Regular Article

Cross-phase modulation instability under delayed response and walk-off effects in the anomalous regime of dispersion

¹ International Institute of Physics, Federal University of Rio Grande do Norte, 59070-405 Natal, Brazil
² Grupo de Física da Matéria Condensada, Núcleo de Ciências Exatas, Campus Arapiraca, Universidade Federal de Alagoas, 57309-005, Arapiraca, A.L., Brazil
³ Observatório Nacional, 20921-400 Rio de Janeiro, R.J., Brazil
⁴ Departamento de Física, Universidade Federal da Paraíba, Caixa Postal 5008, 58059-900 João Pessoa, P.B., Brazil

^a e-mail: askery.canabarro@arapiraca.ufal.br

Received: 14 December 2018
Published online: 14 May 2019

Abstract

The dynamics of the modulation instability induced by cross phase modulation is studied by considering the influence of the walk-off and noninstantaneous response effects for two copropagating optical fields travelling in the anomalous regime of dispersion. To do so, we make use of extensions of the nonlinear Schrdinger equation jointly with the Debye model for polarization, which is shown to be effective and simplified when compared to the implementation of other methods for the noninstantaneous nonlinear response. In analyzing the sideband formation, two bands are observed with different behaviors with respect to the way the maximum gain and the respective frequency vary with increasing phase mismatch. Further, we also show the manner in which the maximum gain as well as its corresponding frequency scale with the delay parameter τ is substantially different from the cases of both fields experiencing the normal group-velocity dispersion regime and the case of mixed regimes. These facts may give rise to many new possibilities for the evolution of the modulated wave when compared to the nonanomalous cases studied in the literature.