Semivector Finite-Difference Formula for the Analysis of a Step-Index Waveguide With a Tilted Interface

A three-point finite-difference formula is derived for the analysis of a step-index waveguide with a tilted interface. The formula is suitable for the use of the alternating-direction implicit method. Through the analysis of a rib waveguide with a sloped side wall and a hollow triangular waveguide, improvement in accuracy and stability is demonstrated.