Finite difference split step method for non-paraxial semivectorial beam propagation in 3D

Abstract

A non-paraxial semivectorial method in the finite difference split step scheme is proposed. The method can model wide-angle beam propagation in waveguides with high index contrast and gives good accuracy even for moderate discretization. A new method for splitting of operators is used to maintain the continuity of terms. This splitting also makes the propagation more efficient. The method is relatively insensitive to the choice of the reference refractive index.

A stable complex Jacobi iterative solution of 3D semivectorial wide-angle beam propagation using the iterated Crank–Nicholson method

“…That polarization effects on high-index-contrast waveguides play an important role on an accuracy of BPM was already shown in (Bhattacharya and Sharma 2009). In this paper, we will investigate how polarization effects affect the convergence rate of the CJI method and its execution speed in comparison with the DMI method.…”

“…However, it will be overcome if we investigate the first two terms in Eq. (1) together (Bhattacharya and Sharma 2009). Using the SVEA, in which the wave function (x, y, z) propagating in the z direction can be separated into a slowly varying envelope function (x, y, z) and a very fast oscillating phase term exp(−ikz), the Helmholtz equation is given by:…”

“…We begin by considering the semivectorial Helmholtz equation for the electric field component (Bhattacharya and Sharma 2009)…”

“…This approximation does not hold for modeling optical propagation in waveguides on semiconductor substrates which frequently involve abrupt index changes. For these cases a full vectorial analysis is needed (Bhattacharya and Sharma 2009). Unfortunately, full vectorial schemes require large computational efforts.…”