Diffracted field computations by a series expansion

Abstract

The possibility of a series expansion for the diffracted fields by a dielectric sphere or circular cylinder is considered by first expanding the Mie scattering coefficients into a geometric series (Debye expansion), and then applying a modified Watson transformation to each term of the series. The diffracted fields can then be obtained by finding poles of the D. ebye expansion, and evaluating the residues. The locations of the poles due to the Debye expansion as well as the Mie scattering coefficients themselves are discussed. Numerical values of the poles are tabulated. The diffracted field contributions associated with the first five terms of the Debye expansion are presented in the form of a radar scattering cross section. The geometrical optics contribution arising from each term of the Debye expansion is asymptotically evaluated. To compare the magnitude of a sum of the geometrical optics and diffracted field contributions, the radar scattering cross section of the total backscattered field, obtained from the exact Mie theory, is also plotted. 1. 1970]. The diffracted fields may be evaluated by a Copyright • 1975 by the American Geophysical Union. singularity expansion method. A direct application of a Watson transformation to the Mie solution results in geometrical optics and diffracted field contributions. The former can be evaluated by a saddlepoint method using a series expansion of the Mie scattering coefficients (Debye expansio.n), whereas the latter can be evaluated by the calculus of residues. The residue series thus obtained converges slowly because of the existence of many surface wave poles with a small imaginary part. The diffracted field contributions have been shown to be the dominant contributions to the total backscattered field [Inada and Plonus, 1970b]. An alternative approach is first to expand the Mie scattering coefficients into a geometric series (Debye expansion), and then apply a Watson transformation to each term of the series. Each term of the series then consists of geometrical optics and diffracted field contributions [Rubinow, 1961; Nussenzveig, 1969a, b]. Poles associated with the Debye expansion have a large imaginary part and move away from the real axis with increasing ka. This could lead to a rapidly convergent residue series. But no numerical results for the diffracted field contributions are available.In the present paper we shall investigate diffracted field contributions arising from each term of the Debye expansion in connection with the backscattering of an electromagnetic plane wave by a dielectric sphere. Numerical computations were performed for 205 206 HITOSHI INADA

Analysis of High Frequency Plane Wave Transmission Into a Double Negative Cylinder by the Modified Watson Transformation and Debye Series Expansion: First Term of the Debye Series

“…The Debye series expansion was used first by Debye in [16]. In [24][25][26][27], some other applications of the Debye series expansion are given.…”

Analysis of High Frequency Plane Wave Scattering From a Double Negative Cylinder via the Modified Watson Transformation and Debye Expansion

“…The first use of the Watson transform is in [35] by Watson. Some other realizations of the Watson transform are given in [36][37][38][39][40][41][42][43]. The Debye expansion is first introduced and applied by Debye in his work [34] for examining the scattering by a dielectric cylinder.…”

“…The Debye expansion is first introduced and applied by Debye in his work [34] for examining the scattering by a dielectric cylinder. Some applications of the Debye expansion are given in [40][41][42][43]. The Debye expansion along with the modified Watson transform is used in [40] and [41] for analyzing the scattering from infinitely long dielectric cylinders.…”

“…Some applications of the Debye expansion are given in [40][41][42][43]. The Debye expansion along with the modified Watson transform is used in [40] and [41] for analyzing the scattering from infinitely long dielectric cylinders. In all of these works, the dielectric cylinders are double positive, i.e., the permittivity and permeability parameters are positive constants.…”