Closed-Form Expressions for the On-Axis Scattered Fields by a Subwavelength Circular Aperture in an Infinite Conducting Plane

Closed-form analytical expressions for the on-axis scattered fields by a subwavelength circular aperture in an infinite perfectly conducting plane were derived using a vector potential formulation and the equivalence principle. The final expressions are valid for the near-field, intermediate-field, and far-field zones. The underlined formulation is based on the equivalent quasi-static magnetic current distributions in the aperture, which were derived by Bethe and Bouwkamp in the mid 40's and early 50's. The resulting scattered-field integrals, which involve the free-space Green's function, were evaluated analytically after introducing Taylor series expansion and using transformations. The final closed-form expressions of the scattered fields are given in terms of a recursion formula. Obtained results based on these closed-form expressions are in excellent agreement with data generated by a numerical integration scheme.