SEM approach to the transient scattering by an inhomogeneous, lossy dielectric slab; Part 2: The inhomogeneous case

• Published in: Wave motion Vol. 6; no. 2; pp. 167 - 182
• Main Authors: Tijhuis, Anton G., Blok, Hans
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 1984
• ISSN: 0165-2125; 1878-433X
• DOI: 10.1016/0165-2125(84)90013-1

In two companion papers, the singularity expansion method is applied to the computation of the transient scattering of a pulsed electromagnetic wave of finite duration by an isotropic, inhomogeneous, lossy dielectric slab. The time-domain electric field is expressed as a Laplace inversion integral over the Bromwich contour. Conditions for the validity of a representation in terms of natural-mode quantities only are derived, i.e. for a vanishing integral along the closing contour in the left halfplane, the latter being the contribution from the essential singularity at infinity. In the first of these two papers, this procedure was analyzed for the case of a homogeneous slab. Here, this analysis is generalized for the inhomogeneous case. For that case, an alternative method exists, where the nonvanishing contribution from the essential singularity at infinity is suppressed by taking into account at each instant only the part of the incident pulse that has emerged into the slab. This method also applies when the closing conditions are violated. The location of the poles and the corresponding natural-mode field distributions and coupling coefficients are determined numerically with the aid of a Runge-Kutta integration method and Muller's root-finding procedure. In the subsequent summation of the residual contributions, acceleration of the convergence is applied. Numerical results are presented and discussed.