A Fourier expansion solution to plane wave scattering from isosceles right triangle groove in perfect conducting plane

While scattering from a rectangular groove, or rectangular slit, in a perfectly conducting plane has been studied extensively, an analytical solution for the scattering problem from an isosceles right triangle (IRT) groove in a perfectly conducting plane has not yet been found. The triangle groove is of practical use in optical and microwave diffraction. An exact analytical solution for the scattering of a plane wave from an IRT groove in a perfectly conducting plane is presented. The spectrum of the scattered fields is expressed as a Fourier expansion related to the field in the groove. Near and far fields can be determined by this presentation of the scattered field in series form.