Effect of a slight bend in an optical fiber on the radiation characteristics

The characteristics of a trial function of the vector wave equation which give rise to a longitudinal shift of the field amplitude along the radius of curvature, on the one hand, and to the existence of a transverse component of the propagation constant, on the other, satisfy a variational principle. Results derived for a slightly inhomogeneous medium lead to the conclusion that the characteristics of the field and of a ray path are interdependent. The method used in this paper makes it possible to determine the propagation constant as a function of the curvature of the bend in the fiber at an arbitrary accuracy.