We develop the vectorial scattering holography approach, as an inverse design method, with both single-channel and multiple-channel regimes for flexibly designing versatile on-chip QE-coupled metasurfaces. Based on the proposed approach, we design, fabricate, and characterize on-chip quantum light sources of two well-collimated single-photon beams propagating along different off-normal directions with orthogonal linear polarizations. Furthermore, we experimentally demonstrate on-chip generation of multichannel quantum emission encoded with different SAMs and OAMs in each channel. The multichannel holography approach is further extended for tempering the strength of QE emission into a particular channel. The holography-based inverse design approach developed and demonstrated on-chip quantum light sources with multiple degrees of freedoms enable thereby a powerful platform for quantum nanophotonics, especially relevant for advanced quantum photonic applications, e.g., high-dimensional quantum information processing.
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