  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.
