Finite element method analysis of propagation in a non magnetic coupled waveguide structure having α-power refractive index profile

Abstract

The work presented in the paper is a numerical study of a waveguiding component. The structure studied is a coupler consisting of three closely-coupled weakly-guiding one-dimensional waveguides. The refractive index profile of the coupler has been allowed to vary arbitrarily. The scalar finite element method (FEM) has been used to separately extract the TE and TM modes supported by this coupler and propagate them along the structure using a beam propagation method (BPM). We excite structure with Eigen mode profile which can be well approximated by Gaussian shape pulse. The effect of waveguide separation has been well demonstrated by using an example. The Crank-Nicolson (CN) scheme has been used to stabilize the propagation and transparent boundary conditions (TBC) which have been used to absorb energy leaked by the waveguides to the outer boundaries. The work’s main finding is that the coupling period of the structure can be changed by altering the index profile of the middle waveguide; step-, parabolic- and triangular-profile distributions have been studied and compared. In FEM analysis we have used the variable discretization step (δ) for the better accuracy of the results.