Finite element analysis of bent graded-index planar dielectric waveguide

Abstract

Millimeter wave and optical wave integrated circuits have made significant progress recently. However, device development has been limited by a lack of fundamental understanding in many areas. The propagation characteristics including modal solutions of bent dielectric waveguide are in need of basic research. Many methods (including analytical methods and numerical methods) have been utilized for the analysis of this problem; however, they are either approximate or are computationally intensive. [11.[31 In comparison, a new numerical approach based on the finite element method is proposed in this paper. Rigorous functional expression that include the gradient index is derived from Maxwell's equations in local bent coordinate system. After the finite element discretization of the local field, the generalized algebatic eigenvalue problem is obtained by the variational approach; and then, the eigenvalues and eigenfunctions of the bent dielectric waveguide can be obtained. Fig.1 shows the bent graded-index dielectric waveguide in the local bent coordinate system (x,y,$). We assume that the electromagnetic fields are invariant in the y direction, thus TE modes and TM modes can be considered independently in the structure. The solutions of the eigenmodes can be obtained from the following scalar wave equation