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Spatiotemporal imaging of nonlinear optics in van der Waals waveguides

Nature Nanotechnology volume 20, pages 374–380 (2025)Cite this article

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Abstract

Van der Waals (vdW) semiconductors have emerged as promising platforms for efficient nonlinear optical conversion, including harmonic and entangled photon generation. Although major efforts are devoted to integrating vdW materials in nanoscale waveguides for miniaturization, the realization of efficient, phase-matched conversion in these platforms remains challenging. Here, to address this challenge, we report a far-field ultrafast imaging method to track the propagation of both fundamental and harmonic waves within vdW waveguides with femtosecond and sub-50 nanometre spatiotemporal precision. We focus on light propagation in slab waveguides of rhombohedral-stacked MoS2, a vdW semiconductor with large nonlinear susceptibility. Our method allows systematic optimization of nonlinear conversion by determining the phase-matching angles, mode profiles and losses in waveguides without prior knowledge of material optical constants. Using this approach, we show that both multimode and single-mode rhombohedral-stacked MoS2 waveguides support birefringent phase matching, demonstrating the material’s potential for efficient on-chip nonlinear optics.

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Fig. 1: Imaging the propagation of FW and SH light in 3R-MoS2 waveguides.
Fig. 2: Anisotropic waveguided FW and SH properties.
Fig. 3: Determining phase-matching conditions through spatiotemporal imaging.
Fig. 4: Modal phase matching in thin waveguides.

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Data availability

All data are shown in the main text, supplementary information and supplementary videos. Source data to reproduce main text figures are available via Zenodo at https://doi.org/10.5281/zenodo.14231910 (ref. 59). Alternative data formats are available from the corresponding author upon request.

References

  1. Chai, Z. et al. Ultrafast all-optical switching. Adv. Opt. Mater. 5, 1600665 (2017).

    Google Scholar 

  2. Chang, D. E., Vuletić, V. & Lukin, M. D. Quantum nonlinear optics—photon by photon. Nat. Photon. 8, 685–694 (2014).

    CAS  Google Scholar 

  3. Hohenleutner, M. et al. Real-time observation of interfering crystal electrons in high-harmonic generation. Nature 523, 572–575 (2015).

    CAS  PubMed  Google Scholar 

  4. Tancogne-Dejean, N., Mücke, O. D., Kärtner, F. X. & Rubio, A. Ellipticity dependence of high-harmonic generation in solids originating from coupled intraband and interband dynamics. Nat. Commun. 8, 745 (2017).

    PubMed  PubMed Central  Google Scholar 

  5. Basov, D. N., Fogler, M. M. & García de Abajo, F. J. Polaritons in van der Waals materials. Science 354, 195 (2016).

    CAS  Google Scholar 

  6. Datta, I. et al. Low-loss composite photonic platform based on 2D semiconductor monolayers. Nat. Photon. 14, 256–262 (2020).

    CAS  Google Scholar 

  7. Yao, K. et al. Continuous wave sum frequency generation and imaging of monolayer and heterobilayer two-dimensional semiconductors. ACS Nano 14, 708–714 (2020).

    CAS  PubMed  Google Scholar 

  8. Trovatello, C. et al. Optical parametric amplification by monolayer transition metal dichalcogenides. Nat. Photon. 15, 6–10 (2021).

    CAS  Google Scholar 

  9. Abdelwahab, I. et al. Giant second-harmonic generation in ferroelectric NbOI2. Nat. Photon. 16, 644–650 (2022).

    CAS  Google Scholar 

  10. Guo, Q. et al. Ultrathin quantum light source with van der Waals NbOCl2 crystal. Nature 613, 53–59 (2023).

    CAS  PubMed  Google Scholar 

  11. Lee, M. et al. Wafer-scale δ waveguides for integrated two-dimensional photonics. Science 381, 648–653 (2023).

    CAS  PubMed  Google Scholar 

  12. Zograf, G. et al. Combining ultrahigh index with exceptional nonlinearity in resonant transition metal dichalcogenide nanodisks. Nat. Photon. 18, 751–757 (2024).

