Uniform physical optics analysis of scattered electromagnetic field by the edge of concave conducting surface

A physical optics approximation is discussed for the analysis of the scattered electromagnetic field when a cylindrical wave radiated from a line source is incident near the edge of a concave conducting surface with its radius of curvature slowly varying as a function of position. By analyzing approximately the integral of the scattered electromagnetic field expressed in terms of the physical optics current, a uniform asymptotic solution is derived by superposition of the geometrical optics wave and the edge diffraction wave. The diffraction coefficient for the edge diffraction wave is expressed in terms of the Fresnel function, while the expressions on the reflection boundary (RB) side and the shadow boundary (SB) side have symmetry. The argument of the Fresnel function uses a new representation containing information on the radius of curvature of the wave front of the diffracted wave and the location of the caustic, or the radius of curvature of the wave front of the incident wave, so that a scattered field continuous on the RB and SB is formed. The effectiveness of the uniform asymptotic solution is numerically clarified by comparison with the rigorous solution obtained by the Wiener-Hopf method and the reference solution obtained by direct numerical integration of the integral on the scattered field. The results are compared with analytical results based on the physical optics approximation published elsewhere. The causes of the difference from the present results are discussed.