Scattering of a transient electromagnetic wave by a dielectric sphere

Abstract

The transient scattered field from a lossless dielectric sphere is evaluated by the inverse Laplace transform of the frequency-domain solution. Two methods of obtaining the inverse transform are employed. In the first approach, direct numerical evaluation of the Bromwich integral is carried out. To overcome the slow convergence of the Mie series at high frequencies (HF), asymptotic expressions are used in the large | s | portion of a properly chosen Bromwich contour, allowing a significant reduction of the computation time. In the second approach, the asymptotically compensated singularity expansion method is employed. In this method, a multiplicative function is chosen to compensate for the asymptotic growth of the field in the right half of the s–plane, leading to a singularity expansion without entire functions. The transient scattered field is then recovered. The numerical results obtained from both methods are in complete agreement. Reference to the physical origins of the various structures appearing in the time-domain response is made by considering the dependence of their magnitude and time of arrival on the permittivity. Verification of the various predictions previously given by frequency-domain analysis can be carried out in a different perspective with new physical insight.