Improved imaginary-distance beam propagation method for full-vectorial eigenmode analysis of optical waveguides

Two schemes are developed to improve the computational accuracy of the full-vectorial imaginary-distance beam propagation method (FV-ID-BPM). In the first scheme, the cross-coupling terms (CCTs) demanded for the FV analysis are expressed in explicit forms, which are independent of specific types of waveguides, by using an improved finite-difference formula. In the second one, the generalized Douglas (GD) scheme is adopted for discretizing the second-order partial derivatives in the FV-ID-BPM equations. A detailed comparative study between the two schemes in improving the computational accuracy is performed by taking a strongly-guiding rib waveguide as a testing example. The highest accuracy is demonstrated in case of the combination of the two schemes. Nevertheless, the improved FD formula for the CCTs is proved to play a much more significant role than the GD scheme in improving the computational accuracy. Moreover, the effectiveness of the GD scheme diminishes as the FD grid is refined.