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Full-vectorial beam propagation method for waveguide modeling

The beam propagation method (BPM) is one of the most popular approaches in modeling electromagnetic field propagation. The conventional BPM is established on scalar Helmholtz equation using paraxial approximation. There are limits in the analysis of the vector properties of electromagnetic field and wide-angle propagation. This paper presents the techniques of removing these limits. A full-vectorial BPM bases on finite-difference technique is described from vector wave equations, called finite-difference vectorial beam propagation method (FD-VBPM). The main disadvantage of FD-VBPM is the calculation inefficiency, especially in three dimensional modeling. To obtain two dimensional equivalent structures, a precise optimization approach is adopted. Propagation constant and field of fundamental mode best match those of the original waveguide. The method has very high accuracy. The decoupled semi-vectorial BPM is also derived. The full-vectorial method is extended to wide-angle BPM removing paraxial limit. The method bases on Pade approximant. Simulations are made on rib waveguide.