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Photonic crystals, the artificially created multilayer structures with dielectric permittivity and geometric dimensions varying with a period comparable to the wavelength, were studied by the calculation of light interference in a given multilayer system. The developed calculation programs using the matrix method made it possible to obtain the optical characteristics (reflection, transmission, etc.) for any multilayer coatings. The focus was on the analysis of the influence of defects associated with the violation of the layer periodicity. Spectral dependences of the reflection coefficient, argument of Chebyshev polynomial and argument module of the Chebyshev polynomial are given. The calculation of the optical characteristics of multilayer coatings by the matrix method provided the opportunity to identify the presence of barrier zones for periodic and defective systems and to propose their use as the contrast or narrowband interference filter.
