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1. Inverse Design Framework With Invertible Neural Networks for Passive Vibration Suppression in Phononic Structures

   https://doi.org/10.1115/1.4052300  

   Oddiraju, Manaswin; Behjat, Amir; Nouh, Mostafa; Chowdhury, Souma (February 2022, Journal of Mechanical Design)

   null (Ed.)

   Abstract Automated inverse design methods are critical to the development of metamaterial systems that exhibit special user-demanded properties. While machine learning approaches represent an emerging paradigm in the design of metamaterial structures, the ability to retrieve inverse designs on-demand remains lacking. Such an ability can be useful in accelerating optimization-based inverse design processes. This paper develops an inverse design framework that provides this capability through the novel usage of invertible neural networks (INNs). We exploit an INN architecture that can be trained to perform forward prediction over a set of high-fidelity samples and automatically learns the reverse mapping with guaranteed invertibility. We apply this INN for modeling the frequency response of periodic and aperiodic phononic structures, with the performance demonstrated on vibration suppression of drill pipes. Training and testing samples are generated by employing a transfer matrix method. The INN models provide competitive forward and inverse prediction performance compared to typical deep neural networks (DNNs). These INN models are used to retrieve approximate inverse designs for a queried non-resonant frequency range; the inverse designs are then used to initialize a constrained gradient-based optimization process to find a more accurate inverse design that also minimizes mass. The INN-initialized optimizations are found to be generally superior in terms of the queried property and mass compared to randomly initialized and inverse DNN-initialized optimizations. Particle swarm optimization with INN-derived initial points is then found to provide even better solutions, especially for the higher-dimensional aperiodic structures. 

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2. Inverse design and flexible parameterization of meta-optics using algorithmic differentiation

   https://doi.org/10.1038/s42005-021-00568-6  

   Colburn, Shane; Majumdar, Arka (March 2021, Communications Physics)

   Abstract Ultrathin meta-optics offer unmatched, multifunctional control of light. Next-generation optical technologies, however, demand unprecedented performance. This will likely require design algorithms surpassing the capability of human intuition. For the adjoint method, this requires explicitly deriving gradients, which is sometimes challenging for certain photonics problems. Existing techniques also comprise a patchwork of application-specific algorithms, each focused in scope and scatterer type. Here, we leverage algorithmic differentiation as used in artificial neural networks, treating photonic design parameters as trainable weights, optical sources as inputs, and encapsulating device performance in the loss function. By solving a complex, degenerate eigenproblem and formulating rigorous coupled-wave analysis as a computational graph, we support both arbitrary, parameterized scatterers and topology optimization. With iteration times below the cost of two forward simulations typical of adjoint methods, we generate multilayer, multifunctional, and aperiodic meta-optics. As an open-source platform adaptable to other algorithms and problems, we enable fast and flexible meta-optical design. 

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3. Reflection-mode diffraction tomography of multiple-scattering samples on a reflective substrate from intensity images

   https://doi.org/10.1364/OPTICA.547372  

   Li, Tongyu; Zhu, Jiabei; Shen, Yi; Tian, Lei (March 2025, Optica)

   We introduce a reflection-mode diffraction tomography technique that enables the simultaneous recovery of forward- and backward-scattering information for high-resolution 3D refractive index reconstruction. Our technique works by imaging a sample on a highly reflective substrate and employing a multiple-scattering model and a reconstruction algorithm. It combines the modified Born series as the forward model, Bloch and perfect electric conductor boundary conditions to handle oblique incidence and substrate reflections, and the adjoint method for efficient gradient computation in solving the inverse-scattering problem. We validate the technique through simulations and experiments, achieving accurate reconstructions in samples with high refractive index contrasts and complex geometries. Forward scattering captures smooth axial features, while backward scattering reveals complementary interfacial details. Experimental results on dual-layer resolution targets, 3D randomly distributed beads, phase structures obscured by highly scattering fibers, fixed breast cancer cells, and fixedC. elegansdemonstrate its robustness and versatility. This technique holds promise for applications in semiconductor metrology and biomedical imaging. 

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4. Inverse designed achromatic flat lens operating in the ultraviolet

   https://doi.org/10.1364/OSAC.395767  

   Banerji, Sourangsu; Sensale-Rodriguez, Berardi (July 2020, OSA Continuum)

   We demonstrate an inverse designed achromatic, flat, polarization-insensitive diffractive optic element, i.e., a multilevel diffractive lens (MDL), operating across a broadband range of UV light (250 nm – 400 nm) via numerical simulations. The simulated average on-axis focusing efficiency of the MDL is optimized to be as high as ∼86%. We also investigate the off-axis focusing characteristics at different incident angles of the incoming UV radiation such that the MDL has a full field of view of 30°. The simulated average off-axis focusing efficiency is ∼67%, which is the highest reported till date for any chromatic or achromatic UV metalens or diffractive lens to the best of our knowledge. The designed MDL is composed of silicon nitride. The work reported herein will be useful for the miniaturization and integration of lightweight and compact UV optical systems. 

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5. Fast Inverse Design of 3D Nanophotonic Devices Using Boundary Integral Methods

   https://doi.org/10.1021/acsphotonics.2c01072  

   Garza, Emmanuel; Sideris, Constantine (October 2022, ACS Photonics)

   Recent developments in the computational automated design of electromagnetic devices, otherwise known as inverse design, have significantly enhanced the design process for nanophotonic systems. Inverse design can both reduce design time considerably and lead to high-performance, nonintuitive structures that would otherwise have been impossible to develop manually. Despite the successes enjoyed by structure optimization techniques, most approaches leverage electromagnetic solvers that require significant computational resources and suffer from slow convergence and numerical dispersion. Recently, a fast simulation and boundary-based inverse design approach based on boundary integral equations was demonstrated for two-dimensional nanophotonic problems. In this work, we introduce a new full-wave three-dimensional simulation and boundary-based optimization framework for nanophotonic devices also based on boundary integral methods, which achieves high accuracy even at coarse mesh discretizations while only requiring modest computational resources. The approach has been further accelerated by leveraging GPU computing, a sparse block-diagonal preconditioning strategy, and a matrix-free implementation of the discrete adjoint method. As a demonstration, we optimize three different devices: a 1:2 1550 nm power splitter and two nonadiabatic mode-preserving waveguide tapers. To the best of our knowledge, the tapers, which span 40 wavelengths in the silicon material, are the largest silicon photonic waveguiding devices to have been optimized using full-wave 3D solution of Maxwell’s equations. 

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