8B Passive Modelocking

Ultrafast Laser Physics

Ursula Keller / Lukas Gallmann

ETH Zurich, Physics Department, Switzerland www.ulp.ethz.ch

Chapter 8: Passive modelocking

Ultrafast Laser Physics ETH Zurich Pulse-shaping in passive modelocking

U. Keller, Ultrafast solid-state lasers, Landolt-Börnstein, Group VIII/1B1, edited by G. Herziger, H. Weber, R. Poprawe, pp. 33-167, 2007, ISBN 978-3-540-26033-2 Slow saturable absorber and dynamic gain saturation

loss

gain

pulse time

Conditions for stable modelocking: 1) at the beginning loss is larger than gain:

2) absorber saturates faster than the gain:

3) absorber recovers faster than the gain: Colliding pulse modelocking (CPM)

Amplifier jet: Rhodamine 6G (R6G) Saturable absorber jet: DODCI (3,3-Diethylocadicarbocyanin) Colliding pulse modelocking (CPM) Modern example: CPM VECSEL

128 fs 2x 90 mW " ! 3.27 GHz $%& # 994 nm '()* +,)-.)(

A. Laurain et al., J. Opt. Soc. Am. B 34(2), 329 – 337 (2017)

VECSEL = Vertical External Cavity Surface-Emitting Laser Loss modulation for a slow and fast saturable absorber

slow saturable absorber: fast saturable absorber: neglect recovery within pulse duration follows immediately incoming power Slow saturable absorber and dynamic gain saturation

loss

gain

pulse time

Assume slow saturable absorber and slow gain saturation net gain window: resonator loss: s-parameter: Slow saturable absorber and dynamic gain saturation

For stable pulse generation we need to have gT < 0 at both beginning and end of the pulse. (see later that this does not always need to be the case - see soliton modelocking)

loss Shorter pulses for larger gain

pulse time Slow saturable absorber and dynamic gain saturation

For stable pulse generation we assume to have gT < 0 at both beginning and end of the pulse.

loss Shorter pulses for larger gain

pulse time

optimize s-parameter: goal in CPM

s Colliding pulse modelocking (CPM)

jet thickness 30-50 µm jet thickness ≈80 µm

Amplifier jet: Rhodamine 6G (R6G) Saturable absorber jet: DODCI (3,3-Diethylocadicarbocyanin) Optimization of s-parameter: • mode size: factor of 4 • colliding pulse in absorber (bi-directional pulse propagation in ring laser): factor of 2 - 3 need thin absorber < spatial extend of pulses (100 fs pulses) s ≈ 12 Slow saturable absorber and dynamic gain saturation Master equation:

SAM (self-amplitude modulation) time shift of pulse

: unsaturated loss of the absorber

Solution: Rhodamin 6G:

With SPM: factor of 2 shorter (Martinez numerically)

H. A. Haus, Theory of modelocking with a slow saturable absorber, IEEE J. Quantum Electron. 11, 736, 1975 Passive mode locking with an ideally fast saturable absorber

Semiconductor and dye Solid-state lasers (e.g. Ti:sapphire) lasers: Kerr lens modelocking (KLM) Dynamic gain saturation Ideally fast saturable absorber G.H.C. New, Opt. Lett. , 42, 1991 Opt. Com. 6, 188, 1974 16 Ultrashort pulse generation with modelocking

KLM Science 286, 1507 (1999)

A. J. De Maria, D. A. Stetser, H. Heynau Appl. Phys. Lett. 8, 174, 1966 Kerr lens modelocking (KLM): 200 ns/div discovered - initially not understood ( magic modelocking ) D. E. Spence, P. N. Kean, W. Sibbett, Opt. Lett. 16, 42, 1991

50 ns/div KLM mechanism explained for the first time:

Nd:glass U. Keller et al., Opt. Lett. 16, 1022, 1991 first passively modelocked laser Q-switched modelocked World record pulse duration at ETH Tages Anzeiger 7./8. Juni 1997 How does such a short pulse look like?

