A finite-difference beam propagation method (FD-BPM) is outlined and assessed in comparison with a conventional beam propagation method (FFT-BPM) which uses fast Fourier transformation. In the comparative study three straight waveguides with different index profiles that are frequently encountered in integrated optics are utilized. Using both methods normalized effective index values of the eigenmodes of these waveguides are calculated and compared with the exact values obtained from analytical expressions. As a further accuracy criterion, the power loss due to numerical errors when an eigenmode of a waveguide is excited is evaluated. Based on this comparison the accuracy, computational efficiency, and stability of the FD-BPM are assessed. >

An assessment of finite difference beam propagation method

Recently, it has been shown that if the paraxial wave equation is modified such that fields travel imaginary distances, the field resulting from an imaginary-distance propagation is the fundamental mode of an optical waveguide. For the finite-difference beam-propagation method, we derive the factor by which each eigenmode is amplified during one propagation step. This amplification factor places limits on the inputs-step size, input field, effective index guess, and implicitness parameter-and gives clues on how to optimize the inputs. In particular, we identify and study two optimal sets of inputs, which can reduce computational time significantly. We can obtain the fundamental mode and its propagation constant within a few propagation steps. >

A study and optimization of eigenmode calculations using the imaginary-distance beam-propagation method

This paper is concerned with the application of the method of lines (MoL) to the analysis of general dielectric waveguides that are uniform along the direction of propagation, lossfree, and passive. Hybrid-mode dispersion curves, field and intensity distributions for integrated optical waveguides are presented. >

Method of lines for the analysis of dielectric waveguides

An efficient and simple explicit finite difference beam propagation method (EFD-BPM) incorporating nonuniform mesh is described. The criteria for stability are developed, and it is shown that this algorithm is power conserving when the stability criteria are met. EFD-BPM is applied to the analysis of single and coupled semiconductor rib waveguides and its accuracy is confirmed by comparing the results with the reported results. Nonuniform mesh is found to improve the efficiency of the method significantly for the analysis of weakly guiding waveguide structures. Several coupled rib waveguide structures with curved input and output branching sections are analyzed using both three-dimensional EFD-BPM and two-dimensional finite difference BPM combined with effective index approximation. >

Analysis of Z-invariant and Z-variant semiconductor rib waveguides by explicit finite difference beam propagation method with nonuniform mesh configuration

The aim of this study was to investigate the impact of daily atmospheric weather conditions on daily leisure activity engagement, with a focus on physically active leisure. The methods capitalize on time diary data that were collected in Halifax, Nova Scotia to calculate objective measures of leisure activity engagement. Daily meteorological data from Environment Canada and daily sunrise and sunset times from the National Research Council of Canada are used to develop objective measures of the natural atmospheric environment. The time diary data were merged with the meteorological data in order to quantify the statistical association between daily weather conditions and the type, participation rate, frequency, and duration of leisure activity engagement. The results indicate that inclement and uncomfortable weather conditions, especially relating to thermal comfort and mechanical comfort, pose barriers to physically active leisure engagement, while promoting sedentary and home-based leisure activities. Overall, daily weather conditions exhibit modest, but significant, effects on leisure activity engagement; the strongest associations being for outdoor active sports and outdoor active leisure time budgets. In conclusion, weather conditions influence the type, participation rate, frequency, and duration of leisure activity engagement, which is an important consideration for health-promotion programming.

Weather impacts on leisure activities in Halifax, Nova Scotia.

In order to compare various modelling techniques for the eigenmode analysis of integrated optical waveguides, twelve different methods are applied to the analysis of two typical III–V rib waveguidesl Both a single and a coupled waveguide case are considered. Results focus on the effective refractive index value for the lowest order TE-mode in the case of the single waveguide, and on the coupling length between the lowest order symmetric and antisymmetric TE-modes of the coupled waveguides.This paper is the result of the joint effort of thirteen research groups in the framework of the Device Modelling group of the COST-216 project.

H.J.W.M. Hoekstra

Papers

Comparison of different modelling techniques for longitudinally invariant integrated optical waveguides