FIELD DEFORMATION ON A BENT STEP INDEX FIBER

We consider the problem of propagation of light in a bent step index circular core optical fibre. We first derive the exact equations in toroidal coordinates and give an analytic solution at first order with respect to the parameter lambda/(curvature radius), neglecting radiation losses. The field pattern is analysed and discussed in the case of weak guidance. A variational approach has been used to find the second order corrections to the effective index. In the special case of LP1,q modes, the correction is found to depend on the orientation of the field pattern with respect to the curvature plane.