The shortest pulses (≈5 fs at 800 nm) 1.5 µm in the VIS-IR spectral region are still generated with KLM Ti:sapphire lasers speed of light under laser lab conditions KLM is stable spatial extent of a 5-fs pulse Kerr Lens Modelocking (KLM) D. E. Spence, P. N. Kean, W. Sibbett, Optics Lett. 16, 42, 1991

Effective Saturable Absorber Fast Self-Amplitude Modulation Kerr Lens Modelocking (KLM) First Demonstration: D. E. Spence, P. N. Kean, W. Sibbett, Optics Lett. 16, 42, 1991 Explanation: U. Keller et al., Optics Lett. 16, 1022, 1991

Advantages of KLM § very fast thus shortest pulses § very broadband thus broader tunability Disadvantages of KLM § not self-starting § critical cavity adjustments (operated close to the stability limit) § saturable absorber coupled to cavity design (limited application) Kerr Lens Modelocking (KLM)

Ideally fast saturable absorber and cw gain saturation for solid-state lasers (no dynamic pulse-to-pulse gain saturation) Ideally fast saturable absorber modelocking

Master equation: Master equation without SPM and GDD

Limit of very long pulses (cw limit):

H. A. Haus, J. G. Fujimoto, E. P. Ippen, Structures for additive pulse modelocking, J. Opt. Soc. Am. B 8, 2068, 1991 Master equation without SPM and GDD

Comparison with active modelocking:

H. A. Haus, J. G. Fujimoto, E. P. Ippen, Structures for additive pulse modelocking, J. Opt. Soc. Am. B 8, 2068, 1991 Master equation with SPM and GDD Linearized operators: self-phase modulation (SPM) Linearized operators: group delay dispersion (GDD)

Fourier transform: Master equation with SPM and GDD

Here, normalize pulse envelope as follows:

Therefore: Master equation with SPM and GDD

no SPM and GDD:

H. A. Haus, J. G. Fujimoto, E. P. Ippen, Structures for additive pulse modelocking, J. Opt. Soc. Am. B 8, 2068 (1991) Master equation with SPM and GDD

H. A. Haus, J. G. Fujimoto, E. P. Ippen, J. Opt. Soc. Am. B 8, 2068 (1991) Master equation with SPM and GDD

Stability of solution (a simple criterion): Master equation with SPM and GDD

H. A. Haus, J. G. Fujimoto, E. P. Ippen, J. Opt. Soc. Am. B 8, 2068 (1991) Master equation with SPM and GDD

H. A. Haus, J. G. Fujimoto, E. P. Ippen, J. Opt. Soc. Am. B 8, 2068, 1991 Self-starting modelocking?

E. P. Ippen, Principles of passive modelocking, Appl. Phys. B 58, 159, 1994 Ultrashort pulse generation with modelocking A. J. De Maria, D. A. Stetser, H. Heynau Appl. Phys. Lett. 8, 174, 1966 Q-switching instabilities continued to be a problem until 1992

200 ns/div SESAM First passively modelocked (diode-pumped) solid-state laser without Q-switching 50 ns/div U. Keller et al. Nd:glass Opt. Lett. 17, 505, 1992 KLM first passively modelocked laser Q-switched modelocked IEEE JSTQE 2, 435, 1996 Nature 424, 831, 2003

1960 1970 1980 1990 2000 Year Flashlamp-pumped Diode-pumped solid-state lasers solid-state lasers (first demonstration 1963) SESAM technology – a key technical know-how U. Keller et al. Opt. Lett. 17, 505, 1992 IEEE JSTQE 2, 435, 1996 Progress in Optics 46, 1-115, 2004 Nature 424, 831, 2003

Output coupler Gain

SESAM SEmiconductor Saturable Absorber Mirror

self-starting, stable, and reliable modelocking of diode-pumped ultrafast solid-state lasers KLM vs. Soliton modelocking

Kerr lens modelocking (KLM) Soliton modelocking Fast saturable absorber not so fast saturable absorber D. E. Spence, P. N. Kean, W. Sibbett F. X. Kärtner, U. Keller, Opt. Lett. 16, 42, 1991 Opt. Lett. 20, 16, 1995 Passive mode locking with slow saturable absorbers

Semiconductor lasers: Ion-doped solid-state lasers: Dynamic gain saturation Constant gain saturation: G.H.C. New, soliton modelocking Opt. Com. 6, 188, 1974 F. X. Kärtner, U. Keller, Opt. Lett. 20, 16, 1995 Pulse-shaping

