Absorption

Graphene sheets with sp ²-hybridized carbon atoms and associated π networks exhibit optical absorption over a broad spectral range from the ultraviolet to the near-infrared, although their insolubility has made solution-phase studies of optical absorption difficult.Reference Li, Muller, Gilje, Kaner and Wallace^17, Reference Eda, Lin, Mattevi, Yamaguchi, Chen, Chen, Chen and Chhowalla^22, Reference Pan, Guo, Zhang, Xi, Xue, Huang, Li, Zhang, Yu, Chen, Li and Wu^28, Reference Niyogi, Bekyarova, Itkis, McWilliams, Hamon and Haddon^40–Reference Robinson, Tabakman, Liang, Wang, Casalongue, Vinh and Dai⁴² As with other carbon nanomaterials, including carbon nanotubes and even carbon nanoparticles,Reference Itkis, Perea, Jung, Niyogi and Haddon^43–Reference Xu, Sahu, Cao, Anilkumar, Tackett, Qian, Bunker, Guliants, . Parenzan and Sun⁴⁷ π-plasmon absorption plays a major role in photon harvesting by graphene-based materials.Reference Loh, Bao, Eda and Chhowalla^9, Reference Ohta, Bostwick, Seyller, Horn and Rotenberg^48, Reference Eberlein, Bangert, Nair, Jones, Gass, Bleloch, Novoselov, Geim and Briddon⁴⁹

Graphene oxides (GOs) are graphene “derivatives” in which a substantial fraction of the sp ²-hybridized carbons are converted to sp ³ hybridization (up to 60% according to Ruoff and coworkers)Reference Cai, Piner, Stadermann, Park, Shaibat, Ishii, Yang, Velamakanni, An, Stoller, An, Chen and Ruoff⁵⁰ upon typically harsh oxidative treatment such as the Hummers method.Reference Hummers and Offeman⁵¹ Aqueous suspensions of GOs (solution-like, Figure 1a) are readily prepared to allow quantitative optical absorption measurements.Reference Li, Muller, Gilje, Kaner and Wallace^17, Reference Niyogi, Bekyarova, Itkis, McWilliams, Hamon and Haddon^40, Reference Kong, Song, Meziani, Tackett, Cao, Farr, Anderson and Sun⁵² The solubilized GOs (with primarily single-layer sheets) also serve as excellent precursors in various conversion schemes for the preparation of graphene sheets containing different ratios (purposely or by default) of sp ² and sp ³ carbons.Reference Eda, Lin, Mattevi, Yamaguchi, Chen, Chen, Chen and Chhowalla^22, Reference Mkhoyan, Contryman, Silcox, Stewart, Eda, Mattevi, Miller and Chhowalla⁵³ As a typical example, gradual changes in optical absorption can be used to monitor the transformation of a GO film at various stages of reduction (by hydrazine, in the case of Figure 1b).Reference Eda, Lin, Mattevi, Yamaguchi, Chen, Chen, Chen and Chhowalla²² The same strategy was applied to follow the conversion of GOs in a thermal treatment in supercritical fluids at relatively low temperatures.Reference Kong, Song, Meziani, Tackett, Cao, Farr, Anderson and Sun⁵²

Figure 1.

(a) Absorption spectrum of graphene oxides (GOs) in aqueous dispersion. Inset: Photographs of dispersions with low (0.05 mg/ml, left) and high (0.75 mg/ml, middle) GO concentrations and of a GO film on a quartz slide (right). Reproduced with permission from Reference Reference Kong, Song, Meziani, Tackett, Cao, Farr, Anderson and Sun52. ©2011, Elsevier. (b) Absorption spectra of GO thin films progressively reduced by exposure to hydrazine for total times noted in the legend. Reproduced with permission from Reference Reference Eda, Lin, Mattevi, Yamaguchi, Chen, Chen, Chen and Chhowalla22. ©2010, Wiley-VCH.

