On Generation Thresholds of a Chiral Laser of Circularly Polarized Radiation

We have calculated the dispersion of exciton-polariton resonance energies and linewidths, as well as the Stokes parameters of the far-field radiation of a semiconductor microcavity with a chiral photonic crystal of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{C}_{4}}$$\end{document} symmetry on the upper Bragg mirror. Lowering the symmetry of the laser generation region in such a microcavity was shown to break the degeneracy of the generation thresholds of doubly degenerate states at the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Gamma $$\end{document} point of the Brillouin zone. This results in elliptical polarization of the laser radiation in the far field with a high degree of circular polarization. The orientation of the linearly polarized component depends on the shape of the excitation region.