Nonlinear Cavity and Frequency Comb Radiations Induced by Negative Frequency Field Effects

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.

Localized solutions of Lugiato-Lefever equations with focused pump

“…As a mean-field equation, it applies to other settings too, such as Fabry-Perot resonators and ring cavities, fully or partially filled with nonlinear materials [32], crystalline whispering-gallery-mode disk resonators [33], and photonic-crystal-fiber resonators pumped by a coherent continuous-wave input beam [34,35]. In these contexts, the LL equation has been widely used to model Kerr frequency combs [36,37,38,39,40], with applications to optical metrology [41], highprecision spectroscopy [42,43], optical atomic clocks [44,45], phase evolution in pulse trains [46,47], optical communications [48], synthesis of arbitrary optical waveforms [49,50], and radio-frequency photonics [51]. A review of the development of various applications of the LL equations has been published recently [52].…”

Three-dimensional limaçon: Properties and applications

“…research on microlasers [3], filters for communication technology [4] or single molecule sensing [5]. Furthermore, the research on micro-combs [6][7][8] and optomechanics [9,10] benefits from the progresses made in the field of optical microresonators. Established examples of optical microcavites are microdisks [3,11], microspheres [12,13] and microtoroids [14,15] which confine light in whispering gallery modes with high quality factors Q.…”

Superresonant Radiation Stimulated by Higher Harmonics

“…In a recent work, Conforti et al proposed an equation for the analytic signal of an electric field that is formally similar to the NLSE but does not suffer from many of the limitations of the latter [17] and only relies the reasonable assumption of neglecting backward propagating waves [18]. This equation has been found to predict some features of the nonlinear interaction between light and matter that were not present in the original NLSE, related to the so-called negative frequency components of the electromagnetic pulse [19,[21][22][23][24]. In their paper, the authors discuss new phase matching conditions that arise from the new nonlinear polarisation terms in their equation, and theoretically predict the emission of what has been dubbed negative resonant radiation (NRR) and third-harmonic resonant radiation (THRR).…”

“…Equation (1) has been successfully applied to optical fibers, crystals [17,22] and fiber or microring cavities [23].…”

“…The subscript symbol + in the nonlinear part of Eq. (1) means that spectral filtering must be performed, since A must contain only the positive frequency components [17,22,23,25,26].…”