Figure 1: Schematic of the proposed inverse design framework based on solving the pseudo-inverse function.
1. Pre-reading
Plasmonic nanoantennas with desirable far-field characteristics render very useful in numerous applications such as optical wireless links, inter-/intra-chip communications, LiDARs, and photonic integrated circuits due to their nanoscale footprints and exceptional modal confinement. However, there exists a huge gap between RF and the optical regime in terms of design theory and methodologies, as the validity of conventional transmission line theory diminishes in the optical frequencies due to the completely different wave-matter interactions.
To overcome these problems and to fill the mentioned gap, researchers at the University of California San Diego and Boston University, have developed a cutting-edge deep learning framework to revolutionize the design of plasmonic patch nanoantennas. The research team Nano Devices and Applied Optics Lab led by Prof. Abdoulaye Ndao has transformed the plasmonic nanoantenna design into a data-driven task by utilizing neural networks (NNs), through only a one-time training of the network. The framework is designed to determine the optimal geometries for a wide range of nanoantennas (single-band, dual-band, and broadband nanoantennas) to achieve the desired S11and radiation patterns (across the whole frequency range of the design space), simultaneously (as shown in Fig. 2). Contrary to other inverse-design methods based on DNNs, the authors’ proposed approach preserves the one-to-many mappings, which enables the researchers to generate multiple diverse designs. Furthermore, in addition to the primary fabrication constraints considered while generating the training dataset, further design and fabrication constraints can be applied post-training.
The proposed approach is developed to serve as a general framework in the inverse design of photonics components, with its impact extending beyond antenna design, and to open a new paradigm toward real-time design of application-specific nanophotonic devices.
2. Background
Conventional antenna theory has been successful in shaping the design theory and techniques in the radio frequency; however, the validity of this theory falls short in the optical domain, due to the radically different wave-matter interactions. One can transform this problem into an automated, data-driven task using deep neural networks (DNNs) which are receiving significant attention in photonics in order to replace the complex and time-consuming design procedures by approximating the electromagnetic simulations and learning the inverse process.
While promising, DNNs face challenges with inverse problems in photonics due to the direct reliance of their performance on huge datasets (which grow exponentially with increasing degrees of freedom), in conjunction with the fact that discriminative neural networks may lead to sub-optimal results due to the presence of non-uniqueness in the inverse problems. Prior studies addressed the inverse design problem using discriminative networks in combination with brute force, analytical gradient, and evolutionary algorithms. For instance, tandem networks, and generative models such as variational autoencoders and generative adversarial networks have been adapted to enhance the design with more degrees of freedom. However, these approaches encounter critical limitations such as elimination of potential desirable devices from the response space due to the transformation of one-to-many mappings into one-to-one mappings, facing challenges while applying post-training fabrication constraints, and generation of blurry results due to the complexities of training. Additionally, generative models frequently suffer from mode collapse, which restricts their capability to generate diverse designs.
3. Innovative research
The proposed inverse design framework is developed based on the pseudo-inverse function and utilizes a deep neural network as the surrogate solver to model the simulation process and uses particle swarm optimization (PSO) to search the design space. The framework takes a desired response as a query and generates a set of devices that exhibit those responses. In the search process, responses of several devices must be simulated, which is done using the multi-head deep convolutional surrogate solver which is trained to approximate the responses of the given device. The surrogate solver enables the PSO to search the device space in approximately 80 milliseconds to generate one device. After the device space is searched, the mean shift algorithm clusters the resulting particles to locate a set of acceptable solutions (shown in Fig. 1).
Figure 2: Instances of plasmonic patch nanoantennas including single-band, dual-band, and broadband nanoantennas, designed by the inverse design framework.
An important capability of the proposed network that renders very useful in extension of their method to other problems such as in the inverse design of random media, is preserving the one-to-many mappings, which is crucial for capturing the inherent complexity of the problem as it enriches the dataset for training of the network, leads to better generalization and prediction capabilities, and facilitates a comprehensive exploration of the design space. Additionally, many of the output devices may not be exactly realizable due to various factors such as environmental variations in real-life scenarios, special arrangements of scatterers in random media that might be hard to fabricate, etc. As a result, preserving the one-to-many mappings will handle this issue effectively by offering multiple alternative solutions (see Fig. 3). This is in strong contrast with tandem networks which aim to reduce the one-to-many mappings to a one-to-one mapping to learn the inverse mapping directly and may eliminate useful devices from the device space. Furthermore, generative approaches including those based on VAEs and GANs, despite their ability to generate multiple devices, may suffer from mode collapses and fail to adequately capture the diversity of the device space due to the complexity of training.
The proposed approach allows for applying post-training constraints, which is of great importance especially in random media and problems dealing with complex structures, where many of the output devices may not be fabricable and the applications of further constraints are mandatory (which can be done without any retraining in the proposed network). In tandem networks, as mentioned before, one-to-many mappings are eliminated, as a result only one device can exist for each response, making it impossible to have other devices that meet the fabrication or other post-training constraints. In generative networks also, this aspect remains unexplored.
Additionally, in generative approaches and tandem networks, the inverse function is directly modeled, where the entire response is required to generate a device. Which is not favorable as only the response in a specific region might be of interest, and providing arbitrary responses in the rest of the regions may limit the diversity of the generated devices to those that exactly exhibit. In our framework, we can use a query-based approach to search for the desired device simply by defining a few conditions instead of providing the entire response. This results in finding additional devices that exhibit the desired behavior.
Figure 3: Multiple diverse single band nanoantennas designed by the proposed inverse design framework.
4. Applications and perspectives
Apart from the direct applications of the current platform in LiDARs, optical phased arrays, and inter-/intra- chip communications, the proposed approach is developed to serve as a general framework that can be used in a broad range of applications such as in random media, deep tissue imaging, coherent backscattering, quantum information processing, and random metasurfaces. Their approach takes a significant departure from traditional NN-based inverse design methods and sets a precedent for future research in the field dealing with predictive and generative capabilities of DNNs in nanophotonics.
This research is published online with the title “Integrating Deep Convolutional Surrogate Solvers and Particle Swarm Optimization for Efficient Inverse Design of Plasmonic Patch Nanoantennas” in Nanophotonics.
The authors of this article are Saeed Hemayat, Sina Moayed Baharlou, Alexander Sergienko, and Abdoulaye Ndao. The first two authors contributed equally to this work. Abdoulaye Ndao is the corresponding author of this work. Prof. Ndao’s research group is affiliated with Nano Devices and Applied Optics Lab (NDAO Lab), Department of Electrical and Computer Engineering, University of California San Diego, La Jolla, CA 92093, USA, and Department of Electrical and Computer Engineering and Photonics Center, Boston University, Boston, MA 02215, USA.
