Effective medium properties of stealthy hyperuniform photonic structures using multiscale physics-informed neural networks
arxiv(2024)
Abstract
In this article, we employ multiscale physics-informed neural networks
(MscalePINNs) for the inverse retrieval of the effective permittivity and
homogenization of finite-size photonic media with stealthy hyperuniform (SHU)
disordered geometries. Specifically, we show that MscalePINNs are capable of
capturing the fast spatial variations of complex fields scattered by arrays of
dielectric nanocylinders arranged according to isotropic SHU point patterns,
thus enabling a systematic methodology to inverse retrieve their effective
dielectric profiles. Our approach extends the recently developed high-frequency
homogenization theory of hyperuniform media and retrieves more general
permittivity profiles for applications-relevant finite-size SHU systems,
unveiling unique features related to their isotropic nature. In particular, we
demonstrate the existence of a transparency region beyond the long-wavelength
approximation, enabling effective and isotropic homogenization even without
disorder-averaging, in contrast to the case of uncorrelated Poisson random
patterns. We believe that the multiscale network approach introduced here
enables the efficient inverse design of general effective media and finite-size
metamaterials with isotropic electromagnetic responses beyond the limitations
of traditional homogenization theories.
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