Gate-Tunable Nonlinear Refraction and Absorption in Graphene-Covered Silicon Nitride Waveguides

Abstract

The nonlinear optical properties of graphene have received significant interest in the past years. Especially third-order nonlinear effects have been demonstrated to be large. Recently several groups have shown, through four-wave mixing (FWM) and third harmonic generation (THG) experiments, that the optical nonlinearity of graphene can be tuned through electrostatic gating. These effects are quantified by a strongly tunable |σ s(3) |, with σ s (3) the complex third-order conductivity. Here, by simultaneously observing cross-phase and cross-amplitude modulation on a silicon nitride waveguide covered with gated graphene, we are able to confirm such strong tunability for these nonlinear effects as well. Moreover, we can separately quantify the real and imaginary parts of σ s(3) , which respectively represent nonlinear absorption and refraction. This unveils a tunability that is far more drastic than what could be observed through FWM or THG, including sign changes in both the nonlinear absorption and refraction. Our results are confirmed by a theoretical model for the optical nonlinearity of graphene. The ability to tailor the nonlinearity of graphene to this extent can lead to new opportunities, such as nanophotonic devices with electrically tunable nonlinear properties.

Theory of the strongly nonlinear electrodynamic response of graphene: A hot electron model

“…A similar effect was observed and the same interpretation was applied to its explanation in Ref. 45 , where the nonlinear absorption in graphene was measured under different equilibrium conditions with µ 0 = −0.4 eV and T 0 = 300 K. As we have seen above, in reality the quantities T , µ e , and µ h cannot be considered as frequency independent and a more general theory should be applied. In Figure 11(a) we plot the absorption spectra calculated for |µ 0 | = 16 meV, T 0 = 10 K, τ p = 300 fs, and τ ǫ /τ rec = 0.01; the results were found to be weakly dependent on τ ǫ /τ rec as long as this parameter is small as compared to unity.…”

“…[28][29][30] respectively. Experimentally the higher harmonics generation [36][37][38][39][40] , the four-wave mixing [41][42][43][44][45] , the radiation induced absorption changes [46][47][48][49][50] , Kerr effect [51][52][53][54][55] , the photoconductivity 56 and other nonlinear phenomena have been observed. All of them demonstrated very large absolute values of the nonlinear optical parameters of graphene.…”

“…This problem can be partly circumvented by replacing T 0 in the expression for σ (3) αβγδ by an effective temperature T which is considered as a fitting parameter and can be (much) larger than T 0 ; this way to interpret experimental data was used, e.g., in Refs. 40,45,48,56 . However, in general, not only the temperature, but also the chemical potentials of electron (µ e ) and hole (µ h ) gases should be considered to be different from µ 0 .…”

Ultrafast and energy-efficient all-optical switching with graphene-loaded deep-subwavelength plasmonic waveguides

“…However, the observed output waveform is symmetric in time, and its full width at half maximum (FWHM) is 2.5 ps, which is close to that for the autocorrelation width (2.8 ps) of the input pulse. The reported relaxation time of photo-excited carriers in graphene ranges from 10 fs to several ps [18][19][20][21] , and our result indicates that the recovery time is much shorter than t pulse (1.8 ps).…”

Evaluation of graphene optical nonlinearity with photon-pair generation in graphene-on-silicon waveguides

“…Note that, in this work, we use the effective nonlinear refractive index n 2,eff for convenience to compare our results with the various previous works although the conventional nonlinear refractive index n 2 for three-dimensional materials cannot be defined for two-dimensional materials, as discussed in several theoretical papers [28,29,46]. As with the recent experimental works [13,31], the use of the two-dimensional nonlinear conductivity (or the two-dimensional nonlinear susceptibility defined in [46]) would be appropriate for future work. Figure 4(a) shows the net photon-pair generation rate at the output end of the GSWs as a function of pump peak power P p with the fixed graphene length L gr of 100 µm and the graphene position of (iii) fixed input-length II (L in = 0.15 mm).…”