Third harmonic generation in graphene and few-layer graphite films

Abstract

We observe optical third harmonic generation from graphene and few-layer graphite flakes produced by exfoliation. The emission scales with the cube of the intensity of the incident near-infrared femtosecond pulses and has a wavelength that is one-third of the incident wavelength, both consistent with third harmonic generation. We extract an effective third-order susceptibility for graphene that is on the order of 10 −16 m 2 /V 2 , which is comparable to that for materials that are resonantly excited, but larger than for materials that are transparent at the fundamental and third harmonic wavelengths. By measuring a set of flakes with different numbers of atomic layers, we find that the emission scales with the square of the number of atomic layers, which suggests that the susceptibility of graphene is independent of layer number, at least for a few layers.Graphene is a monolayer of carbon atoms arranged in a hexagonal two-dimensional lattice. It has a linear dispersion relationship between energy, E, and wavenumber, k, E(k) = ±hv F k, where the Fermi velocity v F ≈ 10 6 m/s [see Fig. 1 -3]. Since the material became readily available less than a decade ago [4], it has been the subject of extensive investigations [e.g., see Refs. 5 and 6 and references therein]. Graphene exhibits a number of unusual and remarkable transport properties that make it attractive for nano-electronic applications [7][8][9], including high mobilities [4,5,9, 10] and nearly-ballistic transport at room temperature [5,6]; however, it is the optical properties of graphene that are of primary interest here.The linear absorbance of graphene is flat and approximately 2.3% across the entire visible spectrum [11,12]. Thus, graphene can be considered to be both highly absorbing and/or highly transmitting, depending upon one's point of view or application. Since a negligible fraction (< 0.1%) is reflected [12], 97.7% of the incident light is transmitted. In this sense the sample is certainly transparent. On the other hand, if one were to assign an effective absorption coefficient, α, to a monolayer of thickness 0.33 nm (even though it may be questionable to use macroscopic parameters, such as α, for such thin samples), it would be very large (α ≈ 7 × 10 5 /cm). As suggested by this large effective absorption coefficient, graphene interacts strongly with light. The strong broadband nature of the interaction of light with graphene is consistent with its linear bandstructure, where interband transitions of roughly equal strength are available throughout the visible. The combination of broadband transparency and the high mobilities mentioned earlier makes graphene a promising candidate for use as a transparent conductor [13][14][15][16] in photovoltaic devices [17,18] and touch screens [14]. The high broadband absorption (i.e., optical conductivity) and high carrier mobility suggest that graphene may find applications in a range of optically-controlled transport devices, such as broadband and ultrafast photodetectors [19][20][21][22][23][24][25] The s...

Electrically tunable nonlinear plasmonics in graphene nanoislands

“…For comparison, we note that the third-order susceptibility of extended graphene without the involvement of any plasmons has been measured via four-wave mixing experiments as |w (3) |B10 À 7 esu, exceeding the maximum value obtained for a 4-nm-thick gold film measured under the same experimental conditions 20 . In addition, THG measurements have yielded values |w (3) |B10 À 8 esu in graphene 22 .…”

“…For comparison, we note that the third-order susceptibility of extended graphene without the involvement of any plasmons has been measured via four-wave mixing experiments as |w (3) |B10 À 7 esu, exceeding the maximum value obtained for a 4-nm-thick gold film measured under the same experimental conditions 20 . In addition, THG measurements have yielded values |w (3) |B10 À 8 esu in graphene 22 .The linear and nonlinear spectral lineshapes display a dependence on light intensity that is clearly observable above B1 GW m À 2 , as shown through time-domain simulations in Fig. 2d-f, obtained from the Fourier transform of the induced dipole over an optical cycle after reaching a steady-state regime (see Methods).…”

Optical Third-Harmonic Generation in Graphene

“…A recent study experimentally demonstrated THG from graphene for transitions occurring near the K point and was carried out at normal-incidence angle; in that study, the authors report a quadratic dependence of THG on graphene layer number [40]. In contrast, the present work reports experimental THG from graphene under conditions in which the TH is in three-photon resonance with the M point of graphene and at non-normal-incidence angle in order to provide access to other nonlinear susceptibility elements not accessible under a normal-incidence configuration, and to probe thicker films, in the case of multilayer graphene.…”

Quantum Effects in the Nonlinear Response of Graphene Plasmons

“…Owing to its gapless, linear charge-carrier dispersion relation [3,4], graphene is capable of relatively strong, broadband coupling with light [5,6], and offers a large electrically-tunable optical response [7]. Valence and conduction electrons in this material present a uniform velocity that clearly emphasizes their anharmonic response to external fields, which has stimulated considerable interest in the graphene nonlinear optical properties [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. Further motivation to study optical nonlinearities in monolayer graphene is provided by the availability of interband optical transitions within a continuous range of low photon energies, accompanied by a high electrical mobility [24,25].…”