Electromagnetic wave diffraction and propagation in a multilayer dielectric structure containing a diffraction grating

We develop a numerical code for simulating the EH₀₁ mode propagating in a structure composed of a dielectric grating placed on a multi-layer substrate. The dispersion characteristics, the spatial field distribution and the dependence of the transmission and reflection coefficients upon the frequency are calculated for different geometrical dimensions of the structure. The method of volume integral equations is applied. The analytical transformation of the integral equations makes it possible to avoid singularities and to reduce the problem of integrating to standard numerical quadratures. Due to good convergence of series and integrals it is enough to take 15-20 terms in the series and numerical quadratures to get an accuracy not worse than 0.1%. We find the frequency band where the structure can behave as a frequency-selective one. The geometrical grating parameters for the structure to be absolutely reflecting, or, alternatively, completely transparent, are found. The results of this work can form a basis for further investigations of hybrid wave propagation in complex dielectric structures