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

Data-driven methods have increasingly been applied to the development of optical systems as inexpensive and effective inverse design approaches. Optical properties (e.g., band-gap properties) of photonic crystals (PCs) are closely associated with characteristics of their light reflection spectra. Finding optimal PC constructions (within a pre-specified parameter space) that generate reflection spectra closest to a targeted spectrum is thus an interesting and meaningful inverse design problem, although relevant studies are still limited. Here we report a generally effective machine learning-based inverse design approach for one-dimensional photonic crystals (1DPCs), focusing on visible light spectra which are of high practical relevance. For a given class of 1DPC system, a deep neural network (DNN) in a unified structure is first trained over data from sizeable forward calculations (from layer thicknesses to spectrum). An iterative optimization scheme is then developed based on a coherent integration of DNN backward predictions (from spectrum to layer thicknesses), forward calculations, and Monte Carlo moves. We employ this new approach to four representative 1DPC systems including periodic structures with two-, three-, and four-layer repeating units and a heterostructure. The approach successfully converges to solutions of optimal 1DPC constructions for various targeted spectra regardless of their exact achievability. As two demonstrating examples, inverse designs toward a specially constructed "rectangle-shaped" green-light or red-light reflection spectrum are presented and discussed in detail. Remarkably, the results show that the approach can efficiently find out optimal layer thicknesses even when they are far outside the range covered by the original training data of DNN.