The low-frequency scattering by a perfectly conducting strip

Abstract

Various authors, e.g. Sommerfeld (8), Bouwkamp(i), Groschwitz and Hönl(2), Müller and Westpfahl(7), have considered approximate solutions to the problem of the diffraction of a plane wave by a narrow perfectly conducting strip. If the electric vector is polarized parallel to the strip they find that the scattering coefficient, for normal incidence, is given by, where k is the wave number, 2b the width of the strip and γ(= 0·5572…) being Euler's constant. Any attempt to discuss the convergence of such a pseudo-power series requires a knowledge of the higher order terms and naturally leads to the question of what is the proper expansion parameter.