AN ACCURATE AND EFFICIENT ANALYSIS FOR TRANSIENT PLANE-WAVES OBLIQUELY INCIDENT ON A CONDUCTIVE HALF-SPACE (TM CASE)

In this paper, we develop a method for the analytical evaluation of th e inverse Laplace transform representations for a transient transverse magnetic (TM) plane wave obliquely incident on a conductive half-spac e. We assume that the permittivity and conductivity of the dispersive half-space are independent of frequency. The time-domain expressions f or the reflected and transmitted waves are first represented as invers e Laplace transforms. The transient fields are then shown to consist o f two canonical integrals. The canonical integrals, in turn, are solve d analytically, thereby yielding closed-form solutions involving incom plete Lipschitz-Hankel integrals (ILHI's). The ILHI's are computed num erically using efficient convergent and asymptotic series expansions, thus enabling the efficient computation of the transient fields. The e xact, closed-form expressions are verified by comparing with previousl y published results and with results obtained using standard numerical integration and fast Fourier transform (FFT) algorithms. An asymptoti c series representation for the ILHI's is also employed to obtain a re latively simple late-time approximation for the transient fields. This approximate late-time expression is shown to accurately model the fie lds over a large portion of its time history.