Eur. Phys. J. Plus (2013) 128: 145
https://doi.org/10.1140/epjp/i2013-13145-6

Regular Article

Scattering by an elliptic cylinder and the single-slit approximation

Ursinus College, 601 E. Main St., Collegeville, PA, USA

^* e-mail: lferrari500@comcast.net

Received: 10 October 2013
Accepted: 1 November 2013
Published online: 29 November 2013

Abstract

The scattering of electromagnetic waves by a perfectly conducting elliptic cylinder is studied for cases where the ratio of the major diameter to the wavelength, 2a/λ, ranges from approximately 6 to 80, and for aspect ratios, the ratio of the minor to major diameter b/a , from 0.50 to 0.90. Convergence of the Mathieu function series solution for the scattering requires up to 175 terms for each of the four parts, and calculating floating-point numbers to 350 digits precision for the largest values of 2a/λ and b/a . The position of the first minimum relative to the central axis in the diffraction pattern is used in the single-slit approximation formula to determine a dimension that is compared with the ellipse dimension perpendicular to the angle of incidence of the electromagnetic wave. The aspect ratio obtained by this process differs from that of the ellipse by no more than 15% at b/a = 0.50, less than 4% at b/a = 0.75, and less than 1% at b/a = 0.90 , all at 2a/λ = 20/π ≈ 6.4. The single-slit analysis yields a cross-section with a dimension that differs from that of an ellipse by a maximum value of about 28% at 2a/λ = 20/π, and b/a = 0.50 , when the angle of incidence is π/4 , and decreases to a maximum value of less than 1% at b/a = 0.90 . In all of the cases studied the difference between the actual ellipse parameters and those obtained via the single-slit approximation decreases as 2a/λ and b/a are increased.