Abstract

Motivated by recent experimental results [1], we demonstrate that the ubiquitous pulse propagation equation based on a single generalized nonlinear Schrodinger equation (NLSE) is incomplete and inadequate to explain the formation of the so called negative-frequency resonant radiation (NRR) emitted by optical solitons [2]. 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 (SVEA) is unable to capture [2]. 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 NLSE [2]. We use our new equation to derive from first principles the phase-matching condition of the NRR observed in previously reported experiments, see Fig 1, left panel.

© 2015 IEEE