Hierarchy of coupled mode and envelope models for bi-directional microresonators with Kerr nonlinearity

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Abstract

We consider the interaction of counter-propagating waves in a bi-directionally pumped ring microresonator with Kerr nonlinearity. We introduce a hierarchy of the mode expansions and envelope functions evolving on different time scales set by the cavity linewidth and nonlinearity, dispersion, and repetition rate, and provide a detailed derivation of the corresponding hierarchy of the coupled mode and of the Lugiato-Lefever-like equations. An effect of the washout of the repetition rate frequencies from the equations governing the dynamics of the counter-propagating waves is elaborated in details.

Original languageEnglish
Pages (from-to)1364-1375
Number of pages12
JournalOSA Continuum
Volume3
Issue number6
Early online date18 May 2020
DOIs
Publication statusPublished - 30 Jun 2020

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