Forward-Mode Differentiation of Maxwell’s Equations

Abstract

We present a previously unexplored forward-mode differentiation method for Maxwell's equations, with applications in the field of sensitivity analysis. This approach yields exact gradients and is similar to the popular adjoint variable method, but provides a significant improvement in both memory and speed scaling for problems involving several output parameters, as we analyze in the context of finite-difference time-domain (FDTD) simulations. Furthermore, it provides an exact alternative to numerical derivative methods, based on finite-difference approximations. To demonstrate the usefulness of the method, we perform sensitivity analysis of two problems. First we compute how the spatial near-field intensity distribution of a scatterer changes with respect to its dielectric constant. Then, we compute how the spectral power and coupling efficiency of a surface grating coupler changes with respect to its fill factor.

Multiobjective and categorical global optimization of photonic structures based on ResNet generative neural networks

“…implemented in finite-difference time domain (FDTD) and finitedifference frequency domain (FDFD) simulators [37,38]. Compared to generalized differentiable electromagnetic solvers, such as these FDTD and FDFD implementations, our analytic TMM-based algorithms are faster without loss of accuracy because the thin films are described as layers instead of voxels.…”

Physics-augmented deep learning for high-speed electromagnetic simulation and optimization

“…In both cases, the neural networks use 30,000 random device layouts and their associated fields as training data, have outputs consisting of the real and imaginary magnetic field maps, and use Equations 1 and 2 to calculate the electric field maps. Training data are generated using an open source FDFD solver [18]. A summary of the performance of both networks, compiled from 3,000 test data, is presented as scatter plots in Figs.…”

“…The acceleration in computation enabled by WaveY-Net, compared to a conventional full wave solver, is significant due to a combination of software and hardware features. A summary of the computation time required by a conventional FDFD solver [18] and WaveY-Net for different numbers of simulations is shown in Fig. 3.…”

“…During the data generation, the FDFD-based electromagnetic simulator, Ceviche [18], is utilized. The per-fectly matched layer (PML) [61] is adopted in the z direction and the periodic boundary condition is adopted in the x direction.…”

“…These systems operate at frequencies spanning the radio wave to X-ray and include a diversity of antennas [1][2][3], diffractive surfaces [4][5][6][7][8], metamaterials [9][10][11], and guided wave-based photonic circuits [12][13][14]. Amongst the most popular frequency domain Maxwell solvers are the finite element method (FEM) [15,16] and finite difference frequency domain (FDFD) algorithms [17][18][19][20]. In both algorithms, the system domain is subdivided into discrete voxels and the simulator solves for electromagnetic fields by constructing and inverting a sparse matrix with dimensions proportional to the total number of voxels.…”