Comparison of the characteristics of the light field in a one-dimensional photonic crystal with the harmonic dielectric constant obtained according to the theory of the perturbations and with the direct calculation

Abstract

Previously, was developed the method for calculating the light field inside a one-dimensional photonic crystal using perturbation theory by the value detuning from the band edge and calculating using this method the resonance properties of spectral transparency windows adjacent to band edge of a photonic crystal. The method allows to find the field when light propagates with frequencies lying near the band edge by using a set of eigenfunctions corresponding to the band edge for an infinite medium. The analytical expressions are obtained to describe this field and its characteristics, through these eigenfunctions. In the present work, the solution errors obtained by this method are investigated in comparison with direct computer-aided calculation of the field for a medium with a harmonic variation of the dielectric constant under various conditions for implementing this method. The problems of limiting the set of used spatial harmonics when calculating eigenfunctions (2 or more), limiting the number of eigenfunctions involved in constructing a solution (2 or more) are considered.