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Excitonic resonances control the temporal dynamics of nonlinear optical wave mixing in monolayer semiconductors


Monolayer semiconductors are an emerging platform for strong nonlinear light–matter interactions that are enhanced by the giant oscillator strength of tightly bound excitons. Little attention has been paid to the impact of excitonic resonances on the temporal dynamics of such nonlinearities, since harmonic generation and optical wave mixing are generally considered instantaneous processes. We find that a significant time difference, ranging from −40 to +120 fs, is necessary between two light pulses for optimal sum-frequency generation (SFG) and four-wave mixing (FWM) to occur from monolayer WSe2 when one of the pulses is in resonance with an excitonic transition. These resonances involve both band-edge A excitons and high-lying excitons that comprise electrons from conduction bands far above the bandgap. Numerical simulations in the density-matrix formalism rationalize the distinct dynamics of SFG and FWM. The interpulse delays for maximal SFG and FWM are governed primarily by the lifetime of the one-photon and two-photon resonant states, respectively. The method therefore offers an unconventional probe of the dynamics of excitonic states accessible with either one-photon or two-photon transitions. Remarkably, the longest delay times occur at the lowest excitation powers, indicating a strong nonlinearity that offers exploration potential for excitonic quantum nonlinear optics.

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Fig. 1: Delayed SFG and FWM from monolayer WSe2.
Fig. 2: Excitonic effects on the delay time for maximal SFG and FWM.
Fig. 3: Nonlinear optical wave-mixing spectroscopy simulated using the density-matrix formalism.
Fig. 4: Simulated delay times for maximal SFG and FWM intensities.
Fig. 5: Simulated dependence of the delay time for maximal SFG and FWM on the lifetime of the excitonic states.

Data availability

Any additional data are available from the corresponding authors upon reasonable request. Source data are provided with this paper.

Code availability

The Mathematica code used for the numerical simulations discussed in this paper is available from the corresponding authors upon reasonable request.


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We thank C. Schüller and R. Huber for insightful discussions. Financial support is gratefully acknowledged from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) SFB 1277 (project-ID 314695032) projects B03 (J.M.L. and S.B.) and B11 (K.-Q.L.), SPP 2244 (project-ID LI 3725/1-1, 443378379) (K.-Q.L. and S.B.) and from DFG project number 439215932 (J.M.L.). Growth of the hBN crystals was supported by the Elemental Strategy Initiative conducted by the MEXT, Japan (grant number JPMXP0112101001) and JSPS KAKENHI (grant numbers 19H05790 and JP20H00354).

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Authors and Affiliations



K.-Q.L. conceived and supervised the project. J.M.B., L.C., P.W., K.-Q.L. and S.B. carried out the experiments and simulations. S.B. wrote the simulation code. K.W. and T.T. provided the hBN crystals. All authors analysed the data, discussed the results and contributed to the writing of the manuscript.

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Correspondence to Kai-Qiang Lin.

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Nature Photonics thanks Giulio Cerullo and Christoph Lienau for their contribution to the peer review of this work.

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Supplementary Notes 1 and 2, Figs. 1–9 and Table 1.

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Source Data Fig. 4

Original data for the plots.

Source Data Fig. 5

Original data for the plots.

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Bauer, J.M., Chen, L., Wilhelm, P. et al. Excitonic resonances control the temporal dynamics of nonlinear optical wave mixing in monolayer semiconductors. Nat. Photon. 16, 777–783 (2022).

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