Light Waves in 1D Photonic Crystals with Arbitrarily Changing Dielectric and Magnetic Permittivities

The reflection and transmission of electromagnetic waves in 1D photonic crystals (PCs) is discussed. The periodicities of both dielectric and magnetic permittivity are taken into account. The dielectric and magnetic permittivities are considered as spatially changing arbitrary functions. We show that for a certain, sufficiently large, range of cases this problem can be reduced to a set of two linear differential equations instead of complicated matrix equations of transfer-matrix method. The effects of the Photonic Band Gap (PBG) shift, width change, new transmission zone contacts, etc., in cases of different PC apodization and chirp are investigated. This method works fine for standard PCs, as well as for left media and metamaterials. An important consequence is the condition for PBG suppression for all wavelengths, associated with non-constancy of both dielectric and magnetic permittivities.