To rigorously evaluate the propagation characteristics of an inhomogeneous and/or anisotropic waveguide, a Vectorial wave analysis is necessary, with at least two field components. These formulations are fundamentally more accurate than scalar forms, since they can represent true hybrid modes in a general dielectric waveguide. A semi-vectorial Beam Propagation Method (BPM) can identify polarization dependence; however, only a full Vectorial approach can calculate power coupling between two polarization states.

OptiBPM includes a vector BPM based on the finite-difference schemes (FD-VBPM). This versatile, efficient, and accurate numerical approach has the following main features:

•     solves the vectorial modes of a z-invariant waveguide structure with arbitrary index distribution in the cross section and takes both polarization dependence and polarization coupling into consideration.

•     models the propagation of vectorial electromagnetic wave in a z-varying waveguide structure with arbitrary cross section.

•     handles anisotropic material so that the polarization dependence and coupling due to both materials and geometry can be considered.

•     perfectly matched Layers are included in order to effectively absorb the nonphysical radiation waves.

•     Wide Angle BPM is implemented using high order Pade recursion, making it possible to simulate multiple propagating modes traveling a widely different off- axis, with no need to accurately guess the “reference” index n0 .

•     Formulations can be based on the electric or magnetic field components which are naturally continuous across the dielectric interfaces.

•     The axial component is eliminated by using the zero divergence constraint

∇ ⋅ ( n2 E ) = 0 (Gauss’s Law) for E formulation or ∇ ⋅ = 0 for the formulation based on magnetic field. Therefore, the transverse components are sufficient to describe the full-vectorial natures of the electromagnetic field.

Note: The inclusion of divergent condition guarantees the complete elimination of spurious modes.

•     The formulation is optimized by the use of efficient sparse techniques to solve the resultant complex matrix equations.