Abstract
The reflection of scalar plane waves from periodic surfaces (in two dimensions) is studied. Particular attention is devoted to the sinusoidal surface upon which the wave function vanishes. The formulation of the problem rests upon Green's theorem, and it is shown that in the sinusoidal case one is led to an infinite set of coupled algebraic equations. These are essentially different from the equations derived by Rayleigh in his original formulation of the problem. Numerical results are obtained, and the more interesting properties of the results are discussed. As a sidelight, it is shown that the matrix of reflection coefficients for an arbitrary periodic nonabsorbing surface has interesting symmetry properties reminiscent of the quantum-mechanical S-matrix.
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