's the difference?," IEEE J. Sel. Top. Quan. Electron. 4, 159-168 (1998). [126] M. B. Danailov, G. Cerullo, V. Magni, D. Segala, and S. De Silvestri, "Nonlinear mirror mode locking of a cw Nd:YLF laser," Opt. Lett. 19, 792- 794 (1994).

150

Bibliography

[127] O. Pronin, J. Brons, C. Grasse, V. Pervak, G. Boehm, M. C. Amann, V. L. Kalashnikov, A. Apolonski, and F. Krausz, "High-power 200 fs Kerr-lens mode-locked Yb:YAG thin-disk oscillator," Opt. Lett. 36, 4746-4748 (2011). [128] J. Brons, O. Pronin, M. Seidel, V. Pervak, D. Bauer, D. Sutter, V. L. Kalashnikov, A. Apolonski, and F. Krausz, "120 W, 4 μJ from a purely Kerr- lens mode-locked Yb:YAG thin-disk oscillator," presented at the Advanced Solid-State Lasers (ASSL), Paris (France), 2013. [129] P. K. Datta, Shivanand, S. Mukhopadhyay, A. Agnesi, and A. Lucca, "Picosecond pulse generation and its simulation in a nonlinear optical mirrormode-locked laser," Applied Optics 43, 2347-2352 (2004). [130] G. M. Thomas, A. Bäuerle, D. J. Farrell, and M. J. Damzen, "Nonlinear mirror modelocking of a bounce geometry laser," Opt. Express. 18, 12663-12668 (2010). [131] G. M. Thomas, S. P. Chard, and M. J. Damzen, "High power modelocking of a stigmatic bounce geometry laser using a nonlinear mirror," Appl. Phys. B 101, 553-557 (2010). [132] J. Rothhardt, S. Demmler, S. Hädrich, T. Peschel, J. Limpert, and A. Tünnermann, "Thermal effects in high average power optical parametric amplifiers," Opt. Lett. 38, 763-765 (2013). [133] V. A. Shvets, V. S. Aliev, D. V. Gritsenko, S. S. Shaimeev, E. V. Fedosenko, S. V. Rykhlitski, V. V. Atuchin, V. A. Gritsenko, V. M. Tapilin, and H. Wong, "Electronic structure and charge transport properties of amorphous Ta2O5 films," Journal of Non-Crystalline Solids 354, 3025-3033 (2008). [134] T. V. Perevalov, V. A. Gritsenko, S. B. Erenburg, A. M. Badalyan, H. Wong, and C. W. Kim, "Atomic and electronic structure of amorphous and crystalline hafnium oxide: X-ray photoelectron spectroscopy and density functional calculations," Journal of Applied Physics 101, 053704 (2007). [135] G. P. Agrawal, "Chapter 5 - Optical Solitons," in Nonlinear Fiber Optics (Fifth Edition), G. Agrawal, (Academic Press, 2013), pp. 129-191. [136] K. Kato, "Temperature-tuned 90 deg phase-matching properties of LiB3/O5," IEEE Journal of Quantum Electronics 30, 2950-2952 (1994). [137] J.-P. Negel, A. Loescher, D. Bauer, D. Sutter, A. Killi, M. A. Ahmed, and T. Graf, "Second Generation Thin-Disk Multipass Amplifier Delivering Picosecond Pulses with 2 kW of Average Output Power," in Lasers Congress 2016 (ASSL, LSC, LAC), (Optical Society of America, Boston, Massachusetts, 2016), paper ATu4A.5. [138] C. M. Caves, "Quantum limits on noise in linear amplifiers," Phys. Rev. D 26, 1817-1839 (1982). [139] F. Meyer, N. Hekmat, S. Mansourzadeh, F. Fobbe, F. Aslani, M. Hoffmann, and C. J. Saraceno, "Optical rectification of a 100 W average power modelocked thin-disk oscillator," Opt. Lett. 43, 5909-5912 (2018).

151

Bibliography

[140] K. Fritsch, M. Poetzlberger, V. Pervak, J. Brons, and O. Pronin, "All-solid- state multipass spectral broadening to sub-20 fs," Opt. Lett. 43, 4643-4646 (2018). [141] P. Russbueldt, J. Weitenberg, J. Schulte, R. Meyer, C. Meinhardt, H. D. Hoffmann, and R. Poprawe, "Scalable 30 fs laser source with 530 W average power," Opt. Lett. 44, 5222-5225 (2019).

