Unconditionally stable procedure to propagate beams through optical waveguides using the collocation method

Perfectly matched layer in numerical wave propagation: factors that affect its performance

The perfectly matched layer (PML) boundary condition is generally employed to prevent spurious reflections from numerical boundaries in wave propagation methods. However, PML requires additional computational resources. We have examined the performance of the PML by changing the distribution of sampling points and the PML's absorption profile with a view to optimizing the PML's efficiency. We used the collocation method in our study. We found that equally spaced field sampling points give better absorption of beams under both optimal and nonoptimal conditions for low PML widths. At high PML widths, unequally spaced basis points may be equally efficient. The efficiency of various PML absorption profiles, including new ones, has been studied, and we conclude that for better numerical efficiency it is important to choose an appropriate profile.

Variable-transformed collocation method for field propagation through waveguiding structures

We show that an appropriate variable transformation can redistribute the sample points for the field in the collocation method such that the numerical accuracy of the field-propagation algorithm improves significantly. We also present results for some specific transformations that improve the accuracy by more than 2 orders of magnitude.