  The waveguide-integrated metasurface introduces a novel photonic chip capable
of converting guided modes into free-space light. This enables functions such
as off-chip beam focusing, steering, and imaging. The challenge lies in
achieving hypermultiplexing across diverse parameters, including guided-wave
mode type, direction, polarization, and notably, multiple wavelengths. Here, we
introduce a comprehensive end-to-end inverse design framework, rooted in a
physical model, for the multifunctional design of on-chip metasurfaces. This
framework allows for metasurface optimization through a target-field-driven
iteration process. We demonstrate a hypermultiplexed on-chip metasurface
capable of generating red-green-blue holograms at multiple target planes, with
both independent and cooperative control over guided-wave direction.
Significantly, the proposed method streamlines the design process utilizing
only the positions of meta-atoms as the design variable. We demonstrate 9
independent holographic channels through a combination of wavelength and
distance multiplexing. Moreover, by incorporating the excitation direction into
the design, the metasurface produces a total of 36 distinct holograms. The
robustness of these results against fabrication discrepancies is validated
through 3D full-wave electromagnetic simulations, aligning well with advanced
manufacturing techniques. Our research presents a universal design framework
for the development of multifunctional on-chip metasurfaces, opening up new
avenues for a wide range of applications.
