Dielectric matrices with air cavities as a waveguide photonic crystal

Frequency dependences of the transmission coefficient of a microwave photonic crystal that represents a structure containing alternating layers of ceramic material (Al$_{2}$O$_{3}$) with a relatively large number of cavities and foam plastic are studied in the presence and absence of distortions of the periodicity of a photonic structure. The frequency dependences of the transmission coefficient can be analyzed using a model of effective medium that makes it possible to consider the interaction of electromagnetic wave and photonic crystal using a transfer matrix of a 1D photonic crystal. The band character of the frequency dependence of the transmission coefficient of the photonic crystal related to the periodicity of the photonic crystal in the transverse plane for the waveguide with a standard cross section is not manifested in a certain range of material permittivities.