A Fast Analytical Approach for the Simulation of Stratified Hemispherical Lens

A fast analytical approach for accurately and efficiently simulating the radiation field of stratified hemispherical lens antennas (HLAs) with arbitrary feeds is presented. The scattering problem of stratified spherical lens antennas (SLAs) excited by plane wave is studied first. Then, the scattering problem of a stratified HLA excited by a plane wave is solved by the equivalence principle. It is only appropriate in situations when the relative permittivities of the HLA are not excessively high (i.e., $\varepsilon _{r}\lt 5$ ), as reflections from the bottom of the HLA are ignored. Finally, the radiation field of the stratified HLA fed by arbitrary feeds is simulated by the reciprocity theorem. The numerical results of the proposed approach are in good agreement with those achieved by commercial software, as demonstrated by the examples of several stratified HLAs. In addition, the proposed approach outperforms commercial software in terms of simulation speed and can be applied to the optimal design of large-sized stratified HLAs.