Abstract
In this paper, we employ the emerging paradigm of physics-informed neural networks (PINNs) for the solution of representative inverse scattering problems in photonic metamaterials and nano-optics technologies. In particular, we successfully apply mesh-free PINNs to the difficult task of retrieving the effective permittivity parameters of a number of finite-size scattering systems that involve many interacting nanostructures as well as multi-component nanoparticles. Our methodology is fully validated by numerical simulations based on the finite element method (FEM). The development of physics-informed deep learning techniques for inverse scattering can enable the design of novel functional nanostructures and significantly broaden the design space of metamaterials by naturally accounting for radiation and finite-size effects beyond the limitations of traditional effective medium theories.
Highlights
For over two centuries, the science and engineering of electromagnetic waves in optical materials relied on either analytical solutions or numerical approximations of differential equations derived from physical models
Differently from standard deep learning approaches, physics-informed neural networks (PINNs) restrict the space of admissible solutions by enforcing the validity of partial differential equation (PDE) models governing the actual physics of the problem
We demonstrated in this paper the solution of representative inverse scattering problems that are interesting in photonic metamaterials and nano-optics technologies
Summary
The science and engineering of electromagnetic waves in optical materials relied on either analytical solutions or numerical approximations of differential equations derived from physical models While enormously successful, this approach fails to capture the multi-scale behavior of heterogeneous media whose structural complexity prevents the precise formulation and the solution of the high-frequency inverse scattering problem, which has numerous applications to optics, acoustics, geophysics, astronomy, medical imaging, microscopy, remote sensing, and nondestructive testing. This approach fails to capture the multi-scale behavior of heterogeneous media whose structural complexity prevents the precise formulation and the solution of the high-frequency inverse scattering problem, which has numerous applications to optics, acoustics, geophysics, astronomy, medical imaging, microscopy, remote sensing, and nondestructive testing This problem consists of determining the characteristics of an object from a limited set of measured data on how it scatters incoming radiation; solving this may enable the predictive design of artificial optical materials, i.e. metamaterials and complex optical nanostructures, starting directly from desired optical functionalities within a prescribed frequency range. This ability establishes remote sensing functionalities in the optical regime whereby the unknown dielectric permittivity of complex optical nanostructures can be unambiguously retrieved from near-field optical imaging data
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