Fast multi-source nanophotonic simulations using augmented partial factorization

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.
• 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.