Spectral Galerkin mode-matching method for applications in photonics

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.