EM Wave Propagation in Dielectric Medium with Sinusoidal Time-Modulation

Abstract

In this chapter, first the EM wave-equations are derived for electric and magnetic fields in a general time-varying but space-invariant infinitely extended medium. The concept of velocity modulation is discussed for the scenarios when the ratio of permittivity and permeability functions is constant or both are slowly varying with time. We then introduce a more compact quasi-analytical paradigm based on ODEs (ordinary differential equations) of electric flux density to handle the same problem. We showcase how the numerical solutions of these ODEs using MATLAB can predict the EM wave propagation behaviour in an infinitely extended time-varying medium. We then take up the specific problem of EM wave interaction with a finitely extend time-varying dielectric slab and provide some initial insights based on assumptions regarding slab thickness and modulation index. Finally, modified 1D-FDTD update equations are formulated to handle EM wave interaction with the sinusoidally time-varying dielectric slab. Several numerical examples with new visualization and post-processing schemes are included to demonstrate the EM impact of the dielectric modulator parameters like slab-length, modulation index and the ratio of modulating frequency with the carrier. The frequency spectra of the FDTD-computed field emanating out of the dielectric modulator are critically assessed to shed light onto interesting effects of non-linear phase and amplitude modulation, which often leads to suppression of carrier signal.