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The research of metamaterials has achieved enormous success in themanipulation of light in an artificially prescribed manner using delicatelydesigned sub-wavelength structures, so-called meta-atoms. Even though modernnumerical methods allow to accurately calculate the optical response of complexstructures, the inverse design of metamaterials is still a challenging task dueto the non-intuitive and non-unique relationship between physical structuresand optical responses. To better unveil this implicit relationship and thusfacilitate metamaterial design, we propose to represent metamaterials and modelthe inverse design problem in a probabilistically generative manner. Byemploying an encoder-decoder configuration, our deep generative modelcompresses the meta-atom design and optical response into a latent space, wheresimilar designs and similar optical responses are automatically clusteredtogether. Therefore, by sampling in the latent space, the stochastic latentvariables function as codes, from which the candidate designs are generatedupon given requirements in a decoding process. With the effective latentrepresentation of metamaterials, we can elegantly model the complexstructure-performance relationship in an interpretable way, and solve theone-to-many mapping issue that is intractable in a deterministic model.Moreover, to alleviate the burden of numerical calculation in data collection,we develop a semi-supervised learning strategy that allows our model to utilizeunlabeled data in addition to labeled data during training, simultaneouslyoptimizing the generative inverse design and deterministic forward predictionin an end-to-end manner. On a data-driven basis, the proposed model can serveas a comprehensive and efficient tool that accelerates the design,characterization and even new discovery in the research domain of metamaterialsand photonics in general.

Probabilistic representation and inverse design of metamaterials based on a deep generative model with semi-supervised learning strategy