  Compact photonic elements that control both the diffraction and interference
of light offer superior performance at ultra-compact dimensions. Unlike
conventional optical structures, these diffractive optical elements can provide
simultaneous control of spectral and spatial profile of light. However, the
inverse-design of such a diffractive optical element is time-consuming with
current algorithms, and the designs generally lack experimental validation.
Here, we develop a neural network model to experimentally design and validate
SpliCons; a special type of diffractive optical element that can achieve
spectral splitting and simultaneous concentration of broadband light. We use
neural networks to exploit nonlinear operations that result from wavefront
reconstruction through a phase plate. Our results show that the neural network
model yields enhanced spectral splitting performance for phase plates with
quantitative assessment compared to phase plates that are optimized via local
search optimization algorithm. The capabilities of the phase plates optimized
via neural network are experimentally validated by comparing the intensity
distribution at the output plane. Once the neural networks are trained, we
manage to design SpliCons with 96.6 $\pm$ 2.3% accuracy within 2 seconds, which
is orders of magnitude faster than iterative search algorithms. We openly share
the fast and efficient framework that we develop in order to contribute to the
design and implementation of diffractive optical elements that can lead to
transformative effects in microscopy, spectroscopy, and solar energy
applications.
