Modulational instability in metamaterials with saturable nonlinearity and higher-order dispersion

Abstract

Modulational instability (MI) in negative refractive metamaterials with saturable nonlinearity, fourth-order dispersion (FOD), and second-order nonlinear dispersion (SOND) is investigated by using standard linear stability analysis and the Drude electromagnetic model. The expression for the MI gain spectrum is obtained, which clearly reveals the influence of the saturation of the nonlinearity, FOD, and SOND parameters on the temporal MI. The evolution of the MI in negative refractive metamaterials is numerically investigated. Special attention is paid to study the effects of the higher-order dispersion terms on the formation and evolution of the solitons induced by MI. It is shown that as the third-order dispersion term increases, the solitons travel toward the right. Moreover, the magnitude of the FOD term influences considerably the number of wave trains induced by MI.

Modulation Instability Induced by Cross Phase Modulation in a Negative Refractive Index Material with Saturable Nonlinear Responses

“…The dimensionless coupled system of nonlinear Schrödinger equations (NLSEs) governing the dynamical interaction of two co-propagating, along the positive z direction, waves in NIMs with saturable nonlinearity, is [1][2][3][4] ( ) ( )…”

Exact quasi-soliton solutions and soliton interaction for the inhomogeneous coupled Hirota–Maxwell–Bloch equations

“…Serkin et al [31] introduced the inhomogeneous NLS (INLS) equation and obtained the one-and two-soliton solution through the Lax pair technique [32]. Very recently, we have extended the study in the inhomogeneous CNLS (ICNLS) equations [33]. In this work, we have modified the ICNLS equations to suit the pulse propagation in erbium-doped fibers, wherein the effect of higher-order dispersion and SIT should be included and the governing equation is now called the GICH-MB equation in the following forms:…”

“…To understand the effect of doped erbium atoms, we include the soliton solutions for the ICNLS equations without the MB part obtained in [33], which is also given by equations ( 9), but with…”