Transmission of Electromagnetic Waves through a Conducting Slab. I. The Two-Sided Wiener-Hopf Solution

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Abstract
This is the first of a series of papers dealing with propagation of electromagnetic waves through a metallic slab of finite thickness. In this first paper, we present a method for solving the integrodifferential equation governing the electric field in the interior of the metal when the electrons in the interior of the metal suffer diffuse reflection at each surface. The method is potentially of use in a wide class of problems, namely, the finite‐slab generalization of all those semi‐infinite‐medium problems which are conventionally studied by the Wiener‐Hopf technique. The solution given here is an iterative one with successive terms converging as e−L/l, where L is the thickness of the slab and l is the range of the kernel of the integral term in the equation.