Regenerative oscillation and four-wave mixing in graphene optoelectronics

Journal name:
Nature Photonics
Year published:
Published online


The unique linear and massless band structure of graphene in a purely two-dimensional Dirac fermionic structure has led to intense research in fields ranging from condensed matter physics to nanoscale device applications covering the electrical, thermal, mechanical and optical domains. Here, we report three consecutive first observations in graphene–silicon hybrid optoelectronic devices—ultralow-power resonant optical bistability, self-induced regenerative oscillations and coherent four-wave mixing—all at few-femtojoule cavity recirculating energies. These observations, in comparison with control measurements on solely monolithic silicon cavities, are enabled only by the dramatically large and ultrafast χ(3) nonlinearities in graphene and the large Q/V ratios in wavelength-localized photonic crystal cavities. These third-order nonlinear results demonstrate the feasibility and versatility of hybrid two-dimensional graphene–silicon nanophotonic devices for next-generation chip-scale high-speed optical communications, radiofrequency optoelectronics and all-optical signal processing.

At a glance


  1. Graphene-clad silicon photonic crystal nanostructures.
    Figure 1: Graphene-clad silicon photonic crystal nanostructures.

    a, Scanning electron micrograph (SEM) of the tuned photonic crystal cavity, with lattice constant a = 420 nm. Example SEM with separated graphene monolayer on silicon for illustration. Scale bar, 500 nm. Inset: example Ez-field from finite-difference time-domain computations. b, Measured Raman scattering spectra of monolayer CVD-grown graphene on the photonic crystal cavity membrane. The Lorentzian lineshape FWHM of the G-band (34.9 cm−1) and 2D-band (49.6 cm−1) peaks and the G-to-2D peak ratio indicate that the graphene is monolayer, and the single symmetric G peak indicates good uniformity of the graphene. Homogeneity across the sample was examined by excitation at different locations across the cavity membrane (blue, red and grey). c, SEM of the suspended graphene–silicon membrane. Dark patches represent bilayer graphene. Left inset: Dirac cone illustrating the highly doped Fermi level (dashed blue circle), allowing the two-photon transition (blue arrows) but forbidding the one-photon transition (orange dashed arrow). Right inset: computed Ey-field along the z-direction, with graphene at the evanescent top interface. Scale bar, 500 nm. d, Example measured graphene-clad cavity transmission with asymmetric Fano-like lineshapes (red line) and significantly larger redshift compared to a control bare silicon cavity sample with symmetric Lorentzian lineshapes (black line). Both spectra were measured with an input power of 0.6 mW, and are centred to the intrinsic cavity resonances (λcavity_0 = 1,562.36 nm for the graphene sample and λcavity_0 = 1,557.72 nm for the silicon sample), measured at low power (input power <100 µW). The intrinsic cavity quality factors of the graphene and control samples are similar.

  2. Bistable switching in graphene-clad nanocavities.
    Figure 2: Bistable switching in graphene-clad nanocavities.

    a, Steady-state input/output optical bistability for the quasi-TE cavity mode with laser-cavity detuning of δ = 1.5 (λlaser = 1,562.66 nm) and 1.7 (λlaser = 1,562.70 nm). The dashed black line represents the coupled-mode theory simulation with effective nonlinear parameters for the graphene–silicon cavity sample. b, Switching dynamics with triangular-waveform drive input (dashed grey line). Bistable resonances are observed for both positive and negative detuning. Blue open circles, δ(t=0) = −1.3 (λlaser = 1,562.10 nm); red filled circles, δ(t=0) = 1.6 (λlaser = 1,562.68 nm). Inset: schematic of high- and low-state transmissions.

  3. Regenerative oscillations in graphene-clad nanocavities.
    Figure 3: Regenerative oscillations in graphene-clad nanocavities.

    a, Observations of temporal regenerative oscillations in the cavity for optimized detuning (λlaser = 1,562.47 nm). The input power has a quasi-triangular waveform with peak power of 1.2 mW. The grey line is the reference output power, with the laser further detuned at 1.2 nm from cavity resonance (λlaser = 1,563.56 nm). b, Mapping of output power versus input power with slow up (blue crosses) and down (red circles) power sweeps. In the up-sweep process, the cavity starts to oscillate when the input power is beyond 0.29 mW. c, Nonlinear coupled-mode theory model of cavity transmission versus resonance shift, in the regime of regenerative oscillations. With a detuning of 0.15 nm (δ(t=0) = 0.78) the free carrier density swings from 4.4 to 9.1 × 1017 cm−3 and the increased temperature ΔT circulates between 6.6 and 9.1 K. d, Radiofrequency spectrum of output power below (0.4 mW, grey dashed line) and above (0.6 mW, blue solid line) oscillation threshold at the same detuning δ(t=0) = 0.78 (λlaser − λcavity =  0.15 nm), as in c. Inset: normalized transmission from the model (blue line) and experimental data (red circles) at the same constant power level.

  4. Parametric four-wave mixing in graphene-clad silicon nanocavities.
    Figure 4: Parametric four-wave mixing in graphene-clad silicon nanocavities.

    a, Measured transmission spectrum with signal laser fixed at −0.16 nm according to cavity resonance wavelength, while scanning the pump laser detuning from −0.1 to 0.03 nm. Inset: band diagram of the degenerate four-wave mixing process with pump (green), signal (blue) and idler (red) lasers. b, Measured transmission spectrum with pump laser fixed on cavity resonance, and signal laser detuning scanned from −0.04 to −0.27 nm. c, Modelled conversion efficiency versus pump and signal detuning from the cavity resonance. The solid and dashed lines mark the regions plotted in a and b, respectively. d, Observed and simulated conversion efficiencies of the cavity. Red filled dots are measured with signal detuning as in b, and open circles are obtained with pump detuning as in a, plus 29.5 dB (offset due to the 0.16 nm signal detuning). Solid and dashed black lines are modelled conversion efficiencies for the graphene–silicon and monolithic silicon cavities, respectively. Grey dashed line (superimposed): illustrative pump/signal laser spontaneous emission noise ratio.


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Author information


  1. Department of Electrical Engineering, Columbia University, New York, New York 10027, USA

    • T. Gu &
    • J. F. McMillan
  2. Department of Mechanical Engineering, Columbia University, New York, New York 10027, USA

    • N. Petrone,
    • A. van der Zande,
    • J. Hone &
    • C. W. Wong
  3. The Institute of Microelectronics, 11 Science Park Road, Singapore Science Park II, Singapore 117685, Singapore

    • M. Yu,
    • G. Q. Lo &
    • D. L. Kwong


T.G. and J.F.M. performed the experiments. T.G., N.P., A.V.D.Z. and J.H. prepared the graphene transfer and synthesis. M.Y., G.Q.L. and D.L.K. nanofabricated the membrane samples. T.G. and C.W.W. performed the numerical simulations. T.G. and C.W.W. prepared the manuscript.

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