  The need for optically multi-functional micro- and nano-structures is growing
in various fields. Designing such structures is impeded by the lack of
computationally low-cost algorithms. In this study, we present a hybrid design
scheme, which relies on a deep learning model and the local search optimization
algorithm, to optimize a diffractive optical element that performs spectral
splitting and spatial concentration of broadband light for solar cells. Using
generated data set during optimization of a diffractive optical element, which
is a one-time effort, we design topography of diffractive optical elements by
using a deep learning-based inverse design scheme. We show that further
iterative optimization of the reconstructed diffractive optical elements
increases amount of spatially concentrated and spectrally split light. Our
joint design approach both speeds up optimization of diffractive optical
elements as well as providing better performance at least 57% excess light
concentration with spectral splitting. The algorithm that we develop here will
enable advanced and efficient design of multi-functional phase plates in
various fields besides the application that we target in solar energy. The
algorithm that we develop is openly available to contribute to other
applications that rely on phase plates.
