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Spectral and Angle-Resolved Magneto-Optical Characterization of Photonic Nanostructures

Spectral and Angle-Resolved Magneto-Optical Characterization of Photonic Nanostructures

Published on: November 21, 2019

Spectral Galerkin mode-matching method for applications in photonics.

Nan Zhang¹, Ya Yan Lu¹

¹Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong, China.

Physical Review. E

|June 22, 2024

Summary

This summary is machine-generated.

A new spectral Galerkin mode matching method (SGMM) enhances photonic device simulations. SGMM improves numerical stability and accuracy, even with many eigenmodes, for efficient device design.

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Area of Science:

Photonics and optical engineering
Computational physics
Numerical methods

Background:

Engineered photonic devices often have separable material properties, enabling efficient simulation via mode-matching.
Existing piecewise polynomial methods face numerical instability with numerous eigenmodes.
Global Fourier or low-order finite schemes offer less accuracy.

Purpose of the Study:

Introduce a stable and accurate numerical method for simulating photonic devices with separable variables.
Address the limitations of existing mode-matching techniques, particularly numerical instability.
Enhance the efficiency and reliability of photonic device simulations.

Main Methods:

Developed the spectral Galerkin mode matching method (SGMM).
Employs a global piecewise-polynomial basis and Galerkin method to solve for eigenmodes.
Leverages pseudo-orthogonality of numerical eigenmodes to ensure well-conditioned systems.

Main Results:

SGMM numerical eigenmodes preserve the pseudo-orthogonality of analytical eigenmodes.
The method results in typically well-conditioned linear systems.
Demonstrated superior stability and reliability compared to other methods, even with large numbers of eigenmodes.

Conclusions:

SGMM offers a robust solution for simulating photonic devices with separable properties.
The method overcomes the numerical instability issues of traditional techniques.
SGMM provides accurate and reliable results, facilitating advanced photonic device design.