Higher order dispersion effects in the noninstantaneous nonlinear Schrödinger equation

Abstract

We present a systematic analysis of the effects, of higher-order dispersion, noninstantaneous nonlinear response, as well as stochastic coefficients in optical fiber. This study is motivated by recent experimental observation of a new modulational instability spectral window induced by fourth-order dispersion in a normally dispersive singlemode optical fiber. Analytical expression of pulse amplitude is deduced with the second-order gain nonuniformity and the stimulated-Brillouin scattering-induced third-order as well as fourth-order dispersion effects involved. The influence of stochasticity, as well as the delayed Raman response in the nonconventional sidebands obtained due to the fourth-order dispersion, is considered. We note that the shape of the spectrum, and in particular the relative intensities of the higher order harmonics, is highly sensitive to the initial presence of classical noise, and can therefore be taken as a signature that the MI is seeded by vacuum fluctuations. Some direct simulations to see the evolution of different continuous wave states are reported. These show the formation of modulation instability pulses as well as transitions from lower amplitude continuous wave states to higher amplitude continuous wave states. The present results fit well with recent experimental investigations.

Effect of power-law nonlinearity on ${ \mathcal P }{ \mathcal T }$-symmetric optical system with fourth-order diffraction

“…Most early works concentrated on the formation of solitonic solution under the exact balance between  -symmetric potentials with a second order dispersion term and different order nonlinearities. However, higher-order dispersion/diffraction must be considered when the width of an optical beam is narrow [41][42][43]. Because of the higher-order diffraction, it is difficult to find exact analytical solutions of NLS equations and they require some kinds of techniques.…”