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Fast multi-source nanophotonic simulations using augmented partial factorization.

Ho-Chun Lin¹, Zeyu Wang¹, Chia Wei Hsu²

¹Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, CA, USA.

Nature Computational Science

|January 4, 2024

Summary

This summary is machine-generated.

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This study introduces a faster method for simulating large electromagnetic systems by directly computing results, significantly reducing computation time for nanophotonics and electromagnetics applications.

Area of Science:

Nanophotonics and Electromagnetics
Computational Physics

Background:

Numerical solutions of Maxwell's equations are crucial for nanophotonics and electromagnetics.
Simulating large, multi-channel systems (e.g., disordered media, metasurfaces, photonic circuits) is computationally intensive.
Conventional methods solve full-basis discretizations, often one input at a time, leading to inefficiency.

Purpose of the Study:

To develop a novel computational approach for efficiently solving Maxwell's equations for large-scale electromagnetic systems.
To bypass the need for full-basis solutions and repetitive single-input simulations.
To accelerate the computation of quantities of interest in nanophotonics and electromagnetics.

Main Methods:

Augmenting the Maxwell operator with all input source and output projection profiles.

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Employing a single partial factorization to compute the generalized scattering matrix via the Schur complement.

This method is an exact numerical solution, limited only by discretization.

Main Results:

The proposed method achieves significant speedups, ranging from 1,000 to 30,000,000 times faster than existing techniques for 2D systems with ~10 million variables.
Demonstrated successful simulations of complex phenomena like entangled photon backscattering from disorder.
Enabled simulations of large-scale (thousands of wavelengths) high-numerical-aperture metalenses.

Conclusions:

The developed technique offers a highly efficient and scalable solution for electromagnetic simulations.
This approach dramatically reduces computational cost and time for complex nanophotonic and electromagnetic systems.
The method is broadly applicable to any linear partial differential equation, promising wider scientific impact.