Design of Nonlinear Integrated Devices for Quantum Optics Applications
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M. SANTANDREA DESIGN OF NONLINEAR INTEGRATED DEVICES FOR QUANTUM OPTICS APPLICATIONS Design of nonlinear integrated devices for quantum optics applications Der Naturwissenschaftlichen Fakultät der Universität Paderborn zur Erlangung des Doktorgrades Dr. rer. nat. vorgelegt von MATTEO SANTANDREA 2019 Erklärung der Selbstständigkeit Hiermit versichere ich, die vorliegende Arbeit selbstständig verfasst und keine an- deren als die angegebenen Quellen und Hilfsmittel benutzt sowie die Zitate deutlich kenntlich gemacht zu haben. Paderborn, den November 21, 2019 Matteo Santandrea Erstgutachter: Prof. Dr. Christine Silberhorn Zweitgutachter: Prof. Dr. Torsten Meier Vertreter des Mittelbaus: Dr. Uwe Gerstmann Vorsitzender der Prüfungskommission: Prof. Dr. Dirk Reuter Tag der Abgabe: 28. 11.2019 Contents Erklärung der SelbstständigkeitE Summaryv Zusammenfassung vii Preface ix Introduction xiii List of abbreviations and nomenclature xv I Background1 1 Integrated waveguides3 1.1 Ray optics description . .3 1.2 Rigorous mathematical description . .5 1.3 Asymmetric slab waveguide . .8 1.4 Numerical methods . 11 2 Nonlinear optics in waveguiding structures 13 2.1 Nonlinear material response . 13 2.1.1 Second-order nonlinear polarisation density . 17 2.2 Nonlinear coupled-mode theory in waveguides . 19 2.2.1 Three wave mixing in waveguides . 20 2.2.2 SFG at perfect phase matching . 22 2.2.3 Phase matching spectrum of SHG processes under NPDA . 23 i Contents 2.2.4 Final remarks . 25 2.3 Understanding and tailoring three wave mixing . 27 2.3.1 Birefringent phase matching . 27 2.3.2 Quasi-phase matching . 31 2.4 Elements of ultrafast quantum optics . 34 2.4.1 PDC and broadband modes . 35 2.4.2 FC and broadband modes . 36 2.4.3 Decorrelated JSA . 38 3 Nonlinear materials and waveguide fabrication 41 3.1 Lithium niobate . 41 3.1.1 Optical properties . 42 3.1.2 Diffused waveguide in LN . 45 3.1.3 Thin film LNOI . 47 3.2 KTP . 48 3.2.1 Optical properties . 50 3.2.2 Rb exchanged waveguides in KTP . 51 3.3 Linear characterisation . 54 3.3.1 Propagation losses . 54 3.3.2 Waveguide-fibre coupling efficiency . 56 3.4 Periodic poling . 57 II Design of nonlinear processes 59 4 Design of nonlinear processes in KTP 61 4.1 Frequency conversion IR! UV........................ 61 4.1.1 Sample fabrication . 62 4.1.2 Linear characterisation . 65 4.1.3 Frequency conversion measurement . 67 4.2 Decorrelated PDC source at 1300nm . 76 5 Effect of inhomogeneities in nonlinear systems 83 5.1 Qualitative model . 84 ii Contents 5.1.1 Numerical analysis of j@w∆βj for Ti:LN waveguides . 86 5.2 Phase matching in inhomogeneous waveguides. 90 5.2.1 Mathematical modelling of waveguide inhomogeneities . 90 5.2.2 Analysis of different types of noises . 92 5.2.3 Impact of fabrication errors in squeezing generation. 96 5.2.4 Impact of fabrication errors on quantum information encoding. 99 5.2.5 Impact of fabrication errors on the performance of a bandwidth compressor. 100 5.3 Reconstruction of sample inhomogeneity . 105 5.3.1 Experiment . 105 5.4 Correction of fabrication imperfection . 111 5.4.1 Simulation of the inhomogeneous system and its correction . 112 5.5 General theory of waveguide inhomogeneities . 115 5.5.1 Mathematical formulation . 116 5.5.2 Simulation of inhomogeneous systems . 117 5.5.3 General design rule for nonlinear systems . 118 5.5.4 Comparison with simulations of different physical systems . 120 6 Second harmonic losses 123 6.1 Measurement Strategy and Theory . 124 6.2 Fitting procedure . 127 6.3 Results . 128 7 Design of nonlinear processes in LNOI 135 7.1 Dispersion relations of LNOI waveguides . 135 7.1.1 Modelling of LNOI waveguides . 135 7.1.2 Numerical derivation of the dispersion relations . 137 7.1.3 Dependence of the dispersion relation on the waveguide geome- try: a qualitative analysis . 138 7.2 Process engineering in LNOI waveguides . 143 7.2.1 ∆β contour lines: a novel method of analysis . 143 7.2.2 Engineering of PDC processes in LNOI waveguides . 144 7.3 Pure degenerate PDC states in LNOI . 151 iii Contents 7.3.1 Identification of the design parameters . 151 7.3.2 Sensitivity of the PDC process to fabrication errors . 153 7.3.3 Conversion efficiency of type II PDC . 155 7.4 Analysis of facet reflectivity . 