Standard scalar wave propagation techniques, such as Fourier optics, struggle with the multi-scale challenges inherent in the inverse design of optical metasurfaces. Conventional approaches often assume that the source and observation planes are axially aligned and share the same spatial size and discretization. This becomes problematic in the case of metasurface design where often the source and observation planes are on the order of the wavelength. Designing metasurfaces nanometer by nanometer for large-scale applications is computationally prohibitive. Current metasurface inverse design methods generally approximate amplitude and phase under the local phase approximation. However, this is insufficient when considering the intricate interactions among nearest neighbors in a metasurface. A more comprehensive understanding requires the consideration of the complex near electric field, which holds richer information about the metasurface’s physics. Yet, computing the resultant complex field at a far distance from the metasurface is both essential for inverse design and challenging. This work presents an evaluation of three computational approaches, i.e., padded field propagation, shifted field propagation, and propagation by the chirp-z-transform, for the explicit purpose of metasurface inverse design. These techniques are implemented in the Pytorch Lightning deep learning framework facilitating optimization using the backpropagation algorithm.
Understanding wave propagation is fundamental across numerous scientific domains, underpinning crucial tasks in acoustics, seismology, radar technology, materials science, and optics. Machine learning methods offer a promising avenue to deepen our understanding of wave propagation dynamics, providing insights into the behavior of nearfield wave patterns. Moreover, well-trained machine learning models have the capacity to generalize beyond specific training data, allowing for predictions in scenarios not explicitly encountered during training. This paper presents a machine learning approach using time-series neural networks to predict the complex near-field wave patterns emerging from metasurface devices. The recurrent neural network (RNN) and the long short term memory (LSTM) models are presented along with a custom dataset that includes 3x3 configurations of meta-atoms. The experiment focuses on assessing the models’ capabilities with varying amounts of input data and explores the challenges posed by predicting propagating waves. Results indicate that the LSTM outperforms the RNN, markedly in learning training data, highlighting its efficacy in capturing complex dependencies. Analysis of error metrics reveals insights into the impact of dataset size on model performance, with larger datasets posing computational challenges but potentially enhancing generalization. Overall, this study lays the foundation for advancing the use of time-series machine learning models for applications involving wave propagation, with implications for various applications in photonics and beyond.
The integration of neural networks and differentiable scalar wave optics has facilitated a modern approach to the design of optical systems, where simulation and optimization are carried out concurrently. These techniques encode the equations of wavefront propagation and modulation directly as layers of a neural network where the forward pass carries out simulation and the backward pass carries out optimization using the backpropagation algorithm. While this allows standard optical optimization as well as classifier-driven optimization of diffractive optics, it suffers from the ubiquitous simulation-to-reality gap. Identifying, characterizing, and ultimately reducing this simulation-to-reality gap is an ever-present objective – as the adage goes, “all models are wrong, some are useful.” To this end, this work extends recent advancements in physics-aware training where an optimizable physical device is used alongside in-silico simulation. By comparing the simulation output with the measured result from the physical device, an additional error term is introduced to the optimization objective. This work analyzes the multi-criteria loss function by varying weighting terms and analyzing performance. It is found that minimizing this new error term reduces the simulation-to-reality gap but at the cost of device performance. The optimizable device in this work is implemented using a reprogrammable spatial light modulator.
Improving a machine’s ability to reason about the unknown has been a prominent commonality across the different emerging areas of modern supervised learning. While there are different approaches that formalize this problem, many focus on generalized target recognition tailored to the known vs unknown problem setting. Overall, these approaches have created a meaningful foundation that promotes algorithm enhancement with respect to factors like detection, robustness, and internal knowledge expression. However, one major shortcoming across numerous prior works is the question of how to make use of unknown classifications for an algorithm deployment setting. Herein, we address this shortcoming by proposing an self-supervised comparison assessment methodology for computer vision tasks. Specifically, we leverage the features of foundational models across different dimensionality spaces to facilitate a comparison analysis of unknown information. Preliminary results are encouraging and demonstrate that this process not only has benefits in computer vision applications, but also is flexible for methodology alterations.
Optical metasurfaces enable devices to interact with light in unique ways by modulating phase, polarization, or intensity. A metasurface, composed of individual subwavelength scatterers known as meta-atoms, can be designed to provide unparalleled control of wavefronts for a variety of optical applications, yet the design of such devices is often unintuitive and challenging due to computationally expensive forward simulations and the number of free parameters. To overcome this, there is interest in developing inverse design methods as an alternative to conventional forward design. Inverse design leverages machine learning algorithms to effectively search a problem space, starting from application and resulting in solution parameters. In this work, we adopt an inverse design approach that involves targeted forward simulations of arbitrary meta-atoms. To ensure that the dataset captures all possible shapes and rotations of near field responses with second order accuracy, it is constructed using meta-atoms with varying geometries and corresponding phase shifts, including the effect of nearest neighbors. A custom deep learning system is developed to extract meaningful features from this near field response. The proposed framework provides flexibility to produce an inverse design paradigm for generalized metasurface applications without the need for repeated forward simulations. Additionally, the machine learning model is highly effective in reconstructing electric fields, irrespective of the loss function used.
The adoption of neural networks for optical component design has increased rapidly in recent years. In this design framework, the numerical simulation of optical wave propagation and material wave modulation are encoded directly as layers of a neural network. This direct encoding enables the optimization of physical quantities (e.g., the transmissivity values of the diffractive optical elements) by gradient descent and the backpropagation algorithm. For the body of work which uses these networks for simulation and optimization, there is a tendency to treat the training process as identical to traditional deep neural networks. However, to the best of our knowledge, there is yet an explicit evaluation of training parameters to support this intuition. This work aims to help fill this gap by providing an exploration and evaluation of data variety to help accelerate those in the community who wish to use this emerging design framework.The application of neural networks in optical component design has witnessed rapid growth in recent years. This design framework encodes the numerical simulation of optical wave propagation and material wave modulation directly within neural network layers, enabling the optimization of physical quantities, such as transmissivity values of diffractive optical elements, through gradient descent and backpropagation algorithms. Physics-informed neural networks have been employed in designing diffractive deep neural networks, optimizing holograms for near-eye displays and creating multi-objective traditional optics. However, there remains a lack of evaluation for training parameters, and discrete sampling considerations are often overlooked. To address these gaps, this study examines the impact of dataset variety on physics-informed neural networks in optimizing lenses that either satisfy or violate the Nyquist sampling criteria. Results show that increased data variety enhances optimized lens performance across all cases. Optimized lenses demonstrate improved imaging performance by reducing diffraction orders present in aliased analytical lenses. Moreover, we reveal that low data variety leads to overfit lenses that function as selective imagers, providing valuable insights for future lens design and optimization.
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