Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

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

Abstract

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.

This is a preview of subscription content, access via your institution

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

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.

References

  1. Ono, M. et al. Ultrafast and energy-efficient all-optical switching with graphene-loaded deep-subwavelength plasmonic waveguides. Nat. Photon. 14, 37–43 (2020).

    Article  ADS  Google Scholar 

  2. Li, C. Nonlinear Optics: Principles and Applications (Springer, 2016).

  3. Klimmer, S. et al. All-optical polarization and amplitude modulation of second-harmonic generation in atomically thin semiconductors. Nat. Photon. 15, 837–842 (2021).

  4. Sun, Z., Martinez, A. & Wang, F. Optical modulators with 2D layered materials. Nat. Photon. 10, 227–238 (2016).

    Article  ADS  Google Scholar 

  5. Yao, K. et al. Enhanced tunable second harmonic generation from twistable interfaces and vertical superlattices in boron nitride homostructures. Sci. Adv. 7, eabe8691 (2021).

    Article  ADS  Google Scholar 

  6. Ehren, M. et al. Ultrafast electronic and structural response of monolayer MoS2 under intense photoexcitation conditions. ACS Nano 8, 10734–10742 (2014).

    Article  Google Scholar 

  7. Ghazal, H. et al. Single nanoflake hexagonal boron nitride harmonic generation with ultralow pump power. ACS Photonics 8, 1922–1926 (2021).

    Article  Google Scholar 

  8. DinparastiSaleh, H. et al. Towards spontaneous parametric down conversion from monolayer MoS2. Sci. Rep. 8, 3862 (2018).

    Article  ADS  Google Scholar 

  9. Wang, Y., Jöns, K. D. & Sun, Z. Integrated photon-pair sources with nonlinear optics. Appl. Phys. Rev. 8, 011314 (2021).

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  11. Lin, K. Q., Bange, S. & Lupton, J. M. Quantum interference in second-harmonic generation from monolayer WSe2. Nat. Phys. 15, 242–246 (2019).

    Article  Google Scholar 

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

    Article  Google Scholar 

  13. Chen, H. et al. Enhanced second-harmonic generation from two-dimensional MoSe2 on a silicon waveguide. Light Sci. Appl. 6, e17060 (2017).

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  15. Wu, L. et al. Giant anisotropic nonlinear optical response in transition metal monopnictide Weyl semimetals. Nat. Phys. 13, 350–355 (2017).

    Article  Google Scholar 

  16. Li, Y. et al. Probing symmetry properties of few-layer MoS2 and h-BN by optical second-harmonic generation. Nano Lett. 13, 3329–3333 (2013).

    Article  ADS  Google Scholar 

  17. Malard, L. M., Alencar, T. V., Barboza, A. P. M., Mak, K. F. & De Paula, A. M. Observation of intense second harmonic generation from MoS2 atomic crystals. Phys. Rev. B 87, 201401 (2013).

    Article  ADS  Google Scholar 

  18. Wang, G., Marie, X. & Gerber, I. et al. Giant enhancement of the optical second-harmonic emission of WSe2 monolayers by laser excitation at exciton resonances. Phys. Rev. Lett. 114, 097403 (2015).

    Article  ADS  Google Scholar 

  19. Nagler, P. et al. Giant magnetic splitting inducing near-unity valley polarization in van der Waals heterostructures. Nat. Commun. 8, 1551 (2017).

    Article  ADS  Google Scholar 

  20. Mennel, L. et al. Optical imaging of strain in two-dimensional crystals. Nat. Commun. 9, 516 (2018).

    Article  ADS  Google Scholar 

  21. Robert W. Boyd Nonlinear Optics 4th edn (Academic Press, 2020).

  22. Liu, F. et al. Disassembling 2D van der Waals crystals into macroscopic monolayers and reassembling into artificial lattices. Science 376, 903–906 (2020).

    Article  ADS  Google Scholar 

  23. Wang, Q., Kalantar-Zadeh, K. & Kis, A. et al. Electronics and optoelectronics of two-dimensional transition metal dichalcogenides. Nat. Nanotechnol. 7, 699–712 (2012).

    Article  ADS  Google Scholar 

  24. Säynätjoki, A., Karvonen, L. & Rostami, H. et al. Ultra-strong nonlinear optical processes and trigonal warping in MoS2 layers. Nat. Commun. 8, 893 (2017).

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  26. Shi, J. et al. 3R MoS2 with broken inversion symmetry: a promising ultrathin nonlinear optical device. Adv. Mater. 29, 1701486 (2017).

    Article  Google Scholar 

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

    Article  Google Scholar 

  28. Song, B. et al. Layer-dependent dielectric function of wafer-scale 2D MoS2. Adv. Opt. Mater. 7, 1801250 (2019).

    Article  Google Scholar 

  29. Ermolaev, G. A. et al. Giant optical anisotropy in transition metal dichalcogenides for next-generation photonics. Nat. Commun. 12, 854 (2021).

