Novel boundary condition for the finite-element solution of arbitrary planar junctions

A novel boundary condition for a two-dimensional finite-element method (2D- FEM) is developed to simulate accessing waveguides to planar optical juncti ons, This new boundary condition is based on a paraxial approximation to th e field's derivatives over the junction's ports, The formulation is very ea sily adapted within the 2D-FEM framework while providing good simulation re sults. Two examples are provided to show the applicability and reliability of the present method: a waveguide step discontinuity and a sharp waveguide bend.