TRANSIENT WAVE-FORMS AND NONPERIODIC WAVE S IN DISPERSIVE MEDIA (EXACTLY SOLVABLE MODELS)

Exactly solvable models for the impulse-time domain electromagnetics o f dispersive media are developed to describe the interaction of ultras hort (few-cycle) transients with certain classes of insulators and con ductors. Transient-excited fields are described analytically based on new, exact, nonperiodic and nonstationary solutions to Maxwell's equat ions, obtained directly in time domain using a no Fourier-expansion, n o time-space separation method. Such nonseparable solutions form the m athematical basis of the time-domain electromagnetics of nonperiodic w aves and make the standard harmonic wave concepts of frequency, phase, refraction index, and phase velocity irrelevant to the time descripti on of nonperiodic waves. Extensions to spherical and MHD single-cycle pulses, shock-excited distributed transmission lines, and some heterog eneous and nonlinear media are presented. The flexible technique of mo deling real transients by Laguerre functions enables the shape and dur ation dependence of the refraction and reflection of single-cycle wave forms to be presented explicitly. It is shown that the frequency and t ime domain approaches are two independent branches of the electromagne tics of dispersive media, complementary to each other in the analysis of quasistationary and transient wave processes.