A Meshless Based Solution to Vectorial Mode Fields in Optical Micro-Structured Waveguides Using Leaky Boundary Conditions

Leaky boundary conditions are implemented in a meshless numerical method to solve vectorial mode fields in optical waveguides which allow for the solution of both guided and leaky modes. The modes are found using an approximating solution, the Finite Cloud Method (FCM), to the coupled field equations of the transverse components of the magnetic field. In this paper we extend the method by implementing two absorbing boundary conditions, Transparent Boundary Conditions (TBC) and Perfectly Matched Layers (PML), to solve the leaky modes for several microstructured air hole waveguides. Presented are methods to further refine the boundary conditions and to stabilize the solutions. A comparison between these methods and previously published results show close agreement. Finally, we conclude that the TBC boundary condition is the superior method due to its robustness and lack of fitting parameters.