Towards compact phase-matched and waveguided nonlinear optics in atomically layered semiconductors

Nonlinear frequency conversion provides essential tools for generating new colors and quantum states of light. Transition metal dichalcogenides possess huge nonlinear susceptibilities; further, 3R-stacked transition metal dichalcogenide crystals possess aligned layers with broken inversion symmetry, representing ideal candidates to boost the nonlinear optical gain with minimal footprint. Here we report the second-order nonlinear processes of 3R-MoS₂ along the ordinary and extraordinary directions. Along the ordinary axis, by measuring the thickness-dependent second-harmonic generation, we present the first measurement of the second-harmonic-generation coherence length of 3R-MoS₂ and achieve record nonlinear optical enhancement from a van der Waals material, >10⁴ stronger than a monolayer. It is found that 3R-MoS₂ slabs exhibit similar conversion efficiencies of lithium niobate, but within 100-fold shorter propagation lengths. Furthermore, along the extraordinary axis, we achieve broadly tunable second-harmonic generation from 3R-MoS₂ in a waveguide geometry, revealing the coherence length in such a structure. We characterize the full refractive-index spectrum and quantify its birefringence with near-field nanoimaging. Our results highlight the potential of 3R-stacked transition metal dichalcogenides for integrated photonics, providing critical parameters for designing highly efficient on-chip nonlinear optical devices including periodically poled structures, optical parametric oscillators and amplifiers, and quantum circuits.