152

Curriculum Vitae

Omitted from the electronic version.

153

Acknowledgements

During my PhD journey, I realized that to go far, you need to stay motivated and focused over a long period and despite all the ups and downs. This, in my opinion, is possible only if you are surrounded by like-minded people, who support you or challenge you depending on the situation. I believe that I had this at ETH Zurich in the Ultrafast Laser Physics group. Thus, I would like to thank some of the people who shared part of this journey with me. I thank Prof. Ursula Keller for offering me this position, giving me the free- dom to develop my ideas, and creating the conditions in which I could perform at my best. I would also like to thank Prof. Thomas Südmeyer for being my co-examiner. It is exciting to have the chance to present my work on thin-disk lasers in front of a scientist who gave a significant contribution to the development of the thin-disk technology, since the early days. I would like to thank Dominik from TRUMPF for his work on the SESAMs, and, in general, the fruitful discussions about thin disks. Also, I would like to thank Dirk and Tom from TRUMPF for many interesting chats at confer- ences. Talking about SESAMs, of course, I would also like to thank Matthias for growing all my SESAMs and guiding me in the design phase. I am very grateful for the research collaborations I had during this thesis. From the University of Neuchâtel, I thank Valentin, Olga, and Thomas, your IBS coated mirrors were a real asset for me. Additionally, from the University of Glasgow, Gregoire, I am looking forward to seeing the results of the project we started together.

155

Acknowledgements

A special thank goes to the thin-disk team. Among many, two things particularly resonated with my attitude, the passion for setting new benchmarks and the excitement for fighting deadlines. I hope this spirit will survive. Prof. Clara Saraceno, the first person I met when I came to ETH for my interview, your determination and passion for laser physics inspired me during this journey. Andreas, my lab buddy for the first year and a half of my PhD, you opened my eyes to the many career options we have. Ivan, we shared the work on the nonlinear-mirror modelocked thin-disk laser, one of the most exciting pro- jects I did in my life. Lukas, you are an ETH MSc, you must know everything. Finally, thank you, Chris, for the numerous discussions, great ideas, and your help to improve my English. You empowered me with some of the finest scripts I could have. I would like to thank my office mates for the time spent together and the pleasant discussions we had. Matteo, to whom I asked for information even before joining this group. Lamia, you guided me through my very first steps at ETH. Jaco, I think we share interests and ambitions more than the office. Arthur, please reveal your breakthroughs to the world. I am very grateful to the Italian community in the ULP group. Cesare, you gave me useful tips about life in Switzerland and delighted me with your elo- quence and diction. Laura, with whom I often had lunch together and who shared some time with me also during the corona time. Last but not least, Luca, we started our journey at ETH the very same day, among the many things we shared I particularly enjoyed our BBQs and I believe that the best is yet to come in our data science journey. A special thank goes to Fabian S., I include you in this list since I expect you to be fluent in Italian after doing tandem with me, I still remember our ultimate two-hour workout. Among the members of the ULP team, Dominik, the hotel room we had in Japan is the best I have had in my life. Jannie, it was nice to share many lunches with you. Lukas G., I really enjoyed discussing with you about short- pulsed Ti:Sapphire lasers, I believe you lived the gold era of laser development. I also would like to thank all the other present and past ULP members for the friendly atmosphere in the group: Ajanta, Aline, Benjamin, Carolin, Cornelia, Fabian B., Jacob, Jannie, Jochen, Jonas, Justinas, Leonard, Marco,

156

Acknowledgements

Misha, Nadja, Nico, Özgür, Pierre-Alexis, Sandro, Sergej, Stefan, Zeno. I wish you all the best! The facilities of the D-PHYS department at ETH Zurich were crucial to many of our successes. In particular, the engineers Marcel and Walter, who empowered our thin-disk lasers with bespoken mechanical solutions. Additionally, thank you, Sandra, for making sure that everything runs flawlessly in the ULP group. Last, I thank my family for their support and, in particular, my uncle Angelo for his guidance during my academic career.

Zurich, July 2020

157