Theoretical analysis of nonlinear pulse propagation in ferrite-dielectric-metal structures based on the nonlinear Schrödinger equation with higher order terms

Abstract

An analysis of nonlinear magnetostatic surface wave pulse propagation in planar ferrite-dielectric-metal (FDM) structures has been performed. The analysis was based on numerical solutions to the higher-order nonlinear Schrödinger (HONLS) equation, with third-order (D3) and nonlinear (Q) dispersion terms taken into account. The analysis focuses on (1) the crossover dispersion region for FDM structures and the point in wave-number k where the second-order dispersion parameter D2 is a positive maximum, the Lighthill criterion for envelope soliton propagation is satisfied, and D3 is close to zero, and (2) the end points of this crossover region where D2 is zero. All operational HONLS equation parameters were evaluated from analytical dispersion expressions for the FDM structure and for magnetic field and structure parameters which match experiments. For (1), the pulse results indicate nondispersive propagation consistent with envelope solitons. The only effect of the Q term is to decrease slightly the propagation speed. For (2), both end points give nondispersive propagation as well. At the low-k crossover point, this result is consistent with condition D3Q<0 and the existence of an analytic soliton solution. For the high-k crossover point, the nondispersive propagation is likely due simply to the relatively small value of the third-order dispersion D3 parameter. In both cases, one finds a rapidly oscillating wave-packet structure which propagates ahead of the main pulse. For the low-k crossover point, this structure travels at approximately twice the main pulse velocity. For the high-k crossover point, the structure travels with the main pulse. The Q term has a small effect on the pulse amplitude for the low-k crossover point, and serves to reduce the pulse amplitude by 20%–30% at the high-k crossover point.