Implementation of a finite difference frequency domain mode solver incorporating subpixel smoothing

Area of Science:

• Computational electromagnetics
• Photonics and optical engineering
• Numerical methods in physics

Background:

• Finite difference frequency domain (FDFD) mode solvers are common but struggle with convergence in high-contrast dielectric structures.
• Accurate waveguide mode analysis is crucial for photonic device design and simulation.

Purpose of the Study:

• To improve the convergence properties of full-vectorial FDFD mode solvers.
• To introduce subpixel smoothing as a technique for enhancing FDFD solver performance.
• To demonstrate the effectiveness of tensor smoothing in analyzing complex waveguide structures.

Main Methods:

• Formulation of a generalized eigenproblem on a Yee grid.
• Incorporation of subpixel smoothing to handle tensor effective dielectric constants.
• Investigation of convergence using step-index fibers, microstructured fibers, and plasmonic waveguides.

Main Results:

• Subpixel smoothing significantly improves the convergence of the FDFD mode solver.
• The proposed method allows for the use of less dense computational grids.
• Accurate mode analysis was achieved for diverse waveguide types, including plasmonic ones.

Conclusions:

• Subpixel smoothing is an effective technique for accelerating FDFD mode solver convergence.
• The generalized eigenproblem formulation with tensor smoothing enhances computational efficiency and accuracy.
• The open-source implementation facilitates wider adoption in photonic simulations.