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

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.

References in corpus (5)

• Frequency combs and platicons in optical microresonators with normal GVD
• Dynamics of localized and patterned structures in the Lugiato-Lefever equation determine the stability and shape of optical frequency combs
• Observation of dispersive wave emission by temporal cavity solitons
• Third-order chromatic dispersion stabilizes Kerr frequency combs
• Effects of inhomogeneities and drift on the dynamics of temporal solitons in fiber cavities and microresonators

Cited by in corpus (4)

• Localized solutions of Lugiato-Lefever equations with focused pump
• Parametrically tunable soliton-induced resonant radiation by three-wave mixing
• The 3D Limaçon: Properties and Applications
• Super-resonant radiation stimulated by high-harmonics