Manifold Learning for Knowledge Discovery and Intelligent Inverse Design of Photonic Nanostructures: Breaking the Geometric Complexity

Here, we present a new approach based on manifold learning for knowledge discovery and inverse design with minimal complexity in photonic nanostructures. Our approach builds on studying sub-manifolds of responses of a class of nanostructures with different design complexities in the latent space to obtain valuable insight about the physics of device operation to guide a more intelligent design. In contrast to the current methods for inverse design of photonic nanostructures, which are limited to pre-selected and usually over-complex structures, we show that our method allows evolution from an initial design towards the simplest structure while solving the inverse problem.

Knowledge Discovery In Nanophotonics Using Geometric Deep Learning

We present here a new approach for using the intelligence aspects of artificial intelligence for knowledge discovery rather than device optimization in electromagnetic (EM) nanostructures. This approach uses training data obtained through full-wave EM simulations of a series of nanostructures to train geometric deep learning algorithms to assess the range of feasible responses as well as the feasibility of a desired response from a class of EM nanostructures. To facilitate the knowledge discovery and reduce the computation complexity, our approach combines the dimensionality reduction technique (using an autoencoder) with convex-hull and one-class support-vector-machine (SVM) algorithms to find the range of the feasible responses in the latent (or the reduced) response space of the EM nanostructure. We show that by using a small set of training instances (compared to all possible structures), our approach can provide better than 95% accuracy in assessing the feasibility of a given response. More importantly, the one-class SVM algorithm can be trained to provide the degree of feasibility (or unfeasibility) of a response from a given nanostructure. This important information can be used to modify the initial structure to an alternative one that can enable an initially unfeasible response. To show the applicability of our approach, we apply it to two important classes of binary metasurfaces (MSs), formed by array of plasmonic nanostructures, and periodic MSs formed by an array of dielectric nanopillars. In addition to theoretical results, we show the experimental results obtained by fabricating several MSs of the second class. Our theoretical and experimental results confirm the unique features of this approach for knowledge discovery in EM nanostructures.

Deep Learning Reveals Underlying Physics of Light-matter Interactions in Nanophotonic Devices

In this paper, we present a deep learning-based (DL-based) algorithm, as a purely mathematical platform, for providing intuitive understanding of the properties of electromagnetic (EM) wave-matter interaction in nanostructures. This approach is based on using the dimensionality reduction (DR) technique to significantly reduce the dimensionality of a generic EM wave-matter interaction problem without imposing significant error. Such an approach implicitly provides useful information about the role of different features (or design parameters such as geometry) of the nanostructure in its response functionality. To demonstrate the practical capabilities of this DL-based technique, we apply it to a reconfigurable optical metadevice enabling dual-band and triple-band optical absorption in the telecommunication window. Combination of the proposed approach with existing commercialized full-wave simulation tools offers a powerful toolkit to extract basic mechanisms of wave-matter interaction in complex EM devices and facilitate the design and optimization of nanostructures for a large range of applications including imaging, spectroscopy, and signal processing. It is worth to mention that the demonstrated approach is general and can be used in a large range of problems as long as enough training data can be provided.

Deep learning approach based on dimensionality reduction for designing electromagnetic nanostructures

In this paper, we demonstrate a computationally efficient new approach based on deep learning (DL) techniques for analysis, design, and optimization of electromagnetic (EM) nanostructures. We use the strong correlation among features of a generic EM problem to considerably reduce the dimensionality of the problem and thus, the computational complexity, without imposing considerable errors. By employing the dimensionality reduction concept using the more recently demonstrated autoencoder technique, we redefine the conventional many-to-one design problem in EM nanostructures into a one-to-one problem plus a much simpler many-to-one problem, which can be simply solved using an analytic formulation. This approach reduces the computational complexity in solving both the forward problem (i.e., analysis) and the inverse problem (i.e., design) by orders of magnitude compared to conventional approaches. In addition, it provides analytic formulations that, despite their complexity, can be used to obtain intuitive understanding of the physics and dynamics of EM wave interaction with nanostructures with minimal computation requirements. As a proof-of-concept, we applied such an efficacious method to design a new class of on-demand reconfigurable optical metasurfaces based on phase-change materials (PCM). We envision that the integration of such a DL-based technique with full-wave commercial software packages offers a powerful toolkit to facilitate the analysis, design, and optimization of the EM nanostructures as well as explaining, understanding, and predicting the observed responses in such structures.