Negative Kerr Nonlinearity of Graphene as seen via Chirped-Pulse-Pumped Self-Phase Modulation

Abstract

We experimentally demonstrate a negative Kerr nonlinearity for quasi-undoped graphene. Hereto, we introduce the method of chirped-pulse-pumped self-phase modulation and apply it to graphenecovered silicon waveguides at telecom wavelengths. The extracted Kerr-nonlinear index for graphene equals n2,gr = −10 −13 m 2 /W. Whereas the sign of n2,gr turns out to be negative in contrast to what has been assumed so far, its magnitude is in correspondence with that observed in earlier experiments. Graphene's negative Kerr nonlinearity strongly impacts how graphene should be exploited for enhancing the nonlinear response of photonic (integrated) devices exhibiting a positive nonlinearity. It also opens up the possibility of using graphene to annihilate unwanted nonlinear effects in such devices, to develop unexplored approaches for establishing Kerr processes, and to extend the scope of the "periodic poling" method often used for second-order nonlinearities towards third-order Kerr processes. Because of the generic nature of the chirped-pulse-pumped self-phase modulation method, it will allow fully characterizing the Kerr nonlinearity of essentially any novel (2D) material.

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

“…4(c) and 4(d) exhibit the P 1 p -dependence of the single-count rates rather than the P 2 p -dependence associated with SFWM. This P 1 p -dependence indicates that noise photons are generated via processes other than SFWM (e.g., SPM [18,21,24,25] and inelastic scattering [47]) and the CAR of the GSWs has been reduced due to the graphene-induced loss and such unwanted photon-generation events.…”

“…For example, the experimentally obtained effective nonlinear refractive index n 2,eff of graphene ranges from 10 −11 -10 −13 m 2 /W for stimulated four-wave mixing (FWM) [5,[11][12][13]17] or optical Kerr effect (OKE) [16,[18][19][20][21][22][23][24][25] to 10 −15 -10 −17 m 2 /W for third-harmonic generation (THG) [14,15]. Not only the absolute value, but also the positive/negative sign of the effective nonlinear refractive index n 2,eff of graphene has been under active investigation [23,24]. From theoretical point of view, the 4-6-order difference between the nonlinear coefficients corresponding to the FWM (or the OKE) and the THG has been predicted recently [26][27][28].…”

Nonlinear graphene plasmonics

“…Similarly, while early experimental investigations did not explicitly distinguish between the signs of graphene's nonlinear coefficient, very recent works have unanimously found negative nonlinear refractive indices in the visible and telecommunication wavelengths. Three independent works in 2016, published during June, July and August, respectively, verified the negative index of refraction for graphene [112][113][114]. Demetriou et al [112] measured n 2 to be of the order of −10 −13 m 2 W −1 at wavelengths between 1150 and 2400 nm with a 100 fs source using the Z-scan technique.…”

“…Dremetsika et al [113] also found n 2 to be −1.1 × 10 −13 m 2 W −1 using the optically heterodyne-detected optical Kerr effect (OHD-OKE), as shown in figure 11b, using a 1600 nm Ti : sapphire laser with 180 fs pulses, concurring with the previous Z-scan measurements. Finally, Vermeulen et al [114] conducted SPM measurements, as shown in figure 11c, and also reported n 2 ∼ −10 −13 m 2 W −1 at 1550 nm for 3 ps pulses.…”

Nonlinear optics of graphene and other 2D materials in layered structures

“…Various experiments with graphene in free-space configurations, on waveguides, and on photonic crystals have been performed to investigate different nonlinear phenomena, including PFC [13,21], third harmonic generation (THG) [21][22][23][24][25], second harmonic generation (SHG) [26][27][28][29][30][31], Kerr effects (or self-phase modulation, SPM) and two photon absorption [32][33][34][35][36][37][38][39], and coherent current injection [40,41]. The extracted effective bulk third order susceptibilities eff [37,38,42], the ability to tune the nonlinearity by varying the chemical potential [21,25], and the possibility of having quasi-exponentially growing SPM in graphene on waveguides [39]. Most of the existing microscopic theories [43][44][45][46][47][48][49][50][51][52][53][54][55][56] focus on the dependence of the sheet conductivities σ ( n) ( i n eff wc µ-( ) ) on incident light frequencies, temperature...…”