Interaction between optical fields and their conjugates in nonlinear media

Abstract

Motivated by recent experimental results, we demonstrate that the ubiquitous pulse propagation equation based on a single generalized nonlinear Schrödinger equation is incomplete and inadequate to explain the formation of the so called negative-frequency resonant radiation emitted by optical solitons. The origin of this deficiency is due to the absence of a peculiar nonlinear coupling between the positive and negative frequency components of the pulse spectrum during propagation, a feature that the slowly-varying envelope approximation is unable to capture. We therefore introduce a conceptually new model, based on the envelope of the analytic signal, that takes into account the full spectral dynamics of all frequency components, is prone to analytical treatment and retains the simulation efficiency of the nonlinear Schrödinger equation. We use our new equation to derive from first principles the phase-matching condition of the negative-frequency resonant radiation observed in previously reported experiments.

Superresonant Radiation Stimulated by Higher Harmonics

“…In particular, for a system governed by the nonlinear Schrödinger equation (NLSE) it can only occur when a third (or higher) order dispersion term is present. 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].…”

“…Governing equations -The equation proposed by Conforti et al [17] is, in dimensionless units, where A = A(ξ, τ ) is the envelope of the analytic signal of the electric field, ξ and τ are the dimensionless space and time variables (scaled with the second order dispersion length L D ≡ t 2 0 /|β 2 | and the input pulse duration…”

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

“…(1) corresponds to the usual Kerr term. The third term is the well-known third-harmonic generation, and the second is the so called negative-frequency Kerr term [17]. The subscript symbol + in the nonlinear part of Eq.…”

“…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].…”