Many other methods of altering the ratios between sp ² and sp ³ carbons have been explored, including the formation of isolated sp ² islands in graphene sheets and/or the manipulation of defects (associated with sp ³ carbons), for the creation and tuning of electronic energy gaps. These nanoscale (often quantum-confined) domains in graphene materials, also referred to as graphene quantum dots (GQDs),Reference Loh, Bao, Eda and Chhowalla^9, Reference Eda, Lin, Mattevi, Yamaguchi, Chen, Chen, Chen and Chhowalla^22, Reference Pan, Guo, Zhang, Xi, Xue, Huang, Li, Zhang, Yu, Chen, Li and Wu^28, Reference Pan, Zhang, Li and Wu^29, Reference Peng, Gao, Gupta, Liu, Romero-Aburto, Ge, Song, Alemany, Zhan, Gao, Vithayathil, Kaipparettu, Marti, Hayashi, Zhu and Ajayan⁵⁴ offer distinctive optical absorption and photoluminescence characteristics, as discussed in more detail in the next section. They also generally serve as the basis for nonlinear optical properties in graphene materials. For nonlinear absorption, as an example, GOs in N,N-dimethylformamide were investigated using 532-nm nanosecond and picosecond pulses in a Z-scan setup, where the nonlinear response is monitored as the sample is moved through the focus of a laser beam.Reference Liu, Wang, Zhang, Xu, Chen and Tian⁵⁵ The results suggested significant two-photon absorption, especially with picosecond laser pulses. Other studies on nonlinear optical properties in graphene materials are highlighted and discussed later in this article.

Emission

Photoluminescence emission from graphene sheets has been reported and classified into several mechanism-based categories.Reference Gupta, Chaudhary, Srivastava, Sharma, Bhardwaj and Chand^13, Reference Eda, Lin, Mattevi, Yamaguchi, Chen, Chen, Chen and Chhowalla^22, Reference Luo, Vora, Mele, Johnson and Kikkawa^24, Reference Pan, Zhang, Li and Wu^29, Reference Lu, Yang, Wang, Lim, Wang and Loh^30, Reference Liu, Wu, Schuck, Salmeron, Shen and Wang^34, Reference Radovic and Bockrath^56–Reference Li, Bao, Hou, Sun, Wang and Gu⁵⁹ Among the more classical are those associated with bandgap transitions, where the bandgaps are mostly created by various theoretically established approaches. In fact, opening bandgaps has been a popular way to impart photoluminescence emission to graphene-based materials, for which several strategies have been developed.Reference Loh, Bao, Eda and Chhowalla^9, Reference Bonaccorso, Sun, Hasan and Ferrari^10, Reference Eda, Lin, Mattevi, Yamaguchi, Chen, Chen, Chen and Chhowalla^22–Reference Li, Wang, Zhang, Lee and Dai^31, Reference Peng, Gao, Gupta, Liu, Romero-Aburto, Ge, Song, Alemany, Zhan, Gao, Vithayathil, Kaipparettu, Marti, Hayashi, Zhu and Ajayan^54, Reference Lu, Yeo, Gan, Wu and Loh^60–Reference Jeon, Lee, Pollak, Moreschini, Bostwick, Park, Mendelsberg, Radmilovic, Kostecki, Richardson and Rotenberg⁶³ One of the two primary approaches to opening bandgaps is to physically or chemically treat graphene sheets to reduce the connectivity in the π-electronic network,Reference Luo, Vora, Mele, Johnson and Kikkawa^24–Reference Shukla and Saxena²⁶ including the formation of electron-confined sp ² islands in GOs.Reference Loh, Bao, Eda and Chhowalla^9, Reference Eda, Lin, Mattevi, Yamaguchi, Chen, Chen, Chen and Chhowalla^22, Reference Vogt, Gibson, Tune, Bissett, Voelcker, Shapter and Ellis²⁷ The other approach is to break graphene sheets into nanoribbons or even small dots.Reference Pan, Guo, Zhang, Xi, Xue, Huang, Li, Zhang, Yu, Chen, Li and Wu^28–Reference Li, Wang, Zhang, Lee and Dai³¹ Because of the expected confinement of electrons in these purposely created nanoscale domains, they are often called GQDs, as discussed above.

