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 SemiInversion 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.Hereby we present ARM solution of 2D E-Polarized wave diffraction by a perfectly electrically conductive (PEC) surface that either can be formed by unclosed infinitely thin contour or closed contour of finite thickness. The solution satisfies the homogenous Helmholtz equation everywhere save for the surface contour, Dirichlet boundary condition on the surface contour, Sommerfeld's radiation conditions at the infinity and -for unclosed contour-Meixner's edge conditions at the edges. A smooth parameterization S={(x(u),y(u)):u∈[-1,1]} for unclosed contours is used while S={(x(θ),y(θ)):θ∈ [-π,π)} is used for closed contour. The scattered field from such a PEC boundary S is u s (q)=∫ S J(p)G(q,p)dS q∈R 2 \S everywhere except S. The Dirichlet condition on S leads to an integral equation of the first kind ∫ S J(p)G(q,p)dS=-u i (q) q∈S, where right hand side of this equation is the incident E-polarized wave. Here G(q, p)=[-i/4]H 0 (1) (k|q-p|) is the Green's function of the Helmholtz equation for two dimensional free space with wave number k, where |q-p| is the distance between points p and q. The current density J(p) on S is actually the jump of normal derivatives of the scattering field on both sides of S. For unclosed contour it additionally satisfies Meixner edge conditions at the edges of S, where the corresponding current density has view J(p)=[d 1 (p)d 2 (p)] -1/2 w(p), where d 1 (p) and d 2 (p) are the distances to different corresponding edges, and w(p) is a function of H...
