A new full-vector approach to calculate leaky modes on three-dimensional bending waveguides is developed and demonstrated with the help of the cylindrical perfectly matched layer (CPML) numerical boundary conditions. By utilizing the complex coordinate stretching technique in the cylindrical system, a new set of full-vector wave equations for the bending waveguide structures are derived for the perfectly matched layer regions. Numerical solutions by the finite-difference schemes for the new wave equations are shown to yield highly accurate complex propagation constants (e.g., the bending-induced phase shifts and leakage losses) and modal field patterns, due primarily to the effective CPML.
Ning-Ning Feng, Gui-Rong Zhou, Chenglin Xu, and Wei-Ping Huang, "Computation of Full-Vector Modes for Bending Waveguide Using Cylindrical PerfectlyMatched Layers," J. Lightwave Technol. 20, 1976- (2002)