Abstract

A scale transformation that converts an ellipse into a circle has been suggested in the literature as a method for eliminating the need to evaluate the conventional Mathieu function solution for scattering by an elliptic cylinder. This suggestion is tested by examining the wave equation in the scaled coordinate system and by evaluating the scattering from a thin ellipse for conditions where it is expected that an approximate solution can be obtained using the scalar theory single-slit approximation. It is found that, for a plane electromagnetic wave normally incident on a thin perfectly conducting ellipse, the position of the first minimum in the diffraction pattern, relative to the central axis, differs by approximately a factor of 7 between the single-slit and the scaled theory approach to the problem. The examination of the scaled wave equation and the scattering calculation suggests that, because the scale transformation generates an anisotropic medium, the use of a uniform medium solution in the scaled coordinate system is not appropriate.

© 2011 Optical Society of America

Electromagnetic plane wave scattering by arbitrarily oriented elliptical dielectric cylinders

Grigorios P. Zouros
J. Opt. Soc. Am. A 28(11) 2376-2384 (2011)

Oblique electromagnetic scattering from lossless or lossy composite elliptical dielectric cylinders

Grigorios P. Zouros
J. Opt. Soc. Am. A 30(2) 196-205 (2013)

Three-dimensional scattering by an infinite homogeneous anisotropic elliptic cylinder in terms of Mathieu functions

Shi-Chun Mao, Zhen-Sen Wu, and Hai-Ying Li
J. Opt. Soc. Am. A 26(11) 2282-2291 (2009)

Scattering by an infinite homogenous anisotropic elliptic cylinder in terms of Mathieu functions and Fourier series

Shi-Chun Mao and Zhen-Sen Wu
J. Opt. Soc. Am. A 25(12) 2925-2931 (2008)

Scattering of a Gaussian beam by an elliptical cylinder using the vectorial complex ray model

Keli Jiang, Xiang’e Han, and Kuan Fang Ren
J. Opt. Soc. Am. A 30(8) 1548-1556 (2013)