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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.

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Fig. 1: SHG and DFG emission from 3R-MoS2.
Fig. 2: In-plane SHG coherence length.
Fig. 3: Waveguide SHG in 3R-MoS2.
Fig. 4: Out-of-plane SHG coherence length in waveguide geometry.
Fig. 5: Accessing the dispersion of WMs in 3R-MoS2 via nanoimaging.

Data availability

Source data are provided with this paper. The rest of the data is available from the corresponding authors upon reasonable request.


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We thank A. J. Sternbach for helpful discussions and X. Yan for experimental assistance. This work was supported by Programmable Quantum Materials, an Energy Frontier Research Center funded by the US Department of Energy, Office of Science, Basic Energy Sciences, under award DE-SC0019443. C.T. and G.C. acknowledge support by the European Union’s Horizon 2020 research and innovation programme under grant agreement GrapheneCore3 881603. F.M. gratefully acknowledges support by the Alexander von Humboldt Foundation.

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Authors and Affiliations



X.X. and C.T. conceived the experiment and built the custom transmission microscope. X.X. prepared the samples and performed the nonlinear measurements. F.M. and S.Z. performed the near-field measurements. F.M. analysed the near-field data and implemented the corresponding numerical models. Y.S. and X.X. determined the dielectric function from transmission/reflection experiments. G.C., D.N.B. and P.J.S. supervised the study. X.X., C.T., F.M., G.C., D.N.B. and P.J.S. wrote the article with input from all the authors.

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Correspondence to D. N. Basov, Giulio Cerullo or P. James Schuck.

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Nature Photonics thanks Reuven Gordon, Marinko Jablan and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary Notes 1–4, Figs. 1–7 and refs. 1–4.

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Raw data for Fig. 1b,d,e,f.

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Raw data for Fig. 2a–d.

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Raw data for Fig. 3b.

Source Data Fig. 4

Raw data for Fig. 4a,d,e.

Source Data Fig. 5

Raw data for Fig. 5d–f.

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Xu, X., Trovatello, C., Mooshammer, F. et al. Towards compact phase-matched and waveguided nonlinear optics in atomically layered semiconductors. Nat. Photon. 16, 698–706 (2022).

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