Quickly solving Maxwell’s equations for photonics design

As the governing equations when it comes to light and matter interaction, Maxwell’s equations are essential for designing optical elements in photonic devices.

A typical approach for designing optical elements is to simulate an optical design and iteratively update that design based on the simulation output. These simulations commonly use the finite difference time domain (FDTD) method to solve Maxwell’s equations, which is computationally expensive.

Lim and Psaltis designed MaxwellNet, a deep neural network (DNN), to speed up the process. While typical DNN training uses a paired dataset of inputs and outputs, they produced random outputs, then checked whether the outputs satisfied Maxwell’s equations by measuring the residual of each output. That residual was used as a loss function, penalizing the network.

This is the first time the approach has been used to solve Maxwell’s equations, but it has been previously applied to other fields such as computational fluid dynamics.

MaxwellNet requires a long period of initial training, but once that is complete, the solutions for a particular class of optics can be simulated speedily and accurately. The researchers compared their results to a commonly used commercial finite element method solver, called COMSOL.

“In terms of computation time, we showed more than two orders of magnitude speed-up,” said author Joowon Lim. “We also designed an optical lens using MaxwellNet, and when we compared the output with the output from the COMSOL, it showed great consistency.”

The team hopes to extend the DNN from two to three dimensions, as well as consider nonlinear optical properties in the future. They believe the method opens up new avenues for photonics design and simulation.

Source: “MaxwellNet: Physics-driven deep neural network training based on Maxwell’s equations,” by Joowon Lim and Demetri Psaltis, APL Photonics (2022). The article can be accessed at https://doi.org/10.1063/5.0071616 .