Exact equivalent-profile formulation for bent optical waveguides
  A widespread, intuitive and computationally inexpensive method to analyze light guidance through waveguide bends is by introducing an equivalent straight waveguide with refractive index profile modified to account for actual waveguide bend. Here we revise the commonly used equivalent-index formula, ending up with its simple extension that enables rigorous treatment of one- and two-dimensionally confined, uniformly bent waveguides, including tightly coiled microstructure fibers, curved ridge waveguides and ring microresonators. We also show that such technique is applicable only to waveguides composed of isotropic or uniaxially anisotropic materials, with anisotropy axis directed perpendicular to the curvature plane. 
Dzmitry M. Shyroki