Neural Inverse Design of Nanostructures (NIDN)

Abstract

In the recent decade, computational tools have become central in material design, allowing rapid development cycles at reduced costs. Machine learning tools are especially on the rise in photonics. However, the inversion of the Maxwell equations needed for the design is particularly challenging from an optimization standpoint, requiring sophisticated software. We present an innovative, open-source software tool called Neural Inverse Design of Nanostructures (NIDN) that allows designing complex, stacked material nanostructures using a physics-based deep learning approach. Instead of a derivative-free or data-driven optimization or learning method, we perform a gradient-based neural network training where we directly optimize the material and its structure based on its spectral characteristics. NIDN supports two different solvers, rigorous coupled-wave analysis and a finite-difference time-domain method. The utility and validity of NIDN are demonstrated on several synthetic examples as well as the design of a 1550 nm filter and anti-reflection coating. Results match experimental baselines, other simulation tools, and the desired spectral characteristics. Given its full modularity in regard to network architectures and Maxwell solvers as well as open-source, permissive availability, NIDN will be able to support computational material design processes in a broad range of applications.

Figure 1

Training setup for NIDN; regression and classification as well as RCWA and FDTD are described in detail in Methods.

Figure 2

Comparison of the transmittance of a 380 nm thick layer of ${\text{TiO}}_2$ in NIDN and experimentally measured.

Figure 3

Inversion results for a single-layer ${\text{TiO}}_2$ material using FDTD and regression; (a) displays target and produced spectra, (b) shows the utilized permittivity; differences to Fig. 2 are due to smaller number of discretization grid points.

Figure 4

Inversion results for a single-layer ${\text{TiO}}_2$ material using FDTD and classification; (a) displays target and produced spectra, (b) shows the utilized permittivity; differences to Fig. 2 are due to smaller number of discretization grid points.

Figure 5

Inversion results for a three-layer material using RCWA and regression; (a) displays target and produced spectra, (b) shows the utilized permittivity for each layer.

Figure 6

Inversion results for a three-layer material using RCWA and classification; (a) displays target and produced spectra, (b) shows the utilized permittivity for each layer.

Figure 7

Inversion results for a two-layer patterned material using RCWA and regression; (a) displays target and produced spectra, (b) each line shows the utilized permittivity for a grid cell.

Figure 8

Inversion results for a two-layer patterned material using RCWA and classification; (a) displays target and produced spectra, (b) each line shows the utilized permittivity for a grid cell.

Figure 9

Inversion results for designing a bandpass filter with a ten layer stack using RCWA and regression; (a) displays target and produced spectra, (b) shows the utilized permittivity for each layer and closest material in NIDN (dashed).

Figure 10

Inversion results for designing an anti-reflection coating with an eight layer stack using RCWA and regression; (a) displays target and produced spectra, (b) shows the utilized permittivity for each layer and closest material in NIDN (dashed).

Figure 11

Inversion results for designing an anti-reflection coating with an eight layer stack using RCWA and classification; (a) displays target and produced spectra, (b) shows the utilized permittivity for each layer and closest material in NIDN (dashed).

Figure 12

(a) L1 loss versus model evaluations of the three approaches. (b) Permittivities produced with a neural network in NIDN. (c) Permittivities produced with a voxelized grid representation. (d) Permittivities produced with GRCWA and NLopt.