Gaussian beams and far-field directivities via complex-ray theory

The aim of this paper is to show how certain far-field diffraction coeffici ents associated with cylindrically spreading wavefronts generated by a high -frequency, localized boundary forcing can be calculated explicitly using c omplex ray theory and one elementary integration alone. The construction presented in the paper therefore overcomes one of the prev ious deficiencies of ray theory, namely its inability to yield analytical e xpressions for these important coefficient functions. The analysis begins by constructing a Gaussian beam solution using complex rays-giving results of interest in their own right-and then continues with an integration of these solutions to obtain the aforementioned diffraction coefficients associated with related radiation problems.