Quantitative Modeling of Gain in Quantum Cascade Lasers under Operational Intensities Winge, David 2016 Link to publication Citation for published version (APA): Winge, D. (2016). Quantitative Modeling of Gain in Quantum Cascade Lasers under Operational Intensities. Lund University, Faculty of Science, Department of Physics, Division of Mathematical Physics. 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LUND UNIVERSITY PO Box 117 221 00 Lund +46 46-222 00 00 Quantitative Modeling of Gain in Quantum Cascade Lasers under Operational Intensities by David Winge Thesis for the degree of Doctor of Philosophy Thesis advisors: Prof. Andreas Wacker, Dr. Peter Samuelsson Faculty opponent: Prof. Jacob B. Khurgin To be presented, with the permission of the Faculty of Science of Lund University, for public criticism in the Rydberg lecture hall (Rydbergsalen) at the Department of Physics on Friday, the 25th of November 2016 at 13:15. Organization Document name LUND UNIVERSITY DOCTORAL THESIS Department of Physics Date of disputation Box 118 2016-11-25 221 00 LUND Sponsoring organization Sweden Author(s) David Winge Title Quantitative Modeling of Gain in Quantum Cascade Lasers under Operational Intensities Abstract This thesis adresses modeling of quantum cascade lasers using non-equilibrium Green’s functions. Focus lies on the quantitative modeling of the gain when the systems are exposed to strong laser fields, as under realistic opertional conditions. In the first part, an introduction to the general concepts is provided, together with a discussion on approximate analytic expressions. The second part consists of the six papers listed below. Paper I analyzes the temperature dependence of the gain and current of a terahertz quantum cas- cade laser. Paper II provides details of the implementiation of the non-equilibriun Green’s function formalism for simulations of transport in quantum cascade lasers. Paper III demonstrates a microscopic approach to simulate the second harmonic generation of a mid-IR quantum cascade laser. Paper IV documents the implementation of a rudimentary form of the GW-approximation for the electron-electron scattering self-energy. Paper V analyzes a proposed gain mechanism in superlattices, and presents an optimized structure plausible for laser operation. Paper VI shows simulation results of 16 samples from 5 different laboratories. From this systematic study, trends with repspect to the growth place are identified. DOKUMENTDATABLAD enl SIS 61 41 21 Key words non-linear response, quantum cascade lasers, non-equilibrium Green’s function theory Classification system and/or index terms (if any) Supplementary bibliographical information Language English ISSN and key title ISBN 978-91-7753-046-6 (print) 978-91-7753-047-3 (pdf) Recipient’s notes Number of pages Price 162 Security classification Distributor David Winge, Division of Mathematical Physics, Department of Physics, Sölvegatan 14A, SE-223 62 Lund, Sweden I, the undersigned, being the copyright owner of the abstract of the above-mentioned dissertation, hereby grant to all reference sources the permission to publish and disseminate the abstract of the above-mentioned dissertation. Signature Date 2016-11-01 Quantitative Modeling of Gain in Quantum Cascade Lasers under Operational Intensities by David Winge Thesis for the degree of Doctor of Philosophy Thesis advisors: Prof. Andreas Wacker, Dr. Peter Samuelsson Faculty opponent: Prof. Jacob B. Khurgin To be presented, with the permission of the Faculty of Science of Lund University, for public criticism in the Rydberg lecture hall (Rydbergsalen) at the Department of Physics on Friday, the 25th of November 2016 at 13:15. A doctoral thesis at a university in Sweden takes either the form of a single, cohesive research study (monograph) or a summary of research papers (compilation thesis), which the doctoral student has written alone or together with one or several other author(s). In the latter case the thesis consists of two parts. An introductory text puts the research work into context and summarizes the main points of the papers. Then, the research publications themselves are reproduced, together with a description of the individual contributions of the authors. The research papers may either have been already published or are manuscripts at various stages (in press, submitted, or in draft). Cover illustration: Coherence in Superlattice. Adapted from Fig. 4 of Paper V. Funding information: