Electromagnetic Scattering by 2-D PEC Cylinder of General Cross Section Under $\text {TM}^{z}$ Illumination

A semianalytical method is presented for the evaluation of scattered fields from arbitrarily shaped 2-D Perfect Electric Conductor (PEC) scatterers under TMz wave incidence. Surface equivalence principle for scattered fields is used in conjunction with modal expansion of fields in terms of cylindrical eigenfunctions. It is assumed that no field variation exists in axial (z) direction. Implementation of boundary conditions on scatterer surface leads to a system of linearly independent equations to solve for equivalent surface currents. Scattered fields are calculated by equivalent surface currents leading to evaluation of scattering widths (Radar Cross-Section of 2-D objects) for different observation angles. TMz polarized incident wave does not excite any TEz component. The novelty of proposed method is use of addition theorem of Bessel functions for representation of scattered fields in terms of equivalent surface currents, giving an integral equation with an analytic integrand and a well-behaved impedance matrix. Orthogonality of cylindrical modes results in excitation matrix to be a discrete function of mode numbers. Therefore, contrary to method of moments, there is no need for weighting functions. Four examples are considered, namely, line source and plane wave incidence on a 2-D PEC circular cylinder and also plane wave incidence on 2-D elliptical and equilateral triangular PEC cylinders.