A typical example of the first approach is photoluminescence in GOs and reduced GOs (RGOs).Reference Eda, Lin, Mattevi, Yamaguchi, Chen, Chen, Chen and Chhowalla²² Specifically, GOs prepared using the Hummers oxidation method were reduced by exposure to hydrazine into RGOs, in which the graphene π network was disconnected, equivalent to the formation of isolated sp ² domains (about 3 nm in size edge-to-edge) in the carbon–oxygen sp ³ matrix (Figure 2a–c). These quantum-sized sp ² islands could localize electron–hole pairs and create energy bandgaps, resulting in fluorescence emission through radiative recombination of excitons (Figure 2d). The fluorescence intensities were found to depend on the degree of the reduction treatment in the conversion to RGOs, with significant quenching after extensive treatment. This quenching probably reflects the facilitation of nonradiative excited-state processes by some percolation among the sp ²domains.

Figure 2.

(a–c) Structural models of GO at different stages of reduction. The larger sp ² clusters of aromatic rings are not drawn to scale. The smaller sp ² domains indicated by zigzag lines correspond not to any specific structure (such as olefinic chains) but rather to small and localized sp ² configurations that act as luminescence centers. The photoluminescence intensity is relatively weak for (a) as-synthesized GO but increases with reduction due to (b) formation of additional small sp ² domains between the larger clusters because of evolution of oxygen with reduction. After extensive reduction, the smaller sp ² domains create (c) percolating pathways among the larger clusters. (d) Representative band structure of GO. Within each small fragment, confinement causes the energy levels to be quantized within the overall density of states (DOS) with a large energy gap that depends on the fragment geometry. A photogenerated electron–hole pair recombining radiatively is depicted. E _exc, excitation energy; E _PL, photoluminescence energy. Reproduced with permission from Reference Reference Eda, Lin, Mattevi, Yamaguchi, Chen, Chen, Chen and Chhowalla22. ©2010, Wiley-VCH.

For a typical example of the second approach, micron-sized graphene sheets were prepared by thermal reduction of GOs, followed by oxidization treatment in concentrated H₂SO₄ and HNO₃ and then hydrothermal processing to yield GQDs of one to three layers and an average lateral size of 9.6 nm.Reference Pan, Zhang, Li and Wu²⁹ Such small dots are known to have strong edge effects due to free zigzag sites commonly with a carbene-like triplet ground state.Reference Radovic and Bockrath⁵⁶ The observed photoluminescence in these GQDs was attributed to bandgap transitions associated with the free zigzag sites in the dots.Reference Gupta, Chaudhary, Srivastava, Sharma, Bhardwaj and Chand^13, Reference Pan, Zhang, Li and Wu²⁹ Such a mechanism was supported experimentally by the pH dependence of the photoluminescence emission. The emission intensities were enhanced under alkaline conditions but almost completely quenched under acidic conditions as a result of the protonation of the free zigzag sites.

Photoluminescence due to induced bandgaps can also be excited by nonlinear optical processes.Reference Shen, Zhu, Chen, Yang and Li^64–Reference Zhuo, Shao and Lee⁶⁷ The multiphoton photoluminescence of GO nanoparticles (average sizes around 40 nm) was investigated using laser pulses at 810 nm (∼160 fs) and 1215 nm (∼160 fs) for two- and three-photon excitation, respectively.Reference Qian, Wang, Peng, Xi, Cai, Zhu, He, Hu and He⁶⁶ The photoluminescence spectra were similar to those observed for linear excitation, suggesting that multiphoton excitation also caused electron–hole recombination with energies reflecting quantum confinement in graphitic islands in the GOs.

Shen et al. reduced GOs with hydrazine hydrate and then surface-passivated the reduced GOs with diamine-terminated oligomeric poly(ethylene glycol) to yield GQDs with sizes of 5–19 nm.Reference Shen, Zhu, Chen, Yang and Li⁶⁴ They attributed the up-conversion fluorescence in these GQDs to the anti-Stokes process, such that the π electrons are photoexcited to a higher-energy state (lowest unoccupied molecular orbital) and then transition back to a lower-energy state (σ orbital).Reference Shen, Zhu, Chen, Yang and Li⁶⁴ Nanocomposites of GQDs with TiO₂ were investigated for their photocatalytic activities based on up-conversion and down-conversion fluorescence emission.Reference Zhuo, Shao and Lee⁶⁷ It was proposed that the fluorescence was associated with bandgaps in tiny nanoribbons from the protruding edges in the GQDs.

