Investigation of the features of Bose-Einstein condensation of unitary polaritons in crystalline and photonic-crystalline media

Unitary (transparently associated, transparent) polaritons are quanta of the electromagnetic field in matter for which interaction with the phonon subsystem leads to an effective refractive index equal to unity ("unitary", hence the name). The material medium for such light quanta is optically identical to a vacuum, which makes transparent polaritons extremely interesting both for controlled illumination of optical media and for modeling nonlinear vacuum optical processes in matter (such as, for example, γ→a). In this paper, the possibilities of condensation of transparently associated polaritons in periodic material media (crystalline and photonic crystalline) are investigated and the characteristic features for crystalline and photonic crystalline cases are clarified. It has been established that condensation of transparently associated polaritons in the visible region of the spectrum is impossible in ordinary (non-photonic) crystals, however, in photonic crystals, on the contrary, it can be realized at any required wavelength. The results obtained are interesting for obtaining tunable coherent optical generation based on the parametric optical process γγ → a(φ',φ")→γ'y', in which an intermediate (axion-like) bipolariton a is synthesized and destroyed, and the frequency of useful radiation γ'"is tuned" by auxiliary phonons φ' and φ".