Microwave sources based on high quality factor resonators : modeling, optimization and metrology Zeina Abdallah To cite this version: Zeina Abdallah. Microwave sources based on high quality factor resonators : modeling, optimization and metrology. Optics / Photonic. Université Paul Sabatier - Toulouse III, 2016. English. NNT : 2016TOU30267. tel-01445614v2 HAL Id: tel-01445614 https://tel.archives-ouvertes.fr/tel-01445614v2 Submitted on 22 Jan 2018 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. “It always seems impossible until it’s done!” N. Mandela Acknowledgements My three years journey as a Ph.D. candidate has come to an end. There are countless number of people who believed in me and helped me reach this far. Through this humble acknowledgment, I would like to convey my gratitude to specific individuals that made this leg of the journey possible. These studies were funded by the French national space center (CNES) and the regional council of Midi-Pyrénées, so I would like to take this opportunity to acknowledge them for providing financial assistance. I would like to thank the committee members, Prof. Marc VALLET and Mcf. Anne-Laure BILLABERT for their deep review despite the short time provided to them, as well as their insightful comments and questions. My sincere acknowledgments go to Prof. Vincent GIORDANO, head of my thesis committee and to Dr. Gilles CIBIEL, my technical CNES supervisor, for their helpful comments. I would also thank M. Benoît BENAZET for being part of the committee. And here comes the special acknowledgements… For all these accomplishments, I am extremely indebted to my supervisor and my advisor Prof. Olivier LLOPIS. You encouraged me a lot through these years to overcome many difficulties and you taught me to grow as a self-instructor and as an independent thinker through your guidance, support and encouragement. I would like to thank also Mcf. Arnaud FERNANDEZ, for being helpful and for the deep discussions. In addition, I will never forget the delicious chinese green tea! Thank you again! I thank all the members of MOST team and of the laboratory LAAS-CNRS in general: Audrey, Amar, Olga, Oana, Alexandre, Alessandro, David, Napoléon, Adem, Boris, Vincent and the list goes on and on... Thank you so much for being a great colleagues and a special friends. I am grateful to all the staff and services at LAAS-CNRS. Many thanks to Marie ESTRUGA, Marie-Laure PIERUCCI, Ascension DE SOUSA, Marie-Agnès BELLIERES, and Virginie HUGUENOT for their administrative support and for being helpful every time with a sweet smile. It is extremely hard to convey my deep sense of gratitude to my friends in words: Serge (my lovely evil Wati!), Amani (Dinner? ice-cream? probably both!), Florence (my cutest hostess), Tarek (some aricheh?), Ayad (no weight gainer!!). Simply, you are part of my family. Thank you for your support and help during the difficult moments. It is my fortune to gratefully acknowledge the support of my family members. Mum, Dad, having you in my life is an honor, I know that you gave up things for me to be here today. Mariam, my crazy sister and best friend, thank you for your unlimited support and for always listening to me, mainly thank you for our little Aabous Lulu. Hiba, thank you for the positive vibes. Najah, my sweetest sister-in-law, thank you for always listening to me and never leaving my side when I need. Alaa, Walid, my brothers, my backbones! To you all, I am eternally grateful and thankful. To you all, my precious people, I dedicate this work… Zeina ABDALLAH Toulouse, France December 2016 Table of Contents Gl ossar y ............................................................................ 1 General Introduction ........................................................... 3 Chapter I: Optoelectronic Oscillator ..................................... 7 I.1 Introduction ....................................................................................................... 7 I.2 Microwave oscillators ........................................................................................ 8 I.2.a Noise in microwave oscillators ................................................................... 9 I.2.a.i Phase noise ........................................................................................ 11 I.2.a.ii Phase noise measurements .............................................................. 14 I.2.a.iii Microwave oscillators with best phase noise performances .............. 16 I.3 Optoelectronic oscillators ................................................................................ 18 I.3.a Delay line based OEO .............................................................................. 18 I.3.b Coupled OEO ........................................................................................... 22 I.3.c Optical resonator based OEO................................................................... 23 I.3.c.i Mode matching ................................................................................... 23 I.3.c.ii System stabilization ........................................................................... 25 I.3.c.iii Microwave and optical quality factors ................................................ 25 I.3.d Noises in the OEO: Best phase noise performance .................................. 26 I.4 Conclusion ...................................................................................................... 27 I.5 References ..................................................................................................... 29 Chapter II: Optical Resonator ............................................. 35 II.1 Introduction .................................................................................................... 35 II.2 Optical resonator technologies ....................................................................... 36 II.2.a Fabry-Perot resonator ............................................................................. 36 II.2.b Whispering-gallery mode resonator ......................................................... 37 II.2.c Fiber ring resonator ................................................................................. 39 II.3 Analytical model of an optical ring resonator .................................................. 41 II.3.a Resonator’s transfer function................................................................... 43 II.3.b Optical quality factors .............................................................................. 48 II.3.c Intra-cavity power enhancement factor .................................................... 49 II.4 Characterization techniques ........................................................................... 50 II.4.a Wavelength scan method ........................................................................ 51 II.4.b Cavity ring down method ......................................................................... 52 II.4.c Radio frequency spectral characterization technique ............................... 53 II.4.c.i Measurement setup ........................................................................... 54 II.4.c.ii Measurement example...................................................................... 56 II.5 Active fiber ring resonator and parameters extraction .................................... 57 II.6 100m length passive fiber ring resonator ....................................................... 60 II.6.a FRR 100m P-M without isolator ............................................................... 62 II.6.b FRR characterization .............................................................................. 63 II.7 Conclusion ..................................................................................................... 64 II.8 References .................................................................................................... 66 Chapter III: OEO based on FRR – Modeling ......................... 71 III.1 Introduction ................................................................................................... 71 III.2 Noise sources in an optoelectronic oscillator ................................................. 72 III.2.a Nonlinear optical effects in optical fiber resonator .................................. 72 III.2.a.i Brillouin scattering ............................................................................ 73 III.2.a.ii Rayleigh scattering .......................................................................... 75 III.2.a.iii Raman scattering ............................................................................ 77 III.2.a.iv Four-wave mixing ........................................................................... 77 III.2.b Laser amplitude and frequency noise conversions ................................. 79 III.2.b.i The fiber chromatic dispersion .......................................................... 79 III.2.b.ii The interferometric phenomenon ..................................................... 80 III.2.b.iii The locking method