Abstract
Inferring the properties of a scattering objective by analyzing the optical far-field responses within the framework of inverse problems is of great practical significance. However, it still faces major challenges when the parameter range is growing and involves inevitable experimental noises. Here, we propose a solving strategy containing robust neural-networks-based algorithms and informative photonic dispersions to overcome such challenges for a sort of inverse scattering problem—reconstructing grating profiles. Using two typical neural networks, forward-mapping type and inverse-mapping type, we reconstruct grating profiles whose geometric features span hundreds of nanometers with nanometric sensitivity and several seconds of time consumption. A forward-mapping neural network with a parameters-to-point architecture especially stands out in generating analytical photonic dispersions accurately, featured by sharp Fano-shaped spectra. Meanwhile, to implement the strategy experimentally, a Fourier-optics-based angle-resolved imaging spectroscopy with an all-fixed light path is developed to measure the dispersions by a single shot, acquiring adequate information. Our forward-mapping algorithm can enable real-time comparisons between robust predictions and experimental data with actual noises, showing an excellent linear correlation (R2 > 0.982) with the measurements of atomic force microscopy. Our work provides a new strategy for reconstructing grating profiles in inverse scattering problems.
Highlights
Inverse scattering problems (ISPs) arise in many fields of science and engineering such as computed tomography[1,2], fiber Bragg gratings[3], and optical metrology[4,5,6,7]
Each representative point in the parameter space stands for a group of geometric parameters and components; each representative point in the data space stands for the detected responses corresponding to a ball in the parameter space
The aim of solving ISPs is to try to establish an inverse mapping from data space to parameter space, inferring the parameters of the scattering objectives from the given detected responses
Summary
Inverse scattering problems (ISPs) arise in many fields of science and engineering such as computed tomography[1,2], fiber Bragg gratings[3], and optical metrology[4,5,6,7]. A typical ISP, is composed of three parts: a set of scattering objectives, a set of light responses and a measurement operator. One should make a parameter space whose elements are arrays of parameters, describing the scatters’ geometries and components; for light responses, a data space is needed whose elements correspond to the measured optical responses of scatters in the far field, such as reflectance spectra. As the connection of these two sets, a measurement operator characterizes the mapping from parameter space to data space. ISPs, namely inferring an element of the parameter space from that of the data space, it executes the inversion of the measurement operator—inversion operator. Injectivity requires the acquired data to uniquely characterize the parameters, and stability is closely related to the measurement noises
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