A Technique for Solving Certain Wiener-Hope Type Boundary Value Problems

摘要

The time-harmonic analysis of three boundary value problems containing semi-infinite boundaries is presented. The first problem considered is a parallel plate waveguide with one plate truncated and radiating into free space. The excitation of a dielectric slab and the excitation of an isotropic, incompressible, plasma slab by means of a parallel plate waveguide with one plate truncated are the second and third problems analyzed, respectively. A function of a complex variable is factored in each of these Wiener-Hopf type boundary value problems. The function is analytic in a strip and is factored into a product of two functions. One of these functions is analytic in a half-plane while the other is analytic in the adjacent half-plane with an overlap in the regions of analyticity coinciding with the strip. This factorization is obtained by a technique developed in this work. The technique obtains the factorization for the open-region problem from a function and its factorization that occurs in a related closed-region problem. A closed-region problem is one whose transverse dimensions are finite. The chosen closed-region boundary value problem yields a function of a complex variable which can be factored. The factorization of the function for the open-region boundary value problem is obtained by taking the limit, as a parameter approaches infinity, of the function and factorization appropriate to the closed-region structure. By this means the factorization and hence the solution to the open-region boundary value problem is obtained. (Author)