Numerical evaluation by reciprocity in dielectric gratings

In the theory of gratings, a numerical diffraction solution must be satisfy the energy balance and the reciprocity. The matrix eigenvalues method has been presented to study the diffraction by dielectric gratings. In the method, the error of energy balance always becomes zero except for rounding error. An accuracy criterion of a solution is left as a difficult problem. This paper shows the reciprocity for the diffraction efficiencies of the reflected and transmitted waves, numericaffy. It is suggested that the reciprocity can be used the criterion.