Closed Form Solution to the Incident Power of Gaussian-Like Beam for Scattering Problems

To avoid edge diffraction induced by surface truncation in the method of moments, the Gaussian-like beam is used as the incident source. Such a wave, also referred to as 'tapered wave,' provides concentrated power density near the scattering center and decays rapidly to negligible level before reaching the edge for most of the incident angles. The resulting scattered intensities need to be normalized by the tapered incident power, to quantitatively predict the radar cross section, which is compatible to the far-zone plane wave results from measurements and analytical solutions. Conventionally, the incident power of tapered wave has been computed numerically by summing up the scattered fields of a flat surface over all azimuth angles, which is tedious and inefficient. In this communication, an exact expression of the incident power is analytically elaborated as an onefold definite integral of zero to one. The binomial expansion of this analytical method is also outlined, and the validation data show good agreement between the analytical solution and numerical results.