Physics-informed neural networks for imaging and parameter retrieval of photonic nanostructures from near-field data

TL;DR

This paper introduces a physics-informed neural network framework based on Maxwell's equations for accurately retrieving the complex optical parameters of nanostructures from near-field data, enabling non-invasive imaging and characterization.

Contribution

The paper develops adaptive PINNs that incorporate full Maxwell's equations for inverse retrieval of optical parameters, demonstrating improved accuracy and efficiency over traditional methods.

Findings

PINNs accurately retrieve complex permittivity and permeability from near-field data.

Adaptive PINNs significantly improve reconstruction accuracy for high-index materials.

The method successfully retrieves 3D spatial permittivity distributions.

Abstract

In this paper, we develop a deep learning approach for the accurate solution of challenging problems of near-field microscopy that leverages the powerful framework of physics-informed neural networks (PINNs) for the inversion of the complex optical parameters of nanostructured environments. Specifically, we show that PINNs can be flexibly designed based on the full-vector Maxwell's equations to inversely retrieve the spatial distributions of the complex electric permittivity and magnetic permeability of unknown scattering objects in the resonance regime from near-field data. Moreover, we demonstrate that PINNs achieve excellent convergence to the true material parameters under both plane wave and point source (localized) excitations, enabling parameter retrieval in scanning near-field optical microscopy (SNOM). Our method is computationally efficient compared to traditional data-driven deep learning approaches as it requires only a single dataset for training. Furthermore, we develop and successfully demonstrate adaptive PINNs with trainable loss weights that largely improve the accuracy of the inverse reconstruction for high-index materials compared to standard PINNs. Finally, we demonstrate the full potential of our approach by retrieving the space-dependent permittivity of a three-dimensional (3D) unknown object from near-field data. The presented framework paves the way to the development of a computationally-driven, accurate, and non-invasive platform for the simultaneous retrieval of the electric and magnetic parameters of resonant nanostructures from measured optical images, with applications to biomedical imaging, optical remote sensing, and characterization of metamaterial devices.