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Data-driven methods have increasingly been applied to the development ofoptical systems as inexpensive and effective inverse design approaches. Opticalproperties (e.g., band-gap properties) of photonic crystals (PCs) are closelyassociated with characteristics of their light reflection spectra. Findingoptimal PC constructions (within a pre-specified parameter space) that generatereflection spectra closest to a targeted spectrum is thus an interesting andmeaningful inverse design problem, although relevant studies are still limited.Here we report a generally effective machine learning-based inverse designapproach for one-dimensional photonic crystals (1DPCs), focusing on visiblelight spectra which are of high practical relevance. For a given class of 1DPCsystem, a deep neural network (DNN) in a unified structure is first trainedover data from sizeable forward calculations (from layer thicknesses tospectrum). An iterative optimization scheme is then developed based on acoherent integration of DNN backward predictions (from spectrum to layerthicknesses), forward calculations, and Monte Carlo moves. We employ this newapproach to four representative 1DPC systems including periodic structures withtwo-, three-, and four-layer repeating units and a heterostructure. Theapproach successfully converges to solutions of optimal 1DPC constructions forvarious targeted spectra regardless of their exact achievability. As twodemonstrating examples, inverse designs toward a specially constructed"rectangle-shaped" green-light or red-light reflection spectrum are presentedand discussed in detail. Remarkably, the results show that the approach canefficiently find out optimal layer thicknesses even when they are far outsidethe range covered by the original training data of DNN.

A General Machine Learning-based Approach for Inverse Design of One-dimensional Photonic Crystals Toward Targeted Visible Light Reflection Spectrum