A modified method of variable separation for the problem of TE wave diffraction on a diffraction grating with two-layer lines in the period

The diffraction of an electromagnetic TE wave on multilayer diffraction gratings with several two-layer lines in the period was investigated. Such optical structures are employed in spectral beam combining. The diffraction problem was solved by a modified method of variable separation, which requires the solution of two one-dimensional boundary value problems for eigenvalues of second-order differential equations on a segment with piecewise constant coefficients. Each of the boundary value problems for eigenvalues reduces to the calculation of a second-order determinant. The proposed method was applied to solve the problem of the electromagnetic TE wave diffraction on multilayer diffraction gratings with several different configurations, as well as to determine their diffraction efficiency. The numerical results were presented. For modeling the diffraction gratings, materials that are commonly used in thin-film coatings were selected. The method can be further developed to model more complex diffraction gratings with multilayer reflective coatings.