Finite‐element analysis of plane wave diffraction from metallic gratings with arbitrary complex permittivity

A method of analysis based on the finite-element method is presented for the problem of plane wave diffraction from metallic gratings with arbitrary complex permittivity. First, the problem of diffraction of a plane wave from the metallic reflected-type grating is analyzed rigorously as a two-media boundary value problem by the finite-element method. Next, a new method is proposed in which an approximate boundary condition using the surface impedance is incorporated into the discretized equations by the finite-element method. Especially, in the method of using the surface impedance approximation, the region to be analyzed is reduced substantially from the one for the two-media boundary value problem, and the computational effort is expected to be reduced significantly. The diffraction characteristics of grooved gratings with sinusoidal, triangular and rectangular profiles are actually calculated and the results are compared with those by other methods and experiments. In the case of the TE wave incidence, it is found that the results by the two-media boundary value problem and those by the surface impedance approximation agree well. On the other hand, in the case of the TM wave incidence, the results are substantially different depending on the grating profile. By comparison of the results with those based on the assumption of a perfect conductor, it is found that the loss in the metal must be considered at a longer wavelength in the case of the TM wave incidence than in the case of the TE wave incidence.

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