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

Abstract

We consider 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 dynamics of the counter-propagating waves is elaborated in details.

to appear in OSA Continuum

References in corpus (4)

• Non-Hermitian Ring Laser Gyroscopes with Enhanced Sagnac Sensitivity
• Experimental demonstration of spontaneous chirality in a nonlinear microresonator
• Modulational instability and frequency combs in WGM microresonators with backscattering
• The effect on Kerr comb generation in a clockwise and counter-clockwise mode coupled microcavity

Cited by in corpus (7)

• Two-colour dissipative solitons and breathers in microresonator second-harmonic generation
• Threshold of complexity and Arnold tongues in Kerr ring microresonators
• Coupled-mode theory for microresonators with quadratic nonlinearity
• Finesse and four-wave mixing in microresonators
• Soliton blockade in bidirectional microresonators
• Controlling microresonator solitons with the counter-propagating pump
• Frequency combs with multiple offsets in THz-rate microresonators