Analytic instability thresholds in folded Kerr resonators of arbitrary finesse

Firth, William J. and Geddes, John B. and Karst, Nathaniel J. and Oppo, Gian-Luca (2021) Analytic instability thresholds in folded Kerr resonators of arbitrary finesse. Physical Review A - Atomic, Molecular, and Optical Physics, 103 (2). 023510. ISSN 1050-2947 (https://doi.org/10.1103/PhysRevA.103.023510)

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Abstract

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.