An Exact Line Integral Representation of the Physical Optics Radiation from a Perfectly Conducting Cylindrical Reflector of Arbitrary Cross Section Illuminated by a Plane Wave

A representation of the phyisical optics (PO) field scattered by a cylindrical reflector with an arbitrary cross section for plane wave illumination is developed in the form of a line integral. This is accomplished by interpreting the integration of the PO currents along the generatrices of the cylindrical reflector as the radiation of finite length travelling-wave line sources, which can derived in closed form by exploiting the solution for the field radiated by a semi-infinite travelling-wave current filament in terms of incomplete incomplete cylindrical functions (ICFs). As a result, the PO surface integral is reduced to a line integral of the incremental PO fields from each infinitesimal current line to be collected numerically over the transverse section of the reflector. The proposed representation is exact and valid in any electromagnetic field region, and, since it avoids the numerical calculation of the PO integral along the longitudinal dimension of the reflector, which can be extermely large in terms of wavelengths, it is expected to be very computationally efficient and to constitute a useful tool to analyse the near- and far-zone fields radiated by large, high-gain cylindrical reflectors.