Nonlinear optical properties of multilayer graphene in the infrared

Abstract

A negative value for the nonlinear refraction in graphene is experimentally observed and unambiguously verified by performing a theoretical analysis arising from the conductivity of the graphene monolayer. The nonlinear optical properties of multi-layer graphene are experimentally studied by employing the Z-scan technique. The measurements are carried out at 1150, 1550, 1900 and 2400 nm with a 100-femtosecond laser source. Under laser illumination the multi-layer graphene exhibits a transmittance increase due to saturable absorption, followed by optical limiting due to two-photon absorption. The saturation irradiance Isat and the two-photon absorption coefficient β are measured in the operating wavelength range. Furthermore, an irradiance-dependent nonlinear refraction is observed and discriminated from the conventional nonlinear refraction coefficient n2_, which is not irradiance dependent. The values obtained for the irradiance-dependent nonlinear refraction are in the order of ∼10^-9 cm²W^-1, approximately 8 orders of magnitude larger than any bulk dielectrics.

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

“…In conclusion, we have evaluated the nonlinear coefficients of GSWs through the coincidence measurement of the photon-pair generation via SFWM. According to the theoretical analysis using the coupled-wave equations [38][39][40][41], our results clearly reflected a six to tenfold graphene-induced optical NLE, which is consistent with previously reported values [5,11,12,16,22,23,25]. Because unwanted effects (e.g.…”

“…There are large discrepancies between the reported values of the third-order nonlinear coefficient of graphene. 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].…”

Enhanced optical Kerr effect method for a detailed characterization of the third-order nonlinearity of two-dimensional materials applied to graphene

“…The thirdorder nonlinear optical response of graphene has been investigated by many groups, theoretically [2][3][4][5][6][7][8] , and experimentally [9][10][11][12][13][14][15] . More recently, other 2D materials have also been studied 16,17 .…”

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.…”

“…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.…”