Closed-form tangential edge conditions for finite-thickness perfectly conducting plates

The tangential edge current of infinitely thin perfectly conducting two dimensional (2D) plates, illuminated by a normally-incident plane electromagnetic wave, have been derived analytically in the past using a quasi-static approximation. This result allows the convenient formulation of an edge basis function for use in conjunction with integral equation scattering calculations. In this work, this infinitely-thin derivation is extended to a finite-thickness plate using a three-step perturbation process. First, the current on the infinitely-thin plate is decomposed into its front and back components. Second, the plate is given a finite thickness while maintaining the same front and back currents. And third, the edge current is found by solving, in closed-form, the associated integral equation. The resultant current, and the approximations used, are then validated by comparison with numerical results obtained using the method of moments (MOM).