Method to study diffraction from a stepped grating

The problem of diffraction from a perfectly conducting periodic surface is solved by means of a coordinate transformation followed by the application of the extinction theorem: an integral equation for the diffracted field is derived. Thanks to the particular feature of the kernel, the solution is written as a converging exponential expansion with its coefficients satisfying a recursion formula. The first term of recurrence can be calculated using one of the boundary conditions so that the problem is solved completely.