Homotopic groups of photon propagators in isotropic, bi-isotropic and Faraday materials

With the use of an evolutionary approach the branches of solutions of the tensor dispersion photon equations in isotropic, bi-isotropic and Faraday media are investigated. It is shown that the homotopic groups of photon propagators with the generators being the refractive index operators correspond to these solutions. The latter operators are divided into two groups. These are operators with non-zero trace and traceless operators. The traceless operators correspond to meeting photons and are represented by infinite sets of isometries and involutions of the three-dimensional space. The analysis of polarization states is carried out for photons meeting in non-absorbing and absorbing isotropic media and curvatures, torsions and Darboux-Lagrange vectors of the spiral lines related to such states are found.