    CAS  Google Scholar 

  13. Sortino, L. et al. Van der Waals heterostructure metasurfaces: atomic-layer assembly of ultrathin optical cavities. Preprint at https://arxiv.org/abs/2407.16480 (2024).

  14. Busschaert, S. et al. Transition metal dichalcogenide resonators for second harmonic signal enhancement. ACS Photon. 7, 2482–2488 (2020).

    CAS  Google Scholar 

  15. Hsu, W. T. et al. Second harmonic generation from artificially stacked transition metal dichalcogenide twisted bilayers. ACS Nano 8, 2951–2958 (2014).

    CAS  PubMed  Google Scholar 

  16. Hsu, W.-T. et al. Dielectric impact on exciton binding energy and quasiparticle bandgap in monolayer WS2 and WSe2. 2D Mater. 6, 025028 (2019).

    CAS  Google Scholar 

  17. Zhao, M. et al. Atomically phase-matched second-harmonic generation in a 2D crystal. Light. Sci. Appl. 5, e16131 (2016).

    CAS  PubMed  PubMed Central  Google Scholar 

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

    CAS  Google Scholar 

  19. Trovatello, C. et al. Quasi-phase-matched up- and down-conversion in periodically poled layered semiconductors. Nat. Photon. (in the press).

  20. Li, Z. et al. Direct visualization of phase-matched efficient second harmonic and broadband sum frequency generation in hybrid plasmonic nanostructures. Light. Sci. Appl. 9, 180 (2020).

    CAS  PubMed  PubMed Central  Google Scholar 

  21. Caspani, L. et al. Integrated sources of photon quantum states based on nonlinear optics. Light. Sci. Appl. 6, e17100 (2017).

    CAS  PubMed  PubMed Central  Google Scholar 

  22. Tsuchizawa, T. et al. Microphotonics devices based on silicon microfabrication technology. IEEE J. Sel. Top. Quantum Electron. 11, 232–240 (2005).

    CAS  Google Scholar 

  23. Pu, M. et al. Ultra-efficient and broadband nonlinear AlGaAs-on-insulator chip for low-power optical signal processing. Laser Photon. Rev. 12, 1800111 (2018).

    Google Scholar 

  24. Shi, J. et al. Remote dual-cavity enhanced second harmonic generation in a hybrid plasmonic waveguide. Nano Lett. 22, 688–694 (2022).

    CAS  PubMed  Google Scholar 

  25. Fei, Z. et al. Gate-tuning of graphene plasmons revealed by infrared nano-imaging. Nature 487, 82–85 (2012).

    CAS  PubMed  Google Scholar 

  26. Yoxall, E. et al. Direct observation of ultraslow hyperbolic polariton propagation with negative phase velocity. Nat. Photon. 9, 674–678 (2015).

    CAS  Google Scholar 

  27. Gersen, H. et al. Real-space observation of ultraslow light in photonic crystal waveguides. Phys. Rev. Lett. 94, 073903 (2005).

    CAS  PubMed  Google Scholar 

  28. Kurman, Y. et al. Spatiotemporal imaging of 2D polariton wave packet dynamics using free electrons. Science 372, 1181–1186 (2021).

    CAS  PubMed  Google Scholar 

  29. Niemann, R. et al. Spectroscopic and interferometric sum-frequency imaging of strongly coupled phonon polaritons in SiC metasurfaces. Adv. Mater. 36, 2312507 (2024).

    CAS  Google Scholar 

  30. Autler, S. H. & Townes, C. H. Stark effect in rapidly varying fields. Phys. Rev. 100, 703–722 (1955).

    Google Scholar 

  31. Hayat, A. et al. Dynamic Stark effect in strongly coupled microcavity exciton polaritons. Phys. Rev. Lett. 109, 033605 (2012).

    PubMed  Google Scholar 

  32. LaMountain, T. et al. Valley-selective optical Stark effect of exciton-polaritons in a monolayer semiconductor. Nat. Commun. 12, 4530 (2021).

