Rytov-s Law for Electromagnetic Field Vectors Rotation and Its Generalizations

This paper deals with extensions and modifications of Rytov-s law. Firsr of all, the conventional representation of Rytov-s law in the natural trihedron system related to the ray is compared with the representation in the Popov orthogonal coordinate system that realized the parallel shift of the field vectors along the ray. It is noted that Rytov-s law can be considered as a special case of the Berry topological phase as applied to electromagnetic waves in isotropic media.

Two extensions of Rytov-s law are described: (1) the optical Magnus effect that appears in the second approximation of the method of geometrical optics and (2) the quasi-isotropic approximation of geometrical optics that takes into account weak anisotropy of the medium and lays a bridge between waves in isotropic media (Rytov-s theory) and waves in anisotropic media (the Courant-Lax theory).