Path integrals for solving some electromagnetic edge diffraction problems

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Abstract
Electromagnetic edge diffraction problems involving parallel half‐planes are traditionally attacked by the Wiener–Hopf technique, or asymptotically for a large wavenumber (k→∞) by ray‐optic 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 half‐planes, the path integral is evaluated explicitly to yield an asymptotic solution of order k0 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 half‐planes, the use of a path integral leads to new solutions. We have not succeeded, however, in generating higher‐order terms beyond k0 in the asymptotic solution by path integrals.

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