    CAS  PubMed  PubMed Central  Google Scholar 

  33. Pogna, E. A. A. A. et al. Photo-induced bandgap renormalization governs the ultrafast response of single-layer MoS2. ACS Nano 10, 1182–1188 (2016).

    CAS  PubMed  Google Scholar 

  34. Trovatello, C. et al. Disentangling many-body effects in the coherent optical response of 2D semiconductors. Nano Lett. 22, 5322–5329 (2022).

    CAS  PubMed  PubMed Central  Google Scholar 

  35. Xu, D. et al. Ultrafast imaging of polariton propagation and interactions. Nat. Commun. 14, 3881 (2023).

    CAS  PubMed  PubMed Central  Google Scholar 

  36. Renken, S. et al. Untargeted effects in organic exciton-polariton transient spectroscopy: a cautionary tale. J. Chem. Phys. 155, 154701 (2021).

    CAS  PubMed  Google Scholar 

  37. Delor, M., Weaver, H. L., Yu, Q. & Ginsberg, N. S. Imaging material functionality through three-dimensional nanoscale tracking of energy flow. Nat. Mater. 19, 56–62 (2020).

    CAS  PubMed  Google Scholar 

  38. Boyd, R. W. Nonlinear Optics 3rd edn (Academic Press, 2008).

  39. Bringuier, E., Bourdon, A., Piccioli, N. & Chevy, A. Optical second-harmonic generation in lossy media: application to GaSe and InSe. Phys. Rev. B 49, 16971–16982 (1994).

    CAS  Google Scholar 

  40. Neuschafer, D., Preiswerk, H., Spahni, H., Konz, E. & Marowsky, G. Second-harmonic generation using planar waveguides with consideration of pump depletion and absorption. J. Opt. Soc. Am. B 11, 649 (1994).

    CAS  Google Scholar 

  41. Liu, H. L. et al. Temperature-dependent optical constants of monolayer MoS2, MoSe2, WS2, and WSe2: spectroscopic ellipsometry and first-principles calculations. Sci. Rep. 10, 15282 (2020).

    CAS  PubMed  PubMed Central  Google Scholar 

  42. Stegeman, G. I. & Stolen, R. H. Waveguides and fibers for nonlinear optics. J. Opt. Soc. Am. B 6, 652 (1989).

    CAS  Google Scholar 

  43. Stegeman, G. I. & Seaton, C. T. Nonlinear integrated optics. J. Appl. Phys. 58, 57–78 (1985).

    Google Scholar 

  44. Jankowski, M. et al. Ultrabroadband nonlinear optics in nanophotonic periodically poled lithium niobate waveguides. Optica 7, 40 (2020).

    CAS  Google Scholar 

  45. Suhara, T. & Fujimura, M. Waveguide Nonlinear-Optic Devices (Springer Berlin Heidelberg, 2003).

  46. Lin, Q., Painter, O. J. & Agrawal, G. P. Nonlinear optical phenomena in silicon waveguides: modeling and applications. Opt. Express 15, 16604 (2007).

    CAS  PubMed  Google Scholar 

  47. Munkhbat, B. et al. Self-hybridized exciton-polaritons in multilayers of transition metal dichalcogenides for efficient light absorption. ACS Photon. 6, 139–147 (2019).

    CAS  Google Scholar 

  48. Chervy, T. et al. High-efficiency second-harmonic generation from hybrid light–matter states. Nano Lett. 16, 7352–7356 (2016).

    CAS  PubMed  Google Scholar 

  49. Schmutzler, J. et al. Nonlinear spectroscopy of exciton-polaritons in a GaAs-based microcavity. Phys. Rev. B 90, 075103 (2014).

    CAS  Google Scholar 

  50. Mennel, L. et al. Band nesting in two-dimensional crystals: an exceptionally sensitive probe of strain. Nano Lett. 20, 4242–4248 (2020).

    CAS  PubMed  PubMed Central  Google Scholar 

  51. Yoshikawa, N. et al. Interband resonant high-harmonic generation by valley polarized electron–hole pairs. Nat. Commun. 10, 3709 (2019).

