Bridging Macroscopic and Microscopic Nonlinear Optics with Layered Semiconductors

Nonlinear frequency conversion provides essential tools for light generation, photon entanglement, and manipulation. Conventional nonlinear optical crystals display moderate second-order nonlinear susceptibilities and perform well in benchtop setups with discrete optical components. However, such crystals do not easily lend themselves to miniaturization and on-chip integration. Transition metal dichalcogenides (TMDs) possess 10-100x stronger nonlinear susceptibilities and, thanks to their deeply sub-wavelength thickness, offer a unique platform for on-chip nonlinear frequency conversion and light amplification. Recently, such giant nonlinearity has been exploited to demonstrate nonlinear light amplification at the ultimate thickness limit[1]; however, optical gain was still limited by the sub-nm propagation length.<br/><br/>The nonlinear conversion efficiencycould be scaled by increasing the propagation length through the active medium. This is attainable by increasing the number of layers in the TMD sample. However, the nonlinear optical properties of semiconducting TMDs critically depend on their crystallographic symmetry. 2H-TMDs are naturally centrosymmetric, giving an opposite dipole orientation among consecutive layers. This results in a vanishing nonlinear susceptibility (|χ⁽²⁾| = 0) for crystals with even number of layers and precludes efficient conversion in multilayers. In contrast, 3R-TMDs naturally combines broken inversion symmetry (|χ⁽²⁾| ≠ 0) and aligned layering, representing ideal candidates to boost the nonlinear optical gain with minimal footprint.<br/><br/>The nonlinear optical response of 3R-MoS₂ has been explored in some recent pioneering studies[2,3], so far focusing on thinner crystals, reporting the quadratic enhancement with the layer number at the 2D limit, and showing a maximum SHG enhancement of ≈100 occurring at specific thickness windows. Pushing towards general application, however, requires higher nonlinear enhancements and thus larger layer number, which in turn leads to more intricate interferences and interactions within the crystal.<br/><br/>Here we measure SHG from multilayer 3R-MoS₂ crystals with variable thickness. We report the first measurement of the coherence length of 3R-MoS₂ at telecom wavelengths. Our model is able to capture the role of phase-matching, as well as the intrinsic interference effects. At the coherence length (~ 530 nm) we achieve record nonlinear optical enhancement from a van der Waals material, i.e., &gt;10⁴ stronger than a monolayer, revealing the intrinsic single-pass upper limits of the material[4]. Considering that the reported conversion efficiency of monolayer MoS₂ at FW = 1560 nm is ~10^-10, the overall conversion efficiency of MoS₂ at the coherence length thickness will be ~10^-6. Further enhancement can then be achieved by regularly engineering larger crystals or waveguides with a periodicity on this length scale, or by exploiting birefringence.<br/><br/>Our results highlight the potential of 3R-stacked TMDs for integrated photonics, providing critical parameters for designing highly efficient on-chip nonlinear optical devices. By virtue of the exceptional nonlinear properties and the possibility of integration and phase matching in waveguide geometries, we foresee ultra-compact devices with extremely high nonlinear conversion efficiency – even exceeding multi-pass state-of-the-art photonic resonators of aluminum nitride – opening new frontiers for engineering on-chip integrated nonlinear optical devices including photonic resonators and optical quantum circuits.<br/><br/>[1] <u>Trovatello, C.</u> et al. Nat. Photonics, 15, 6-10 (2021).<br/>[2] Shi, J. et al., Adv. Mater. 29, 1701486 (2017).<br/>[3] Zhao, M. et al., Light: Sci. Appl. 5, e16131 (2016).<br/>[4] Xu, X., <u>Trovatello, C.</u> et al., Nature Photonics, 16, 698-706 (2022).