An efficient full-vectorial finite-element modal analysis of dielectric waveguides incorporating inhomogeneous elements across dielectric discontinuities

A new vectorial finite-element method (FEM) free of spurious modes is proposed for analyzing optical waveguides with sharp corners in the cross section. The method is formulated in terms of the transverse field components H-x and H-y or E-x and E-y, and it explicitly shows the relationships between the semivectorial and the full-vectorial wave equations, In this method,we introduce the distribution concept and an inhomogeneous element to describe the field across the dielectric interface, and the error in the numerical solution caused by the dielectric discontinuity is reduced. We show how the width of such inhomogeneous elements and the number of nodes would affect the numerical result and its convergent rate using the dielectric-loaded rectangular waveguide, the channel waveguide, and the rib waveguide as analysis examples. For the dielectric-loaded rectangular waveguide, we compare our results with the exact solutions, For the rib waveguide, we compare our results with previously published data based on other methods. Also, field convergence near the corners is discussed.