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The interaction between the two kinds of gaps that appear in the band structure of a photonic crystal has been studied. The structure gap appears as a consequence of diffraction in the periodic structure, if the optical contrast between the the two matrials is sufficiently strong. The width of such gaps increases with the optical contrast and the position, for a given structure, scales with the lattice constant. Secondly, the dielectric function of one of the materials may be such that the photonic crystal exhibits an effective stop band. Metals have a dielectric function with a large negative real part in the visible and infrared wavelength regions. Metallo-dielectric photonic crystals have been intensively studied recently, and interesting results have been obtained. Alternatively, a Reststrahlen band can be used, within which the dielectric function is metal-like. The physical mechanism behind such a band is the excitation of polaritons, i.e. lattice oscillations. Only compounds have Reststrahlen bands, and they appear in the infrared. We refer to the corresponding stopband as a polaritonic gap. Transfer matrix calculations have been used to obtain the photonic bandstructure in the infrared for a 2-D square structure consisting of beryllium oxide cylinders in air. Photonic band structure calculations across a reststrahlen band region are numerically demanding because of the strong dispersion. Calculations were made with different lattice constants and fill factors. We have compared a situation when the two gaps are widely separated, with one where the gaps are close or even on top of each other. We report two kinds of forbidden gap states as a function of the imaginary wave-vector. We use normal incidence transmittance spectra to define phonomenological gaps, and report their variation with linear density and lattice constant.
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