Polarization Engineering of Second-Harmonic Generation in 3R-MoS$_2$ Waveguides

Chip-scale nonlinear optics enables strong light-matter interactions within compact devices, serving as a fundamental platform for multifunctional integrated photonics from classical optical signal processing to quantum information technologies. Transition metal dichalcogenide (TMDC) waveguides have recently emerged as a highly promising platform owing to their giant material nonlinearity and extended interaction lengths. To date, however, research has predominantly focused on conversion efficiency, leaving the mechanisms governing the polarization state of nonlinear signal largely unexplored. Here, we establish a comprehensive framework for engineering the polarization of second-harmonic generation (SHG) in 3R-MoS$_2$ waveguides. By synergizing polarization-resolved measurements with theoretical modeling, we reveal that the SHG polarization is determined by guided-mode interactions constrained by waveguide geometry and crystal symmetry, and further reshaped during propagation. We demonstrate that thickness-dependent guided-mode confinement and in-plane crystal symmetry provide robust, static control over SHG polarization, while propagation length offers a dynamic tuning knob for continuously tailoring the nonlinear output. Our findings provide a deterministic approach for on-chip polarization engineering, opening opportunities for reconfigurable nonlinear light sources and quantum photonic circuits.