Finite Element Modeling Of Optical Guided Wave Devices

Abstract

Results for a wide range of optical waveguides and directional couplers with planar, diffusedl, linear, nonlinear, isotropic, anisotropic, lossy (gain), multiple quantum well, and metal plasmon regions are presented using the accurate vector H-field finite element method. The optimization of the performance of the optical guided wave devices requires knowledge of their propagation characteristics and field distributions, and their dependence on the fabrication parameters. As the range of the guiding structures becomes more intricate, so there is the need for versatile modeling techniques which can be used to characterize accurately a wide range of practical optical guided wave devices with material inhomogeneity, nonlinearity or anisotropy. Analytical moldeling techniques available to analyze and design lightwave devices require many restrictive, and sometimes unrealistic assumptions. Various types of numerical anal-ysis methods for optical waveguides have been developed and for a general discussion on this topic, it is appropriate to refer to two review papers by Sorrentino [l] and Saad [ 2 ] . Among the different numerical approaches possible, the finite element method has established itself a s a powerful method throughout engineering for its flexibility and versatility, being used in complicated structural, thermal, fluid flow, semiconductor, and electromagnetic problems. A review paper by Rahman e t a l . [ 3 ] discusses the application of the finite element method to microwave and optical waveguides. This method is particularly advantageous, because of its applicability to waveguides with arbitrary shape, arbitrary refractive index profile, and anisotropic or nonlinear materials. The finite element method has been widely used during the last two decades in the design of various optical waveguide structures and it is probably the waveguide analysis method that is most generally applicable and most versatile. In the finite element method [4,5], the cross-section of the optical waveguide concerned is first suitably divided into a number of subdomains or elements. Each element can have various shapes, such as triangles or rectangles or even with curved sides, and they can also be of various sizes. Using many elements, a given waveguide cross-section with a complex boundary and with arbitrary permittivity distribution can be accurately approximated. Several different variational formulations have been proposed for use with the finite element method to analyze optical waveguides. Among them, the simplest are the scalar formulations, which consider only one field component and these have been used for solving optical waveguide problems [ 6 ] . The scalar formulations are exact for purely TE or TM modes in the one-dimensional planar guides; but they are inadequate, except as an approximation, for the inherently hybrid modes of two-dimensional optical waveguides. Among the vector formulations, the Ez/Hz [ 7 ] , the vector B field [ 8 ] , vector E field 191 and Ht [lo] can be mentioned. The Ez-Hz formulation cannot treat general anisotropic problems without destroying the canonical form of the eigenvalue equation. In this formulation enforcing the field continuity conditions are quite difficult and another weakness is that this formulation is based on the axial components which are not the dominant field components for optical modes. Among the full vector E or H formulation, the H-f ield formulation is more suitable for optical waveguide problems as the magnetic field is; naturally continuous everywhere, whereas, the electric