Near and Far Field Characteristics of Discrete Offset Parabolic Reflector Made of Circular PEC Wires Illuminated by Plane Waves

Abstract

We consider two-dimensional (2-D) scattering of the TE- and TM-polarized plane electromagnetic waves from a discrete gridded offset-parabolic reflector consisting of $N_{c}$ parallel circular perfectly electrically conducting (PEC) wires. Our analysis is performed in the exact formulation, fully taking into account the wave interactions between the wires. We use the method of separation of variables in the local cylindrical coordinate systems in combination with Graf's addition theorem for the cylindrical functions. This approach results in a Fredholm second-kind matrix equation of the $N_{c}\times N_{c}$ block type, where each block has infinite dimension. We calculate the near field patterns in the vicinity of the reflector and evaluate the focusing ability of such a reflector in the both polarization cases. The spatial dependences of the field amplitude near the geometrical focus at the fixed frequency and the frequency dependences of field amplitude in the geometrical focus, as well as the scattered far-field patterns and total scattering cross-sections are calculated and discussed. This study shows that in the both polarization the gridded reflectors are able to focus the incident plane waves.