An accurate and efficient analysis for transient plane waves obliquely incident on a conductive half space (TE case)

A method which allows for the analytical evaluation of the inverse Laplace transform representations for a transient TE plane wave, obliquely incident on a conductive half-space, is discussed. We assume that the permittivity and conductivity of the dispersive half-space are independent of frequency. Starting with the equations for the transmitted wave in the Laplace domain, the corresponding time-domain expressions are first represented as inverse Laplace transforms. The transient fields are shown to consist of two canonical integrals f(beta) and e(beta). The canonical integrals, in turn, are solved analytically, thereby yielding solutions involving incomplete Lipschitz-Hankel integrals (ILHI's). The ILHI's are computed numerically using efficient convergent and asymptotic series expansions, thus enabling the efficient computation of the transient fields. The solutions are verified by comparing with previously published results and with results obtained using standard numerical integration and fast Fourier transform (FFT) algorithms.