High-frequency scattering of a Hermite-Gaussian beam mode by a perfectly conducting cylinder

The scattering of a Hermite-Gaussian beam mode by a perfectly conducting cylinder at high frequencies is persented. A higher-orger beam mode is experssed in terms of complex-source-point multipole fields. Using the Watson transformation, the diffraction field in the shodow region is represented by residue series. The incident and reflected beam fields in the illuminated region are asymptotically obtained by the evaluation of the integral using the stationary phase method.