    Article  ADS  Google Scholar 

  30. Chanyoung, Y. et al. Investigation of the optical properties of MoS2 thin films using spectroscopic ellipsometry. Appl. Phys. Lett. 104, 103114 (2014).

    Article  Google Scholar 

  31. Cai, L., Gorbach, A. V., Wang, Y., Hu, H. & Ding, W. Highly efficient broadband second harmonic generation mediated by mode hybridization and nonlinearity patterning in compact fiber-integrated lithium niobate nano-waveguides. Sci. Rep. 8, 12478 (2018).

    Article  ADS  Google Scholar 

  32. Shoji, I., Kondo, T., Kitamoto, A., Shirane, M. & Ito, R. Absolute scale of second-order nonlinear-optical coefficients. J. Opt. Soc. Am. B 14, 2268–2294 (1997).

    Article  ADS  Google Scholar 

  33. Liu, W. et al. Strong exciton-plasmon coupling in MoS2 coupled with plasmonic lattice. Nano Lett. 16, 1262–1269 (2016).

    Article  ADS  Google Scholar 

  34. Tompkins, H. & Irene, E. A. Handbook of Ellipsometry (William Andrew, 2005).

  35. Vaquero, D. et al. Excitons, trions and Rydberg states in monolayer MoS2 revealed by low-temperature photocurrent spectroscopy. Commun. Phys. 3, 194 (2020).

    Article  Google Scholar 

  36. Hu, D. et al. Probing optical anisotropy of nanometer-thin van der Waals microcrystals by near-field imaging. Nat. Commun. 8, 1471 (2017).

    Article  ADS  Google Scholar 

  37. Sternbach, A. J. et al. Femtosecond exciton dynamics in WSe2 optical waveguides. Nat. Commun. 11, 3567 (2020).

    Article  ADS  Google Scholar 

  38. Kusch, P., Mueller, N. S., Hartmann, M. T. & Reich, S. Strong light-matter coupling in MoS2. Phys. Rev. B 103, 235409 (2021).

    Article  ADS  Google Scholar 

  39. Mrejen, M., Yadgarov, L., Levanon, A. & Suchowski, H. Transient exciton-polariton dynamics in WSe2 by ultrafast near-field imaging. Sci. Adv. 5, eaat9618 (2019).

    Article  ADS  Google Scholar 

  40. Li, Z. et al. High-quality all-inorganic perovskite CsPbBr3 microsheet crystals as low-loss subwavelength exciton–polariton waveguides. Nano Lett. 21, 1822–1830 (2021).

    Article  ADS  Google Scholar 

  41. Hu, F. & Fei, Z. Recent progress on exciton polaritons in layered transition-metal dichalcogenides. Adv. Opt. Mater. 8, 1901003 (2020).

    Article  Google Scholar 

  42. Chen, X. et al. Modern scattering-type scanning near-field optical microscopy for advanced material research. Adv. Mater. 31, 1804774 (2019).

    Article  Google Scholar 

  43. Hu, F. et al. Imaging propagative exciton polaritons in atomically thin WSe2 waveguides. Phys. Rev. B 100, 121301 (2019).

    Article  ADS  Google Scholar 

  44. Passler, N. C. & Paarmann, A. Generalized 4 × 4 matrix formalism for light propagation in anisotropic stratified media: study of surface phonon polaritons in polar dielectric heterostructures. J. Opt. Soc. Am. B 34, 2128–2139 (2017).

    Article  Google Scholar 

  45. Thomas, J. et al. Quasi phase matching in femtosecond pulse volume structured x-cut lithium niobate. Laser Photon. Rev. 7, L17–L20 (2013).

    Article  Google Scholar 

  46. Bruch, A. W. et al. 17000%/W second-harmonic conversion efficiency in single-crystalline aluminum nitride microresonators. Appl. Phys. Lett. 113, 131102 (2018).

  47. Ocelic, N., Huber, A. & Hillenbrand, R. Pseudoheterodyne detection for background-free near-field spectroscopy. Appl. Phys. Lett. 89, 101124 (2006).

    Article  ADS  Google Scholar 

  48. Zhang, S. et al. Nano-spectroscopy of excitons in atomically thin transition metal dichalcogenides. Nat. Commun. 13, 542 (2022).

    Article  ADS  Google Scholar 

  49. Hu, D. et al. Tunable modal birefringence in a low-loss van der Waals waveguide. Adv. Mater. 31, 1807788 (2019).

    Article  Google Scholar 

  50. Malitson, I. H. Interspecimen comparison of the refractive index of fused silica. J. Opt. Soc. Am. 55, 1205–1209 (1965).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

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.

Author information

Authors and Affiliations

Authors

Contributions

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.

Corresponding authors

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

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

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

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

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

Source data

Source Data Fig. 1

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

Source Data Fig. 2

Raw data for Fig. 2a–d.

Source Data Fig. 3

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.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

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). https://doi.org/10.1038/s41566-022-01053-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41566-022-01053-4

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing