Bending Losses of the Asymmetric Slab Waveguide

E. A. J. Marcatili has shown that a bent slab waveguide loses power by radiation. 1 His analysis is based on a solution of the eigenvalue equation of the bent waveguide. It is possible to derive the expression for the bending losses from an approximate theory that is much simpler than the solution of the eigenvalue equation. We use this method to derive the formula for the bending losses of an asymmetric slab waveguide. The symmetric slab waveguide is, of course, included in this treatment as a limiting case. The result of this approximate theory is in very good agreement with the theory of Marcatili. Furthermore, if the parameters of the H E U mode of the round optical fiber are used in the slab waveguide formula, loss values are obtained that agree well with experimental loss values for this mode. 2 The bending loss theory presented in this paper is based on the following idea. A bent slab waveguide can conveniently be described in a cylindrical coordinate system whose axis coincides with the center of curvature of the waveguide (Fig. 1). The solution of Maxwell's equations 2551