We present a simple analytical solution for a one dimensional grooved structure which, when placed concentrically around or flanking a small aperture, has been shown to enhance microwave radiation from it. We will show that the transcendental equation which describes the grooved structure reduces to a transverse resonance condition at the slot openings. For some parameters, the solution to the problem manifests as a complex wave. We demonstrate that this complex wave indeed well approximates the field distribution when a single aperture is excited for frequencies where the enhancement is most significant. In addition, we propose a simple and intuitive design procedure for the grooved structure.