Extended temporal Lugiato-Lefever equation and the effect of conjugate fields in optical resonator frequency combs

TL;DR

This paper derives an extended Lugiato-Lefever equation from the Ikeda map to include conjugate fields, revealing their impact on modulational instability, resonant radiations, and Kerr frequency comb formation in optical resonators.

Contribution

It introduces a novel extended Lugiato-Lefever model accounting for negative frequency fields, enhancing understanding of frequency comb dynamics in various resonator types.

Findings

Negative-frequency resonant radiations affect comb formation.

The model predicts new modulational instability regimes.

Relevance to fiber loops, microrings, and microtoroids.

Abstract

Starting from the infinite-dimensional Ikeda map, we derive an extended temporal Lugiato-Lefever equation that may account for the effects of the conjugate electromagnetic fields (also called `negative frequency fields'). In the presence of nonlinearity in a ring cavity, these fields lead to new forms of modulational instability and resonant radiations. Numerical simulations based on the new extended Lugiato-Lefever model show that the negative-frequency resonant radiations emitted by ultrashort cavity solitons can impact Kerr frequency comb formation in externally pumped temporal optical cavities of small size. Our theory is very general, is not based on the slowly-varying envelope approximation, and the predictions are relevant to all kinds of resonators, such as fiber loops, microrings and microtoroids.