This paper describes exactly a new formulation of the Tmatrix method with R-matrix expression for the electromagnetic wave diffraction efficiency from dielectric coated metallic Fourier grating. We found that the parameters of numerical calculation are widely applied by using R-matrix expression in dielectric coating media whose thickness or depth groove on the Fourier grating is large. The absorption phenomena of diffraction efficiency in particular incident angle are observed in the two cases. One of the factor is a guided mode in the dielectric coated layer. Other factor is resonance absorption that occurs by plasmon anomalies on the substrate for the TM polarization.
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