161 8 Conclusions 169 III Appendix 171 A Coefficients for LNOI waveguides 173 Acknowledgement 179 Bibliography 181 iv Summary In this work, we theoretically and experimentally investigate the design and the performance of integrated nonlinear optical devices for quantum optics applications. We discuss the in-house fabrication of two KTP systems implementing two processes of interest for the quantum optical community. The first sample performs a frequency conversion bridging the gap between the ultraviolet and the infrared range and the sec- ond is an infrared source of decorrelated photon pairs. We show that the performance of the samples is affected by fabrication imperfections and expand the discussion to the case of nonlinear processes in lithium niobate waveguides. We develop a model that provides design rules to optimise the spectral quality of nonlinear devices and discover that such a theory can be extended to nonlinear processes realised in a wide variety of nonlinear systems. To improve the characterisation of our samples, we develop a technique to estimate the losses of the second harmonic field in a nonlinear waveguide system. The work is completed by an in-depth analysis of the effect of the waveguide geometry in deter- mining the dispersion and nonlinear properties of lithium niobate on insulator (LNOI) waveguides. We conclude with a discussion on the impact of fabrication errors on the performance of these systems. v Zusammenfassung Diese Arbeit behandelt die theoretische und experimentelle Untersuchung integri- erter nichtlinearer optischer Bauelemente für quantenoptische Anwendungen. Wir betrachten zwei KTP-Systeme aus eigner Herstellung, welche für die quantenop- tische Gemeinschaft interessante Prozesse realisieren. Die erste Probe führt eine Fre- quenzkonversion durch, um die Lücke zwischen dem Ultraviolett- und dem Infrarot- bereich zu überbrücken. Die zweite Probe ist eine Infrarotquelle für dekorrelierte Pho- tonenpaare. Wir zeigen, dass die nichtlinearen Eigenschaften der Proben durch Imper- fektionen im Herstellungsprozess beeinflusst werden und erweitern die Untersuchun- gen um Lithiumniobat Systeme. Wir entwickeln ein Modell, das Entwurfsregeln zur Optimierung der spektralen Qualität nichtlinearer Bauelemente enthält. Wie zeigen, dass diese Theorie auf eine Vielzahl nichtlinearer Systeme ausgeweitet werden kann. Um die Charakterisierung unserer Proben zu verbessern, entwickeln wir eine Meth- ode zur Verlustabschätzung des zweiten harmonischen Feldes in nichtlinearen Wellen- leitern. Die Arbeit wird durch eine eingehende Analyse des Einflusses der Wellenleit- ergeometrie auf die Bestimmung der Dispersion und der nichtlinearen Eigenschaften von Lithiumniobat auf Isolator (LNOI) Wellenleitern vervollständigt. Wir schließen mit einer Diskussion der Auswirkungen von Fabrikationsfehlern auf die Eigenschaften dieser Systeme. vii Preface The work of this doctoral thesis has been performed during the years 2015-2019 in the IQO (Integrated Quantum Optics) group of Prof. Dr. Christine Silberhorn. We started our doctoral studies with the task of optimising the fabrication of periodically poled waveguides written in potassium titanyl phosphate (KTP). During the first one and a half year, we learnt the pre-existing techniques for the in-house fabrication of periodically poled KTP waveguide and helped optimising them, both by improving the processing steps and by characterising the properties of the fabricated samples. The direct involvement in the fabrication of KTP samples led to a deep understanding of waveguide processing and its limitations. This helped addressing the challenges presented by the fabrication process of nonlinear systems. Beside improving the wave- guide processing, we developed new techniques for the characterisation of the KTP waveguides. In particular, we optimised the technique to measure the propagation losses of these system, providing useful feedback for the improvement of the fabrica- tion process. Alongside the production of KTP samples, we were also actively involved in the modelling of these systems and we helped designing the first periodically poled, rubidium-exchanged ridge KTP waveguide, in collaboration with the group of Prof. Kip (Helmut Schmidt University, Hamburg) - see publications VI and VII here below. Our work in the cleanroom was focused on the production of two different types of KTP samples. The first type implemented a sum frequency generation process to con- vert light from the IR to the UV. The target application was the realisation of a quan- tum frequency converter as an interface between ion qubits and single photons. The second type implemented a parameteric down conversion process for the genertion of heralded pure single photons in the telecom O-band - see publication IV below. Interestingly, the phase matching properties of the second sample were very different from the theoretical expectation. Therefore, we investigated the reasons behind such behaviour and discovered that the effect of fabrication imperfections in our systems was much higher than formerly believed. For this reason, we spent the following years developing a model to properly describe the impact of fabrication imperfections onto the nonlinear performance of the nonlinear systems produced in our cleanroom. This model