High-frequency asymptotic analysis for scattered field by a conducting cylinder

In this study, we consider the high-frequency asymptotic analysis methods for the scattered field when a cylindrical wave is incident on a conducting circular cylinder. We derive the asymptotic solution applicable in each of the transition regions divided by the shadow boundary into the shadow and the lit side. The asymptotic solutions include a novel extended Pekeris caret function to which the second order term in the argument of the exponential in the integrand is added as compared with the Pekeris caret function including the UTD (uniform GTD) solution. By applying the residue theorem and the saddle point technique to the novel extended Pekeris caret function, we derive respectively the surface diffracted ray solution and the reflected geometrical ray solution which are effective exterior to the transition regions. The validity of the various asymptotic solutions derived here is confirmed by comparing with the exact solution.