Gain window can be Solid-state up to 20 times longer KLM and SESAM than the pulse before mode locking becomes unstable VECSEL

fast/broadband sat. abs. not so fast sat. abs. critical cavity adjustment: absorber independent of KLM better at cavity cavity design stability limit self-starting typically not self-starting

For stable pulse generation it was initially assumed that we need gT < 0 at both beginning and end of the pulse. This is however not the case! See SESAM modelocking with slow saturable absorber and soliton modelocking Soliton modelocking: GDD negative, n2 > 0

Passive modelocking with slow absorber

Linearized operator for absorber:

Master equation: Soliton modelocking: GDD negative, n2 > 0 F. X. Kärtner, U. Keller, Optics Lett. 20, 16, 1995 Invited Paper: F. X. Kärtner, I. D. Jung, U. Keller, IEEE JSTQE, 2, 540, 1996

Soliton Perturbation Theory: continuum soliton only GDD & SAM (no SPM)

spreading

Frequency domain Time domain Stabilization: Dispersion spreads continuum out where it sees more loss Soliton modelocking: GDD negative, n2 > 0

Solution: stable soliton pulses ≈ 0

Frequency domain Time domain

Stabilization: Dispersion spreads continuum out where it sees more loss Experimental confirmation: example Ti:sapphire laser

SESAM: LT-GaAs Impulse response measured with 300 fs pulses clearly a slow saturable absorber No KLM: cavity operated in the middle of cavity stability regime (and use etalon for bandwidth limitation)

I. D. Jung, F. X. Kärtner, L. R. Brovelli, M. Kamp, U. Keller, "Experimental verification of soliton modelocking using only a slow saturable absorber," Opt. Lett., vol. 20, pp. 1892-1894, 1995 Experimental confirmation: example Ti:sapphire laser

Solution: soliton pulse soliton phase per resonator roundtrip

Stability (soliton perturbation theory): continuum loss lc is larger than soliton loss ls

Normalized abs. recovery

High dynamic range autocorrelation: 330 fs Opt. Lett. 20, 1889 (1995)

I. D. Jung, F. X. Kärtner, L. R. Brovelli, M. Kamp, U. Keller, "Experimental verification of soliton modelocking using only a slow saturable absorber," Opt. Lett., vol. 20, pp. 1892-1894, 1995 Soliton modelocking with GDD>0, n2<0 (2) Cascaded nonlinearity for effective negative n2: soliton modelocking with positive GDD χ

• Pulse duration: 166 fs • Output power: 1.2 W • Repetition rate: 10.6 GHz

A. S. Mayer, C. R. Phillips, U. Keller, Nature Commun. 8, 1673 (2017) Slow saturable absorber modelocking

R. Paschotta, U. Keller, Appl. Phys. B 73, 653, 2001

Dominant stabilization process: Picosecond domain: absorber delays pulse The pulse is constantly moving backward and can swallow any noise growing behind itself Femtosecond domain: dispersion in soliton modelocking Coupled cavity modelocking

Chapter 8.5: for historical reasons summarized here - not used much anymore The soliton laser L. F. Mollenauer, R. H. Stolen, "The soliton laser," Optics Lett., vol. 9, pp. 13-15, 1984. Additive pulse modelocking (APM) K. J. Blow and D. Wood, "Modelocked lasers with nonlinear external cavities," J. Opt. Soc. Am B, vol. 5, pp. 629-632, 1988 P. N. Kean, X. Zhu, D. W. Crust, R. S. Grant, N. Landford, W. Sibbett, "Enhanced modelocking of color center lasers," Optics Lett., vol. 14, pp. 39-41, 1989 9 E. P. Ippen, H. A. Haus, L. Y. Liu, "Additive Pulse Modelocking," J. Opt. Soc. Am. B, vol. 6, pp. 1736-1745, 1989 Resonant passive modelocking (RPM) U. Keller, W. H. Knox, and H. Roskos, "Coupled-Cavity Resonant Passive Modelocked Ti:Sapphire Laser," Optics Lett., vol. 15, pp. 1377-1379, 1990 H. A. Haus, U. Keller, and W. H. Knox, "Theory of Coupled-Cavity Modelocking with a Resonant Nonlinearity," J. Opt. Soc. Am. B, vol. 8, pp. 1252-1258, 1991