Dynamical diffraction area applicability in case of 1D photonic crystals with sinusoidal permittivity profile

Bragg reflection and transmission spectra of the 1D photonic crystals characterized by a spatially sinusoidal profile of permittivity are studied as a function of the crystal-plate thickness. Applicability of the dynamical theory of diffraction in describing such spectra is considered. In the framework of the dynamical theory, we (i) calculated and analysed the reflection and transmission spectra for oblique incidence of polarized light, (ii) computed the spectra making use of the transfer matrix technique, and (iii) compared quantitatively the results of the two approaches. As a result, the analytical dynamical theory of diffraction is found to be correct in calculating the Bragg spectra in the vicinity of single photonic band-gap when the plate thickness is equal to the integer number of the spatial periods, or the permittivity is symmetric about the middle plane of the structure.