We present a global optimizer, based on a conditional generative neural network, which can output ensembles of highly efficient topology-optimized metasurfaces operating across a range of parameters. A key feature of the network is that it initially generates a distribution of devices that broadly samples the design space, and then shifts and refines this distribution towards favorable design space regions over the course of optimization. Training is performed by calculating the forward and adjoint electromagnetic simulations of outputted devices and using the subsequent efficiency gradients for backpropagation. With metagratings operating across a range of wavelengths and angles as a model system, we show that devices produced from the trained generative network have efficiencies comparable to or better than the best devices produced by adjoint-based topology optimization, while requiring less computational cost. Our reframing of adjoint-based optimization to the training of a generative neural network applies generally to physical systems that can utilize gradients to improve performance.

A key challenge in metasurface design is the development of algorithms that can effectively and efficiently produce high performance devices. Design methods based on iterative optimization can push the performance limits of metasurfaces, but they require extensive computational resources that limit their implementation to small numbers of microscale devices. We show that generative neural networks can train from images of periodic, topology-optimized metagratings to produce high-efficiency, topologically complex devices operating over a broad range of deflection angles and wavelengths. Further iterative optimization of these designs yields devices with enhanced robustness and efficiencies, and these devices can be utilized as additional training data for network refinement. In this manner, generative networks can be trained, with a onetime computation cost, and used as a design tool to facilitate the production of near-optimal, topologically-complex device designs. We envision that such data-driven design methodologies can apply to other physical sciences domains that require the design of functional elements operating across a wide parameter space.

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AbstractMetasurfaces are subwavelength-structured artificial media that can shape and localize electromagnetic waves in unique ways. The inverse design of these devices is a non-convex optimization problem in a high dimensional space, making global optimization a major challenge. We present a new type of population-based global optimization algorithm for metasurfaces that is enabled by the training of a generative neural network. The loss function used for backpropagation depends on the generated pattern layouts, their efficiencies, and efficiency gradients, which are calculated by the adjoint variables method using forward and adjoint electromagnetic simulations. We observe that the distribution of devices generated by the network continuously shifts towards high performance design space regions over the course of optimization. Upon training completion, the best generated devices have efficiencies comparable to or exceeding the best devices designed using standard topology optimization. Our proposed global optimization algorithm can generally apply to other gradient-based optimization problems in optics, mechanics, and electronics.

We report a high-throughput and label-free computational imaging technique that simultaneously measures in three-dimensional (3D) space the locomotion and angular spin of the freely moving heads of microswimmers and the beating patterns of their flagella over a sample volume more than two orders-of-magnitude larger compared to existing optical modalities. Using this platform, we quantified the 3D locomotion of 2133 bovine sperms and determined the spin axis and the angular velocity of the sperm head, providing the perspective of an observer seated at the moving and spinning sperm head. In this constantly transforming perspective, flagellum-beating patterns are decoupled from both the 3D translation and spin of the head, which provides the opportunity to truly investigate the 3D spatio-temporal kinematics of the flagellum. In addition to providing unprecedented information on the 3D locomotion of microswimmers, this computational imaging technique could also be instrumental for micro-robotics and sensing research, enabling the high-throughput quantification of the impact of various stimuli and chemicals on the 3D swimming patterns of sperms, motile bacteria and other micro-organisms, generating new insights into taxis behaviors and the underlying biophysics.

A longstanding objective of machine learning-enabled inverse design is the realization of inverse neural networks that can instantaneously output a device given a desired optical function. For complex freeform devices, generative adversarial networks (GANs) can learn from images of freeform devices, but basic GAN architectures are unable to fully capture the intricate features of topologically complex structures. We show that by coupling progressive growth of the network architecture and training set with the GAN framework, generative networks can be trained to output high-performance, robust freeform metasurface devices. A combination of convolutional and self-attention layers in the network enable the accurate capture of both short-and long-range spatial patterns within topologically complex layouts. In applying this training methodology to metagratings, the best generated devices have efficiency and robustness metrics that compare with or outperform the best devices produced by gradient-based topology optimization with comparable computational cost. This study showcases the capability of generative neural networks to capture highly intricate geometric trends in physical devices, such as robustness constraints in freeform metasurfaces, and demonstrates their potential as black box inverse design tools for complex photonic technologies.

Fused deposition modeling 3D printing has become the most widely used additive manufacturing technology because of its low manufacturing cost and simple manufacturing process. However, the mechanical properties of the 3D printing parts are not satisfactory. Certain pressure and ultrasonic vibration were applied to 3D printed samples to study the effect on the mechanical properties of 3D printed non-crystalline and semi-crystalline polymers. The tensile strength of the semi-crystalline polymer polylactic acid was increased by 22.83% and the bending strength was increased by 49.05%, which were almost twice the percentage increase in the tensile strength and five times the percentage increase in the bending strength of the non-crystalline polymer acrylonitrile butadiene styrene with ultrasonic strengthening. The dynamic mechanical properties of the non-crystalline and semi-crystalline polymers were both improved after ultrasonic enhancement. Employing ultrasonic energy can significantly improve the mechanical properties of samples without modifying the 3D printed material or adjusting the forming process parameters.

Inverse design algorithms are the basis for realizing high-performance, freeform nanophotonic devices. Current methods to enforce geometric constraints, such as practical fabrication constraints, are heuristic and not robust. In this work, we show that hard geometric constraints can be imposed on inverse-designed devices by reparameterizing the design space itself. Instead of evaluating and modifying devices in the physical device space, candidate device layouts are defined in a constraint-free latent space and mathematically transformed to the physical device space, which robustly imposes geometric constraints. Modifications to the physical devices, specified by inverse design algorithms, are made to their latent space representations using backpropagation. As a proof-of-concept demonstration, we apply reparameterization to enforce strict minimum feature size constraints in local and global topology optimizers for metagratings. We anticipate that concepts in reparameterization will provide a general and meaningful platform to incorporate physics and physical constraints in any gradient-based optimizer, including machine learning-enabled global optimizers.