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Computational Methods for Surface Relief Gratings Using Electric and Magnetic Flux Expansions

The relative permittivity and permeability are discontinuous at the grating profile, and the electric and magnetic flux densities are continuous. As for the method of analysis for scattering waves by surface relief gratings placed in conical mounting, the spatial harmonic expansion approach of the flux densities are formulated in detail and the validity of the approach is shown numerically. The present method is effective for uniform regions such as air and substrate in addition to grating layer. The matrix formulations are introduced by using numerical calculations of the matrix eigenvalue problem in the grating region and analytical solutions separated for TE and TM waves in the uniform region are described. Some numerical examples for linearly and circularly polarized incidence show the usefulness of the flux densities expansion approach.