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Modal expansion approach to optical-frequency-comb generation with monolithic whispering-gallery-mode resonators

Yanne K. Chembo and Nan Yu
Phys. Rev. A 82, 033801 – Published 7 September 2010
Physics logo See Viewpoint: Tiny resonators generate a large optical spectrum

Abstract

We describe a general framework based on modal expansion for the study of optical-frequency combs generated with monolithic whispering-gallery-mode resonators. We obtain a set of time-domain rate equations describing the dynamics of each mode as a function of the main characteristics of the cavity, namely, Kerr nonlinearity, absorption, coupling losses, and cavity dispersion (geometrical and material). A stability analysis of the various side modes is performed, which finds analytically the threshold power needed for comb generation. We show that the various whispering gallery modes are excited in a nontrivial way, strongly dependent on the value of the overall cavity dispersion. We demonstrate that the combs are not simply generated through a direct transfer of energy from the pumped mode to all their neighbors but rather through complex intermediate interactions. Anomalous cavity dispersion is also demonstrated to be critical for these cascading processes, and comb generation is thereby unambiguously linked to modulational instability. This theory accurately describes the emergence of spectral modulation and free spectral-range tunability in the comb. It also enables a clear understanding of the various phenomena responsible for the spectral span limitation. Our theoretical predictions are in excellent agreement with the numerical simulations, and they successfully explain the internal mechanisms responsible for the generation of hundreds of Kerr modes in monolithic whispering-gallery-mode resonators.

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  • Received 6 April 2010

DOI:https://doi.org/10.1103/PhysRevA.82.033801

©2010 American Physical Society

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Tiny resonators generate a large optical spectrum

Published 7 September 2010

Theoretical analysis now explains how whispering-gallery-mode resonators can be used to effectively generate broad optical frequency combs.

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Authors & Affiliations

Yanne K. Chembo* and Nan Yu

  • Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, California 91109, USA

  • *yanne.chembo@jpl.nasa.gov; Present address: Optics Department, FEMTO-ST Institute, UMR CNRS 6174, 16 Route de Gray, F-25030 Besançon CEDEX, France.

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Issue

Vol. 82, Iss. 3 — September 2010

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