On-chip vectorial structured light field manipulation by inverse design

Structured light, with its multidimensional control over amplitude, phase, space and frequency, is a key enabler for advanced technologies such as high-capacity communications, quantum information, and super-resolution imaging. Here, we propose a unified inverse-design methodology for arbitrary on-chip vectorial structured-light. Inspired by quantum-state representations, we describe complex vector fields as finite-dimensional vectors in a Hilbert space and introduce a transmission-matrix formalism that links input waveguide modes to target topological edge states. By combining this mapping with adjoint-based topology optimization, we obtain the permittivity distribution within a compact design window that realizes the desired vector transformation while preserving topological transport. We experimentally demonstrate two representative domain-wall configurations on a valley photonic crystal (VPC) platform, termed Type-I and Type-II topological couplers, which efficiently couple the fundamental TE0 mode into valley pseudospin edge states. Simulations of the ideally designed device show insertion losses of 0.04 dB and 0.09 dB at 1550 nm with 3-dB bandwidths of 132 nm and 65 nm, respectively. Experimentally, the fabricated device, which was designed accounting for fabrication tolerances, maintains a broadband low-loss performance, with measured losses of < 0.6 dB at 1550 nm with 3-dB bandwidth over > 60 nm and < 0.8 dB at 1550 nm with 3-dB bandwidth over 87 nm. Mirror-symmetric designs further validate selective excitation of orthogonal pseudospin states. Our results establish this inverse-design methodology as a powerful tool for strictly controlling on-chip vectorial light, paving the way toward compact, broadband, and multifunctional photonic integrated circuits for optical computing, communications, and beyond.