Analytical Regularization Method as a tool for cylindrical antenna design

Mirror antennae formed by curvilinear perfectly conducting screens are classic objects of theoretical and experimental investigations, which already resulted in numerous scientific and engineering publications. The most typical full wave models of such antennae are based on mathematical approach of infinitely thin and perfectly conductive screens. In many cases screen is formed by a surface in 3D space. At the same time, cylindrical antennae and their models as homogenous and infinite in longitudinal direction cylindrical surfaces are also having their place in modern radio science. Our presentation is focused on such cylindrical antennae models both infinitely thin and of finite thickness with various shapes and screen thickness. Namely, we try to estimate how finite thickness influences the antenna characteristics and, in particular, estimate validity of the models based on infinitely thin screens relatively to different physical purposes of modeling. We have chosen Analytical Regularization Method (ARM) as a tool for our investigation. In publications [1, 2] aiming the similar investigation, where Semi-Inversion Procedure (SIP) [3] was used, it was claimed that ARM was used. This mistaken claim occurred due to mismatching of the standard terminology [4, 5, 6 and references therein]. Using ARM instead of SIP gives possibility to obtain algorithms of essentially better quality than those of [1, 2]. Moreover, we implement ARM in such a way that it is super-algebraically (faster than any negative power of the reduced algebraic system) convergent.