An improved three-dimensional full-vectorial finite-difference imaginary-distance beam propagation method

A modified alternating direction implicit approach is proposed to discretize the three-dimensional full-vectorial beam propagation method （3D-FV-BPM） formulation along the longitudinal direction. The cross-coupling terms （CCTs） are neglected at the first substep, and then double used at the second substep. The order of two substeps is reversed for each transverse electric field component so that the CCTs are always expressed in an implicit form, thus the calculation is efficient and stable. Based on the multinomial interpolation, a universal finite difference scheme with a high accuracy is developed to approximate the 3D-FV-BPM formulation along the transverse directions, in which the discontinuities of the normal components of the electric field across the abrupt dielectric interfaces are taken into account and can be applied to both uniform and non-uniform grids. The corresponding imaginary-distance procedure is first applied to a buried rectangular and a GaAs-based deeply-etched rib waveguide. The field patterns and the normalized propagation constants of the fundamental and the first order modes are presented and the hybrid nature of the full-vectorial guided-modes is demonstrated, which shows the validity and utility of the present approach. Then the modal characteristics of the deeply- and shallow-etched rib waveguides based on the InGaAsp/InGaAsP strained multiple quantum wells in InP substrate are investigated in detail. The results are necessary for modeling and the design of the planar lightwave circuits or photonic integrated circuits based on these waveguides.

Modelling of graded index waveguide fabricated by ion exchange on Er^(3+) doped glass

A general numerical tool, based on thermal diffusion equation and full-vectorial eigen-mode equation, has been presented for the systematic analysis of graded index channel waveguide fabricated by ion exchange on Er^3＋ doped glass. Finite difference method with full-vectorial formulation （FV-FDM） is applied to solving the full-vectorial modes of graded index channel waveguide for the first time. The coupled difference equations based on magnetic fields in FV-FDM are derived from the Taylor series expansion and accurate formulation of boundary conditions. Hybrid nature of vectorial guided modes for both pump （980 nm） and signal light （1550 nm） are demonstrated by the simulation. Results show that the fabrication parameters of ion exchange, such as channel opening width and time ratio of second step to first step in ion exchange, have large influence on the properties of waveguide. By optimizing the fabrication parameters, maintenance of monomode for signal light and improvement of the gain dynamics can be achieved in Er^3＋ doped waveguide amplifier （EDWA） fabricated by ion exchange technique. This theoretical model is significant for the design and fabrication of EDWA with ion exchange technique. Furthermore, a single polarization EDWA, which operates at wavelength from 1528 nm to 1541 nm for HE polarization, is numerically designed.