Potential Coupling Through a Slot Backed by an Elliptical Cavity: Neumann and Dirichlet Boundary Conditions

Abstract

Exact, closed-form expressions are presented for the solution to Laplace's equation everywhere in a specific cavity-backed aperture problem. A symmetrically placed slot enables the static field in a half-space above a hard or soft ground plane to penetrate into the interior of an elliptically shaped cavity. Separation-of-variables in elliptic coordinates yields a summable series, whereupon the aperture field or its normal derivative appears naturally as a series of edge-condition weighted Chebyshev polynomials in the Cartesian coordinates. Analytic coefficients explicitly display simple dependence upon the cavity and point-source geometry.

Keywords:

• Laplace's equation
• electrostatics
• aperture
• elliptic coordinates