  Integrating conventional optics into compact nanostructured surfaces is the
goal of flat optics. Despite the enormous progress of this technology, there
are still critical challenges for real world applications due to a limited
efficiency in the visible, on average lower than $60\%$, which originates by
absorption losses in wavelength thick ($\approx 500$nm) structures. Another
issue is the realization of on-demand optical components for controlling
vectorial light at visible frequencies simultaneously in both reflection and
transmission, and with a predetermined wavefront shape. In this work, we
developed an inverse design approach that allows the realization of highly
efficient (up to $99\%$) ultra-flat (down to $50$nm thick) optics for vectorial
light control and broadband input-output responses on a desired wavefront
shape. The approach leverages on a hidden network of universal approximators,
which exist in the physical layer of suitably engineered semiconductor
nanostructures. Near unity performance results from the ultra-flat nature of
these surfaces, which reduces absorption losses to almost negligible values.
Experimentally, we discuss polarizing beam splitters, comparing their
performances with the best results obtained from both direct and inverse design
techniques, and new flat-optics components represented by dichroic mirrors and
the basic unit of a flat optics display that creates full colors by using only
two sub-pixels, overcoming the limitations of conventional LCD/OLED
technologies that require three sub-pixels for each composite color. Our
devices are manufactured with a complementary metal-oxide-semiconductor (CMOS)
compatible process, making them scalable for mass production at inexpensive
costs.

Optics