Nonlinear Modulation of Wave Propagation in Spherical Shell Model and Modified Zhang Model Using Free Space Model as a Bench-Mark

Abstract

This paper presents nonlinear modulation of wave propagation in spherical shell model (SSM) and modified Zhang model (MZM) using free space model (FSM) as a bench-mark. A typical non-linearity is the change in the dielectric constant due to electromagnetic (EM) wave field that propagates through a medium. By modulation, we mean the characteristic departure of EM waves’ propagation in both media as opposed to the free space propagation. Maxwell’s equations were used to derive the basic equation that govern the propagation of electromagnetic waves in nonlinear media. The equations of the models were found to be nonlinear and their solution were obtained numerically using Runge-Kutta scheme implemented in Matlab software. The spatial EM wave profile graphic displays were supplemented by the symmetric spatial Fast Fourier Transform (FFT) analysis. The symmetric implementation of the FFT meant that the actual number of modes present in any solution was half the number of observed spikes. The free space model (FSM) showed periodic propagation for all frequencies ( examined corresponding to a wavenumber per frequency. The result only serves to give some level of confidence that the algorithm performed well. The MZM supports a variety of characteristics. There are amplitude amplifications or wave steeping, lossless or solitary propagation and multiplicity of modes for all frequencies examined. However, at the fundamental frequency _, the SSM is capable of exhibiting amplitude amplification without attenuation. The EM wave propagation characteristics of the MZM and SSP showed that materials which could be fabricated according to this model would be very useful as EM wave guides as they could support waves without losses as opposed to the present known commercial optical fibers.

Keywords: Nonlinear modulation, Wave propagation, Spatial Electromagnetic wave.