It is shown that the magnitude of the Rytov rotation of the plane of polarization about the natural Frenet trihedron can be expressed in terms of the torsion tensor components (Christoffel symbols) in the curvilinear coordinate system where the Frenet trihedron is fixed. It is proposed to extend the Rytov law to an arbitrary curvilinear coordinate system. When applied to a curvilinear coordinate system in which the wavefront surface is a function of two coordinates, the "generalized" Rytov law makes it possible to predict the effect of additional rotation of a beam of rays. The effect is proportional to the average wavefront curvature and is determined by the sign of circular polarization. It is predicted that in the case of a multimode optical waveguide the speckle pattern is rotated by the angle that is equal to the magnitude of the Rytov rotation of field vectors.
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