Practical vectorial mode solver for dielectric waveguides based on finite differences

Area of Science:

• Computational electromagnetics
• Waveguide theory
• Numerical analysis

Background:

• Accurate modeling of electromagnetic wave propagation in dielectric waveguides is crucial for optical device design.
• Existing numerical methods can struggle with boundary condition enforcement and numerical artifacts, especially at material interfaces.

Purpose of the Study:

• To develop and validate a robust finite-difference-based numerical solver for the electric field formulation of vector-wave equations.
• To improve the accuracy of simulations in dielectric waveguides by addressing boundary conditions and numerical artifacts.

Main Methods:

• A generalized eigenvalue problem was constructed using all three components of the electric field.
• A self-consistent formulation was employed to ensure accurate boundary condition enforcement.
• The finite-difference method was utilized for the numerical discretization.

Main Results:

• The solver demonstrated high accuracy in calculating propagation constants for waveguide structures.
• Accurate mode profiles were obtained, validating the solver's performance.
• The formulation effectively reduced numerical artifacts at permittivity discontinuities.

Conclusions:

• The presented finite-difference solver offers a reliable tool for analyzing dielectric waveguides.
• The self-consistent electric field formulation provides superior accuracy and stability.
• This method is suitable for complex waveguide designs and optical simulations.