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Micro-Combs: a Novel Generation of Optical Sources Micro-combs: a novel generation of optical sources Article (Published Version) Pasquazi, Alessia, Peccianti, Marco, Razzari, Luca, Moss, David J, Coen, Stéphane, Erkintalo, Miro, Chembo, Yanne K, Hansson, Tobias, Wabnitz, Stefan, Del’Haye, Pascal, Xue, Xiaoxiao, Weiner, Andrew M and Morandotti, Roberto (2018) Micro-combs: a novel generation of optical sources. Physics Reports, 729 (2018). pp. 1-81. ISSN 03701573 This version is available from Sussex Research Online: http://sro.sussex.ac.uk/id/eprint/78041/ This document is made available in accordance with publisher policies and may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher’s version. Please see the URL above for details on accessing the published version. Copyright and reuse: Sussex Research Online is a digital repository of the research output of the University. Copyright and all moral rights to the version of the paper presented here belong to the individual author(s) and/or other copyright owners. To the extent reasonable and practicable, the material made available in SRO has been checked for eligibility before being made available. Copies of full text items generally can be reproduced, displayed or performed and given to third parties in any format or medium for personal research or study, educational, or not-for-profit purposes without prior permission or charge, provided that the authors, title and full bibliographic details are credited, a hyperlink and/or URL is given for the original metadata page and the content is not changed in any way. http://sro.sussex.ac.uk Physics Reports 729 (2018) 1–81 Contents lists available at ScienceDirect Physics Reports journal homepage: www.elsevier.com/locate/physrep Micro-combs: A novel generation of optical sources Alessia Pasquazi b,a, *, Marco Peccianti b,a , Luca Razzari a, David J. Moss c,a , Stéphane Coen d, Miro Erkintalo d, Yanne K. Chembo e,f , Tobias Hansson a,g , Stefan Wabnitz g, Pascal Del'Haye h, Xiaoxiao Xue i,j , Andrew M. Weiner i, Roberto Morandotti a,k,l, ** a INRS-EMT, 1650 Blvd. Lionel-Boulet, Varennes, Québec J3X 1S2, Canada b Department of Physics and Astronomy, University of Sussex, Brighton BN1 9QH, UK c Centre for Microphotonics, Swinburne University of Technology, Hawthorn Victoria, 3122, Australia d The Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, The University of Auckland, Auckland 1142, New Zealand e FEMTO-ST Institute, Univ. Bourgogne Franche-Comté, CNRS, Optics Department, 15B Avenue des Montboucons, 25030 Besançon cedex, France f GeorgiaTech-CNRS Joint International Laboratory [UMI 2958], Atlanta Mirror Site, School of Electrical and Computer Engineering, 777 Atlantic Drive NW, Atlanta, GA 30332, USA g Dipartimento di Ingegneria dell'Informazione, Università di Brescia, and INO-CNR, via Branze 38, 25123 Brescia, Italy h National Physical Laboratory, Teddington TW11 0LW, UK i School of Electrical and Computer Engineering, Purdue University, 465 Northwestern Avenue, West Lafayette, IN 47907-2035, USA j Department of Electronic Engineering, Tsinghua University, Beijing 100084, China k Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610054, China l National Research University of Information Technologies, Mechanics and Optics, St Petersburg, Russia article info a b s t r a c t Article history: The quest towards the integration of ultra-fast, high-precision optical clocks is reflected Accepted 25 August 2017 in the large number of high-impact papers on the topic published in the last few years. Available online 12 October 2017 This interest has been catalysed by the impact that high-precision optical frequency combs Editor: Donna Strickland (OFCs) have had on metrology and spectroscopy in the last decade [1–5]. OFCs are often referred to as optical rulers: their spectra consist of a precise sequence of discrete and equally-spaced spectral lines that represent precise marks in frequency. Their importance was recognised worldwide with the 2005 Nobel Prize being awarded to T.W. Hänsch and J. Hall for their breakthrough in OFC science [5]. They demonstrated that a coherent OFC source with a large spectrum – covering at least one octave – can be stabilised with a self-referenced approach, where the frequency and the phase do not vary and are completely determined by the source physical parameters. These fully stabilised OFCs solved the challenge of directly measuring optical frequencies and are now exploited as the most accurate time references available, ready to replace the current standard for time. Very recent advancements in the fabrication technology of optical micro-cavities [6] are contributing to the development of OFC sources. These efforts may open up the way to realise ultra-fast and stable optical clocks and pulsed sources with extremely high repetition-rates, in the form of compact and integrated devices. Indeed, the fabrication of high-quality factor (high-Q) micro-resonators, capable of dramatically amplifying the optical field, can be considered a photonics breakthrough that has boosted not only the scientific investigation of OFC sources [7–13] but also of optical sensors and compact light modulators [6,14]. * Corresponding author at: Department of Physics and Astronomy, University of Sussex, Brighton BN1 9QH, UK. ** Corresponding author at: INRS-EMT, 1650 Blvd. Lionel-Boulet, Varennes, Québec J3X 1S2, Canada. E-mail addresses: [email protected] (A. Pasquazi), [email protected] (R. Morandotti). https://doi.org/10.1016/j.physrep.2017.08.004 0370-1573/' 2017 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/). 2 A. Pasquazi et al. / Physics Reports 729 (2018) 1–81 In this framework, the demonstration of planar high-Q resonators, compatible with silicon technology [10–14], has opened up a unique opportunity for these devices to provide entirely new capabilities for photonic-integrated technologies. Indeed, it is well acknowledged by the electronics industry that future generations of computer processing chips will inevitably require an extremely high density of copper-based interconnections, significantly increasing the chip power dissipation to beyond practical levels [15–17]; hence, conventional approaches to chip design must undergo radical changes. On-chip optical networks, or optical interconnects, can offer high speed and low energy per- transferred-bit, and micro-resonators are widely seen as a key component to interface the electronic world with photonics. Many information technology industries have recently focused on the development of integrated ring resonators to be employed for electrically-controlled light modulators [14– 17], greatly advancing the maturity of micro-resonator technology as a whole. Recently [11–13], the demonstration of OFC sources in micro-resonators fabricated in electronic (i.e. in complementary metal oxide semiconductor (CMOS)) compatible platforms has given micro-cavities an additional appeal, with the possibility of exploiting them as light sources in microchips. This scenario is creating fierce competition in developing highly efficient OFC generators based on micro-cavities which can radically change the nature of information transport and processing. Even in telecommunications, perhaps a more conventional environment for optical technologies, novel time-division multiplexed optical systems will require extremely stable optical clocks at ultra-high pulse repetition-rates towards the THz scale. Furthermore, arbitrary pulse generators based on OFC [18,19] are seen as one of the most promising solutions for this next generation of high-capacity optical coherent communication systems. This review will summarise the recent exciting achievements in the field of micro-combs, namely optical frequency combs based on high-Q micro- resonators, with a perspective on both the potential of this technology, as well as the open questions and challenges that remain. ' 2017 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Contents 1. Micro-combs: small, efficient and fast sources ......................................................................................................................................3 2. Micro-resonator technologies for micro-combs.....................................................................................................................................4 2.1. Technologies for bulk whispering-gallery mode resonators.....................................................................................................5 2.2. CMOS—Compatible integrated micro-resonators......................................................................................................................6 3. Modelling of optical micro-resonators with coupled-mode theory...................................................................................................... 10 3.1. Mathematical formulation of the optical field in the resonators.............................................................................................. 11 3.1.1. Spatial problem: eigenvalues and eigenmodes .......................................................................................................... 12 3.1.2. Temporal problem: formal derivation
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