  The design of metamaterials which support unique optical responses is the
basis for most thin-film nanophotonics applications. In practice this inverse
design problem can be difficult to solve systematically due to the large design
parameter space associated with general multi-layered systems. We apply
convolutional neural networks, a subset of deep machine learning, as a tool to
solve this inverse design problem for metamaterials composed of stacks of thin
films. We demonstrate the remarkable ability of neural networks to probe the
large global design space (up to $10^{12}$ possible parameter combinations) and
resolve all relationships between metamaterial structure and corresponding
ellipsometric and reflectance / transmittance spectra. The applicability of the
approach is further expanded to include the inverse design of synthetic
engineered spectra in general design scenarios. Furthermore, this approach is
compared with traditional optimization methods. We find an increase in the
relative optimization efficiency of the networks with increasing total layer
number, revealing the advantage of the machine learning approach in
many-layered systems where traditional methods become impractical.
