Single-cycle waveforms and non-periodic waves in dispersive media (exactly solvable models)

Abstract

Exactly solvable models for impulse time domain electromagnetics of dispersive media are developed to describe the interaction of ultrashort (single-cycle) transients with certain classes of insulators and conductors. Transient-excited fields are described analytically by means on new, exact, non-periodic and non-stationary solutions to Maxwell's equations, obtained directly in the time domain without using Fourier-expansion or time-space separation methods. Such non-separable solutions form the mathematical basis of non-periodic waves optics. Extensions to spherical and MHD single-cycle transients, shock-excited distributed transmission lines, and some inhomogeneous and nonlinear media are presented. A flexible technique for modeling real transients by Laguerre functions is developed which enables the shape and duration dependence of the refraction and reflection features of single-cycle waveforms to be presented explicitly.