Coherent Nonlinear Optical Response of Graphene

Abstract

We investigate the nonlinear optical properties of graphene flakes using four-wave mixing. The corresponding third-order optical susceptibility is found to be remarkably large and only weakly dependent on the wavelength in the near-infrared frequency range. The magnitude of the response is in good agreement with our calculations based on the nonlinear quantum response theory. DOI: 10.1103/PhysRevLett.105.097401 PACS numbers: 78.67.Wj, 42.65.Ky, 78.47.nj Graphene, a single sheet of carbon atoms in a hexagonal lattice, is the basic building block for all graphitic materials. Although it has been known as a theoretical concept for some time [1], a layer of graphene has only recently been isolated from bulk graphite and deposited on a dielectric substrate [2]. The great interest in studying graphene is driven by its linear, massless band structureand many unusual electrical, thermal, mechanical, and optical properties [3,4] [here the upper (lower) sign corresponds to the electron (hole) band, p is the quasimomentum, and V % 10 6 m=s is the Fermi velocity]. For example, the optical absorption of graphene has been shown to be wavelength independent ('2:3% per layer) in a broad range of optical frequencies [5][6][7]. Recently, it has been predicted that the linear dispersion described by Eq. (1) should lead to strongly nonlinear optical behavior at microwave and terahertz frequencies [8]. At higher, optical frequencies one can also expect an enhanced optical nonlinearity as, due to graphene's band structure, interband optical transitions occur at all photon energies. Here we report on the first observation of the coherent nonlinear optical response of graphene at visible and nearinfrared frequencies. We show that graphene has an exceptionally high nonlinear response, described by the effective nonlinear susceptibility j ð3Þ j $ 10 À7 esu (electrostatic units). This nonlinearity is shown to be essentially dispersionless over the wavelength range in our experiments (emission at e ' 760-840 nm). These results are in good agreement with predictions derived from nonlinear quantum response theory. The large optical nonlinearity of graphene can be used for exceptionally high-contrast imaging of single and multilayered graphene flakes.Single-and few-layer graphene samples are fabricated using the method of mechanical exfoliation [2] and deposited onto a 100 m thick glass cover slip. Prior to investigation in the nonlinear microscope, the layer thickness is estimated via contrast measurements under an optical microscope, using a method similar to Ref. [9]. To investigate the nonlinear response of graphene flakes, we employ the four-wave mixing technique [10]. This involves the generation of mixed optical frequency harmonics 2! 1 À ! 2 under irradiation by two monochromatic waves with the frequencies ! 1 and ! 2 .Figure 1(a) illustrates the principle of the method: two incident pump laser beams with wavelengths 1 (tunable from 670 nm to 980 nm) and 2 (1130 nm to 1450 nm) are focused collinearly onto a sample and mix together...

Graphene photonics and optoelectronics

“…In addition, FWM, generating NIR wavelength-tunable light was demonstrated using SLG and FLG 141 . Graphene's third-order susceptibility was measured to be |χ 3 | ∼ 10 −7 esu 141 , one order of magnitude larger than reported so far for CNTs 141 . However, photon-counting electronics is typically needed to measure the output 140 , indicating a low conversion efficiency.…”

“…However, photon-counting electronics is typically needed to measure the output 140 , indicating a low conversion efficiency. Other features of graphene, such as the possibility of tuning the nonlinearity by changing the number of layers 141 , and wavelength-independent nonlinear susceptibility 141 , still could be potentially used for various photonic applications (e.g. optical imaging 141 ).…”

Anomalous Nonlinear Optical Response of Graphene Near Phonon Resonances

“…Different non-linear optical phenomena like second-, third-harmonic generation and four wave mixing (FWM) [5][6][7] can be quite strong in these materials [8][9][10][11][12][13][14][15]. However, the interpretation of the nonlinear optical response is strongly affected by electronic and phonon resonances [16][17][18][19], therefore the knowledge of the interplay between these resonances is desirable.…”

High-Contrast Electrooptic Modulation of a Photonic Crystal Nanocavity by Electrical Gating of Graphene

“…These observations allow cavity-enhanced measurements of the graphene complex dielectric constant under different chemical potentials, in agreement with a theoretical model of the graphene dielectric constant under gating. This graphene-based nanocavity modulation demonstrates the feasibility of high-contrast, low-power frequency-selective electro-optic nanocavity modulators in graphene-integrated silicon photonic chips.Graphene has intriguing optical properties and enables a range of promising optoelectronic devices [1][2][3][4][5][6][7][8][9]. To enhance the inherently weak light-matter interaction in this single atomic layer material, grahene has been coupled to optical waveguides and cavities [6,[10][11][12][13].…”

“…Graphene has intriguing optical properties and enables a range of promising optoelectronic devices [1][2][3][4][5][6][7][8][9]. To enhance the inherently weak light-matter interaction in this single atomic layer material, grahene has been coupled to optical waveguides and cavities [6,[10][11][12][13].…”