A rigorous mathematical approach for the analysis and optimization of choke ring antennas with non-identical grooves is presented, based on the method of singular integral equations (SIE). The effectiveness of the SIE approach enables us to develop a robust synthesis-oriented CAD tool capable of fast optimization of the grooves depth and positioning. In this paper, we limit discussion by a 2-D model and TM polarization case. A two step optimization procedure is used to define the optimal configuration of the antenna. First, dispersion curves for the periodic corrugated substrate are presented and used to analyze the supported modes and the impacts of corrugation parameters on the radiation pattern of the antenna, built of a waveguide with a finite-size corrugated flange. Then, the depth of grooves on this flange is optimized using genetic algorithm with the aim to produce a secant-squared beam. The optimal antenna configuration is then studied in 3-D using commercial software: an excellent agreement between 2-D and 3-D results is obtained. This work is a first step towards an advanced low-profile antenna with a shaped beam and high radiation efficiency suitable for mm-wave exposure systems for bioelectromagnetic studies.
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