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

Abstract

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.

Figures (4)

• Figure 1: SHG in 3R-MoS$_2$ nonlinear TMDC waveguides.a Schematic of the edge-coupling measurement. A linearly polarized femtosecond FW beam is focused onto the input edge of a 3R-MoS$_2$ waveguide to excite waveguide modes via edge scattering. The incident polarization angle $\phi_0$ is defined with respect to the propagation direction ($x$-axis). The generated SH waveguide modes co-propagate with the FW and are out-coupled at the output edge for polarization-resolved detection. The coordinate system is defined with the $x$-axis along the light propagation direction, the $y$-axis parallel to the input edge, and the $z$-axis perpendicular to the substrate. b Microscopic image of a fabricated 3R-MoS$_2$ waveguide ($357\nm$ thick) on a fused silica (SiO$_2$) substrate, overlaid with spatially resolved false-colour images of the FW ($\lambda = 1200\nm$, magenta) and SH ($\lambda = 600\nm$, orange) signals under TE excitation. Dashed lines outline the waveguide boundaries. Scale bar: $5\um$. c Crystal structure of 3R-MoS$_2$ corresponding to the waveguide orientation in (b). Left: top view in the $x$--$y$ plane, with red and black arrows (and dashed lines) indicating the AC and ZZ crystallographic directions, respectively. Right: side view illustrating the 3R stacking sequence. d SHG intensity ($I_{\mathrm{SHG}}$) measured at the output edge of the waveguide in (b) as a function of excitation power under TE and TM excitation, respectively
• Figure 2: Thickness-dependent polarization characteristics in 3R-MoS$_2$ waveguides.a, b Real-space images of the FW (magenta) and SH (orange) signals in $20\um\times20\um$ square waveguides with thicknesses of $123\nm$ and $357\nm$ under TE (a) and TM (b) excitation, respectively. The input edges are aligned along the ZZ crystallographic direction. Scale bar: $5\um$. c, d Polar plots of the normalized total SH (c) and FW (d) emission intensity as a function of the incident polarization angle $\phi_0$ for $123\nm$- (red) and $357\nm$-thick (blue) waveguides. e Thickness dependence of the effective refractive indices of the TE and TM modes at $\lambda=1200\nm$ (FW) and $\lambda=600\nm$ (SH), respectively. The horizontal gray line indicates the refractive index of the SiO$_2$ substrate ($n_{SiO_2} = 1.45$). f Simulated mode profiles of the fundamental TM$_0$ mode for FW and SH in $123\nm$- and $357\nm$-thick waveguides. g--j Polarization-resolved SHG emission under XX and XY detection for waveguides of different thicknesses with the input edge aligned along the ZZ axis (g, h) and the AC axis (i, j), respectively. In (c), (d), and (g--j), dots denote experimental data and solid lines are fits
• Figure 3: Crystal-orientation control of SHG polarization.a Polar plots of the normalized SHG polarization emission for $\theta$ ranging from $0^\circ$ to $110^\circ$ in $10^\circ$ steps under TE excitation. Dots: experimental data; solid curves: fits using Eq. \ref{['eq:shg_field']}. b Extracted SHG polarization azimuthal angle $\varphi$ as a function of the crystal orientation angle $\theta$ (inset: definition of crystal orientation angle $\theta$). Symbols: experimental data; solid line: linear fit, yielding a slope of $2.92 \pm 0.11$ and indicating a near-$3\theta$ dependence of $\varphi$
• Figure 4: Propagation-induced evolution of SHG polarization.a Schematic illustration of SHG polarization evolution. FW waveguide modes generate co-propagating SH fields, and the edge-emitted output polarization evolves continuously with propagation length due to interference among SH fields generated along the waveguide and the accumulated relative phase delay between SH TE and TM components. b Optical micrograph of a set of $225\nm$-thick 3R-MoS$_2$ waveguides ($\theta=0^\circ$) with systematically varied lengths $L$. Scale bar: $10\um$. c Polar plots of the edge-emitted SHG polarization for $L$ from $10\um$ to $13.5\um$ under $\phi_0=45^\circ$ excitation (dots: data; solid lines: fits)