T-matrix analysis of electromagnetic wave diffraction from a multilayer-coated Fourier grating

A new formulation is proposed in the electromagnetic wave diffraction problem from a multilayer-coated Fourier grating by using the T-matrix method with expression of R-matrix propagation. This formulation is also useful expression because our R-matrix propagation algorithm is avoided a singularity of matrix elements for the evanescent mode. The analytical form of the matrix elements is also obtained in the term of the Bessel function. Numerical calculations for the Fourier grating with numbers of the coated-layer and large thick layer can be successfully obtained in the high accuracy. This method for the sinusoidal grating is good agreement with other methods. Numerical results for the Fourier grating have also been checked by percentage power errors. As the numerical examples, we present diffraction efficiencies versus wavelength in the Fourier grating with aluminum substrate.