  With the flourishing development of nanophotonics, Cherenkov radiation
pattern can be designed to achieve superior performance in particle detection
by fine-tuning the properties of metamaterials such as photonic crystals (PCs)
surrounding the swift particle. However, the radiation pattern can be sensitive
to the geometry and material properties of PCs, such as periodicity, unit
thickness, and dielectric fraction, making direct analysis and inverse design
difficult. In this article, we propose a systematic method to analyze and
design PC-based transition radiation, which is assisted by deep learning neural
networks. By matching boundary conditions at the interfaces, Cherenkov-like
radiation of multilayered structures can be resolved analytically using the
cascading scattering matrix method, despite the optical axes not being aligned
with the swift electron trajectory. Once well trained, forward deep learning
neural networks can be utilized to predict the radiation pattern without
further direct electromagnetic simulations; moreover, Tandem neural networks
have been proposed to inversely design the geometry and/or material properties
for desired Cherenkov radiation pattern. Our proposal demonstrates a promising
strategy for dealing with layered-medium-based Cherenkov radiation detectors,
and it can be extended for other emerging metamaterials, such as photonic time
crystals.
