No abstract

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.

We introduce WaveY-Net, a hybrid data-and physics-augmented convolutional neural network that can predict electromagnetic field distributions with ultrafast speeds and high accuracy for entire classes of dielectric nanophotonic structures. This accuracy is achieved by training the neural network to learn only the magnetic near-field distributions of a system and to use a discrete formalism of Maxwell's equations in two ways: to calculate electric fields from the magnetic fields and as physical constraints in the loss function. We show that WaveY-Net can accurately predict the near-fields in periodic, high dielectric contrast nanostructure arrays, and that it can combine with gradientbased algorithms to dramatically accelerate the local and global freeform optimization of diffractive photonic devices by orders of magnitude faster speeds. We anticipate that physics-augmented deep neural networks will transform the practice of nanophotonics simulation and design.

We propose a three-dimensional freeform nanophotonic platform in which wavelength-scale domains comprise basic geometric structures with explicitly defined dimensions, positions, orientations, and minimum feature size constraints. Given a desired wavefront shaping objective, these parameters can be collectively optimized using gradient-based shape optimization with full accounting of near-field interactions between structures. We apply our concept to a variety of metagratings supporting high diffraction efficiencies and polarization control, and we experimentally demonstrate a device with a tailored polarization response as a function of wavelength. The combination of device capability, feature size constraints, and ease of manufacturability enabled by our methodology will facilitate the development of robust, high performance, nanophotonic technologies.

Advances in modern manufacturing have enabled the multiscalar patterning of dielectric media with nearly arbitrary layouts, presenting unique opportunities to revolutionize the design and fabrication pipeline for photonic technologies. In this Perspective, we discuss how algorithms based on classical optimization and deep learning are establishing a new conceptual framework for freeform optical engineering. These tools can specify suitable design parameters for a desired objective, automate the high-speed optimization of freeform devices, and augment manufacturing processes to mitigate challenges set by freeform fabrication. A central feature of many of these algorithms is their utilization of data and physics to model and exploit high-dimensional relationships between geometric structure and electromagnetic response within the constraints of Maxwell's equations. We anticipate that these algorithm-driven methods will streamline optical systems design at the physical limits of structured media and become standard academic and industry tools for scientists and engineers.