Numerically Efficient Line-Integral Representation of Physical-Optics Scattered Field: The Case of Perfectly Conducting Surface Illuminated by Electric Hertzian Dipoles

Abstract

This paper presents a novel line-integral representation of the physical-optics radiation integral from a perfectly conducting surface illuminated by a finite number of electric Hertzian dipoles. By introducing a new dyad potential, this novel representation guarantees the integrand free from singularities along the computational path. As such, it can be easily integrated for arbitrary positions of the source and observation points. Conversely, for certain situations of the Hertzian dipole being on the cone connecting the observation point to the scattering rim, the existing formulations exhibit a nonremovable singularity in their integrands. This will lead to invalid or inaccurate results. Meanwhile, for near-singular integration region, time-consuming computations need to be performed by utilizing a variable mesh integration. The efficiency in numerical calculation is the main objective of this kind of approach, and the time reduction performance would be improved by our singularity-free formula. The line-integral representation offers an alternative method to rapidly solve the scattering problem as it is usually more efficient than producing the same result in conventional surface-integral. Simple and complicated numerical examples are included to demonstrate the beneficial effect of the proposed expressions in terms of efficiency and accuracy.