    PubMed  PubMed Central  Google Scholar 

  52. Choo, H. et al. Nanofocusing in a metal–insulator–metal gap plasmon waveguide with a three-dimensional linear taper. Nat. Photon. 6, 838–844 (2012).

    CAS  Google Scholar 

  53. Mooshammer, F. et al. Enabling waveguide optics in rhombohedral-stacked transition metal dichalcogenides with laser-patterned grating couplers. ACS Nano 18, 4118–4130 (2024).

    CAS  PubMed  Google Scholar 

  54. Zeng, Z. et al. Controlled vapor growth and nonlinear optical applications of large-area 3R phase WS2 and WSe2 atomic layers. Adv. Funct. Mater. 29, 1806874 (2019).

    Google Scholar 

  55. Li, X. et al. Rhombohedral-stacked bilayer transition metal dichalcogenides for high-performance atomically thin CMOS devices. Sci. Adv. 9, eade5706 (2023).

    CAS  PubMed  PubMed Central  Google Scholar 

  56. Bacot, V., Labousse, M., Eddi, A., Fink, M. & Fort, E. Time reversal and holography with spacetime transformations. Nat. Phys. 12, 972–977 (2016).

    CAS  Google Scholar 

  57. Moussa, H. et al. Observation of temporal reflection and broadband frequency translation at photonic time interfaces. Nat. Phys. 19, 863–868 (2023).

    CAS  Google Scholar 

  58. Tulyagankhodjaev, J. A. et al. Room-temperature wavelike exciton transport in a van der Waals superatomic semiconductor. Science 382, 438–442 (2023).

    CAS  PubMed  Google Scholar 

  59. Xu, D. et al. Dataset for “Spatiotemporal imaging of nonlinear optics in van der Waals waveguides” Zenodo https://doi.org/10.5281/zenodo.14231910 (2024).

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Acknowledgements

This work was primarily 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 (D.N.B., P.J.S. and M.D.). Transient reflectance and stroboSCAT measurements were obtained on instruments developed through National Science Foundation grant number CHE-2203844 (M.D.). Linear optical characterization was supported by the Arnold and Mabel Beckman Foundation through a Beckman Young Investigator award. D.X. acknowledges a Kathy Chen Fellowship. C.T. acknowledges the European Union’s Horizon Europe research and innovation programme under the Marie Skłodowska-Curie PIONEER HORIZON-MSCA-2021-PF-GF grant agreement number 101066108.

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Author notes

  1. Aaron Sternbach

    Present address: Department of Physics, University of Maryland, College Park, MD, USA

Authors and Affiliations

  1. Department of Chemistry, Columbia University, New York, NY, USA

    Ding Xu, Shan-Wen Cheng & Milan Delor

  2. Department of Mechanical Engineering, Columbia University, New York, NY, USA

    Zhi Hao Peng, Chiara Trovatello, Xinyi Xu & P. James Schuck

  3. Department of Physics, Columbia University, New York, NY, USA

    Aaron Sternbach & D. N. Basov

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Contributions

D.X., P.J.S. and M.D. conceived and designed the experiment. D.X. built the optical instruments and acquired the experimental data. Z.H.P., X.X., C.T. and S.-W.C. prepared the samples. Z.H.P. and D.X. performed the steady-state measurements of second-harmonic generation. D.X. and A.S. analysed the transport data and implemented the numerical models. M.D., P.J.S. and D.N.B. supervised the study. D.X. and M.D. wrote the article with input from all authors.

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Correspondence to Milan Delor.

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Nature Nanotechnology thanks Jiahua Duan, Kirill Koshelev and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Figs. 1–27, Notes 1–19 and Tables 1 and 2.

Supplementary Video 1

FW propagation in 1.25 μm waveguide.

Supplementary Video 2

SH propagation in 1.25 μm waveguide.

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Xu, D., Peng, Z.H., Trovatello, C. et al. Spatiotemporal imaging of nonlinear optics in van der Waals waveguides. Nat. Nanotechnol. 20, 374–380 (2025). https://doi.org/10.1038/s41565-024-01849-1

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