The thesis work was financially supported by the Swedish Research Council (VR). © David Winge 2016 Paper I ©2013 by Springer Paper II ©2013 by IEEE Paper III ©2014 by Optical Society of America Paper IV published 2016 under licence (CC-BY) by IOP Publishing Ltd Paper V published 2016 under licence (CC-BY) by American Institute of Physics Paper VI ©2016 by American Institute of Physics Faculty of Science, Department of Physics isbn: 978-91-7753-046-6 (print) isbn: 978-91-7753-047-3 (pdf) issn: <ISSN number> Printed in Sweden by Media-Tryck, Lund University, Lund 2016 Acknowledgments I owe my deepest gratitude to my supervisor Andreas Wacker. Thank you for bringing me to Austria to meet the devouted and inspiring quantum cascade laser community, for introducing me to your colleques and showing me all the inter- esting work that could be done. Thank you for letting me choose my own way, and for supporting me in everything I tried. I highly value all the things that you have taught me, and all the things that you have helped me teach myself. Doing my PhD closely together with Martin Frankié has made the studies and the research more fun, much easier, and I think, better. Thank you for sharing thoughts and ideas, for discussing any problem or question, and for inviting me to your and Fridas place for the best soup. Being a part of our bigger research group has been a real pleasure. Thank you Bahareh, Fikkeraddis, Gediminas and Tim, and I wish Kevin the best of luck in Gothenburg! I would like to thank my co-supervisor Peter Samuelsson, for keeping an eye on me these four years. My sincerest thanks to Claudio, for providing valuable discussions on many-body physics. I have had a long and fruitful collaboration with Mauro F. Pereira at Sheffield Hallam University, and we always manage to have a good time when we meet. My warm thanks to Dragan and Andrew for inviting to me to Leeds University, and for taking very good care of me during my short visit. I would like to show my gratitude to the seniors at our division who invest a lot of time in preparing suitable courses for us PhD students. This makes a true difference for us. Thank you Gunnar, for following the tradition of Francesc and Elife in creating the v including and loving atmosphere among the students on our floor, and all of our students, for their wholehearted participation in this endeavor. This place would not be the same without Katarina, whose tireless care of all of us makes this floor like a second home. I would not have enjoyed my time as a PhD student as much if it were not for my old friends from the Physics department, Johannes, Sanna, Fredrik and Jon. You will always be close to my heart, together with friends like Hamse and André. I also want to thank my great parents, Berit and Harald, for always being only a phonecall away, if only so to start my sour car. Thank you Lena, for being a hero when I need it, and for being it all the other times as well. For all your support, and all your love. Even though Malmö can be rough this time of year, together we keep out the cold. vi Populärvetenskaplig sammanfattning Ljus består av elektromagnetiska vågor som pulserar genom universum med olika frekvenser. Vanligt ljus, som det som kommer från solen och från våra lampor, innehåller ett spektrum av många olika frekvenser. De olika vågornas toppar och dalar svänger inte heller i takt, utan är förskjutna i förhållande till varandra. I laser- ljus däremot, svänger alla vågor samtidigt upp och ner och med samma frekvens. Vanligt ljus kan liknas vid de kaosartade applåderna efter ett bejublat framträdan- de, medan laserljuset är det taktfasta klappandet för att få till ett extranummer. Användningsområdena för laserteknik blir hela tiden fler och fler, och idag finns lasern både i dvd-spelaren, i metallindustrin och på ögonklinken. Våra ögon har förmågan att uppfatta en viss del av ljusets spektrum, från de djuprö- daste färgerna till de violetta nyanserna. Andra arter är mer receptiva; näsgrop- sormen kan uppfatta infraröda signaler och tornfalken kan upptäcka ultravioletta reflektioner från gnagares urin på marken. Idag kan vi producera laserljus i många frekvensområden, men ännu inte i hela det elektro-magnetiska spektrumet. En illustration av detta kan ses i kappan till denna avhandling, i figur 1.1. Ett ut- vecklingsområde är ett frekvensområde som kallas Terahertz (THz), som ligger en bit nedanför det infraröda som näsgropsormen kan uppfatta.