Analytic instability thresholds in folded Kerr resonators of arbitrary finesse

William J. Firth, John B. Geddes, Nathaniel J. Karst, Gian-Luca Oppo

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We present analytic threshold formulas applicable to both dispersive (time-domain) and diffractive (pattern- forming) instabilities in Fabry-Perot Kerr cavities of arbitrary finesse. We do so by extending the gain-circle technique, recently developed for counterpropagating fields in single-mirror-feedback systems, to allow for an input mirror. In time-domain counterpropagating systems, walk-off effects are known to suppress cross- phase modulation contributions to dispersive instabilities. Applying the gain-circle approach with appropriately adjusted cross-phase couplings extends previous results to arbitrary finesse, beyond mean-field approximations, and describes Ikeda instabilities.
Original languageEnglish
Article number023510
Number of pages5
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number2
Publication statusPublished - 9 Feb 2021


  • analytic instability thresholds
  • folded Kerr resonators
  • arbitrary finesse
  • gain-circle technique
  • Ikeda instabilities


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