Path integrals for solving some electromagnetic edge diffraction problems
Abstract
Electromagnetic edge diffraction problems involving parallel halfplanes are traditionally attacked by the WienerHopf technique, or asymptotically for a large wavenumber (k→∞) by rayoptic techniques. This paper reports a novel method in which the electromagnetic wave equation is first converted to a heat equation via the Laplace transform. The heat equation together with the original boundary condition is next solved approximately in terms of a path integral over the Wiener measure. For several examples involving two parallel halfplanes, the path integral is evaluated explicitly to yield an asymptotic solution of order k^{0} for the field on the incident shadow boundary. Those solutions agree with the ones derived by traditional techniques, but are obtained here in a much simpler manner. In other examples involving multiple halfplanes, the use of a path integral leads to new solutions. We have not succeeded, however, in generating higherorder terms beyond k^{0} in the asymptotic solution by path integrals.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 June 1978
 DOI:
 10.1063/1.523843
 Bibcode:
 1978JMP....19.1414L
 Keywords:

 Electromagnetic Wave Transmission;
 Half Planes;
 Integral Calculus;
 Wave Diffraction;
 Asymptotic Methods;
 Laplace Transformation;
 Thermodynamics;
 Physics (General);
 42.10.Hc;
 03.50.De;
 Classical electromagnetism Maxwell equations