Finite difference methods in optoelectronic simulation

Large scale numerical models based on two-dimensional or three-dimensional meshes are often used in the study of optical waveguides and related components. The finite difference (FD) method is one such technique. It has proven very effective for calculations of the propagation constants and field profiles of the modes supported by a wide range of waveguide technologies. More recently, it has also been applied in the time domain and in beam propagation. We will review FD mode solvers. The first such solvers were based on the scalar wave equation which is a simple, self-adjoint equation. When written in difference form, this yields a symmetrical coefficient matrix whose eigenvalues are easy to find