Transient Electromagnetic Scattering by a Radially Uniaxial Dielectric Sphere: The Generalized Debye and Mie Series Solutions

In this paper, a theoretical study is carried out to determine the scattering of a transient electromagnetics wave by a radially uniaxial dielectric sphere. This is achieved by inverse Laplace transformation of the frequency-domain scattering solution. To improve understanding of the scattering mechanism from a uniaxial dielectric sphere, two different frequency-domain solutions are employed. In the first approach, the impulse and step responses of a uniaxial dielectric sphere are evaluated by the Mie series solution. Following the high-frequency (HF) scattering solution of a large uniaxial sphere, the Mie series summation is split into high-frequency (HF) and low-frequency terms where the HF term is replaced by its asymptotic expression allowing a significant reduction in computation time of the numerical Bromwich integral. In the second approach, the generalized Debye series solution is introduced, and the generalized Mie series coefficients are replaced by their equivalent Debye series formulations. The results are then applied to evaluate the transient response of each individual Debye term allowing the identification of impulse returns in the transient response of a uniaxial sphere. The effect of variation in permittivity on the arrival time as well as amplitudes of each impulse return is studied, and the results are compared with those computed using the Mie series solution. The numerical results obtained from both methods are in complete agreement.