Geometric optics in a rotating dielectric

Rotating solid-state homogeneous isotropic dielectric without dispersion in the accompanying rotation of the reference frame turns out to be an inhomogeneous anisotropic medium due to the influence of two competing physical mechanisms: the inhomogeneity of free space caused by rotation and entrainment of light by the moving medium. In a rotating dielectric in the geometric optics approximation the eikonal equation and the corresponding system of ordinary differential equations in characteristic form are obtained. The solutions of the equations with the calculated parameters determined using of the first integrals of the system are pairs "opposite "$R$-ray trajectories and $f$-phase trajectories fronts. A formula for the intensity of a light pulse propagating along an arbitrary $R$-trajectories was obtained. "Oncoming "trajectories of both types do not have common points and are shifted to opposite sides of a straight line between end points. Their structural parameters (minimum distance to the axis of rotation, the length of the arc, the region of determination by the azimuthal coordinate, the optical length, etc.) change under the influence of both physical mechanisms, depending on the speed of rotation. Closed optical paths in the RRF for the relay network and for the two-mirror Fabry–Perot resonator in generating laser can be created using two types of mirrors that are adaptable to the frequency of rotation which normals to the reflecting surfaces must have certain different angles with the ray vectors and wavefronts of radiation arriving at the reflector. The Sagnac effect is a consequence inhomogeneity (deformation) of free space along the azimuthal coordinate, and its value is the result of the competing influence of both physical mechanisms.