Diffraction of a plane wave by a half plane under mixed boundary conditions

Abstract

The problem of diffraction of a plane wave by a semi-infinite half plane with mixed boundary conditions (Dirichlet condition on one face and Neumann condition on the other) is solved by a direct and rather straightforward method. The infinite series solution and the far field are in agreement with the previous solutions obtained by the Lebedev–Kontorovich transform method as expected, as the two methods are basically equivalent. An alternate representation of the infinite series solution is presented which is valid for any type of incident field including cylindrical and spherical fields. This representation facilitates easy analysis of transient problems and the special case of an incident plane unit step function on the half plane is given as an example.