Photoluminescence observed in GQDs with average lateral diameters of 3–5 nm and an average height of 0.95 nm (thus mostly single- or double-layer species), including that from up-conversion by multiphoton excitation, was attributed to surface energy traps and zigzag sites in the dots.Reference Zhu, Zhang, Liu, Li, Wang, Tang, Meng, Li, Shi, Hu and Yang⁶⁵

Other photoluminescence mechanisms in graphene-based materials that are associated with nonlinear optical processes include plasmon emission,Reference Stohr, Kolesov, Pflaum and Wrachtrup⁵⁷ nonequilibrium electron-energy distributions,Reference Liu, Wu, Schuck, Salmeron, Shen and Wang^34, Reference Lui, Mak, Shan and Heinz⁶⁸ and hot-carrier recombination.Reference Li, Bao, Hou, Sun, Wang and Gu⁵⁹ It has been suggested that the nonlinear up- and down-converted luminescence emission in graphene and thin graphite species in response to picosecond infrared laser pulses can be attributed to laser-created electron–hole plasmas in these nanomaterials.Reference Stohr, Kolesov, Pflaum and Wrachtrup⁵⁷ The nonlinear nature of the observed optical properties was confirmed by the quadratic power dependence of the luminescence emission before saturation at higher laser powers.

As an example of the nonequilibrium electron distribution mechanism, observation of unusually strong broadband nonlinear photoluminescence in graphene upon femtosecond pulsed laser irradiation has been reported.Reference Liu, Wu, Schuck, Salmeron, Shen and Wang³⁴ The broad distribution of nonequilibrated electrons and holes, whose radiative recombination was responsible for the photoluminescence emission, was attributed to rapid (within tens of femtoseconds after optical excitation) scattering between photoexcited carriers.Reference Liu, Wu, Schuck, Salmeron, Shen and Wang³⁴ The photoluminescence following excitation of single-layer graphene (exfoliated from graphite) by ultrafast laser pulses (30 fs) was found to exhibit a nonlinear dependence on laser excitation power with an exponent of 2.5 (Figure 3).Reference Lui, Mak, Shan and Heinz⁶⁸ The nonlinear process was rationalized mechanistically in terms of the electron distribution being driven strongly out of equilibrium by the ultrafast laser excitation.Reference Lui, Mak, Shan and Heinz⁶⁸

Figure 3.

(a) Spectra of light emission from graphene upon excitation with 30-fs pulses of absorbed fluences of F = 0.17 J/m² and 0.33 J/m². The spectra are compatible with the predictions for thermal emission (dashed blue lines) for T _em = 2760 K and 3180 K, respectively. (b) Light emission as a function of absorbed fluence F. The red circles display experimental values for the total radiant fluence for photons from 1.7 eV to 3.5 eV. The emission can be described phenomenologically by F ^2.5 (dashed blue line). The magenta squares correspond to the emission temperatures deduced from the experimental spectra, T _em. The solid green lines represent a full calculation using a two-temperature model.Reference Lui, Mak, Shan and Heinz⁶⁸ The predicted emission fluence was multiplied by a factor of ∼0.2 to match the scale of the experimental data. Reproduced with permission from Reference Reference Lui, Mak, Shan and Heinz68. ©2010, American Physical Society.

Hot carriers in graphene-based materials can be generated under intense pulsed laser irradiation, with their recombination resulting in luminescence emission. For example, two-photon luminescence emission (peaking at ∼590 nm) from GO nanoparticles (around 30 nm) with ultrafast laser excitation has been observed.Reference Li, Bao, Hou, Sun, Wang and Gu⁵⁹ The emission intensity was found to vary with the incident laser power on a logarithmic scale, and the slope from curve fitting was around 2, as expected (Figure 4).

Figure 4.

Characterization of graphene oxide nanoparticles (GONs). (a) Two-photon luminescence (TPL) spectrum of GONs (cut off at 660 nm by cascading filters), (b) base-10 logarithmic plot of TPL intensity as a function of laser power (P), giving a slope of approximately 2. Reproduced with permission from Reference Reference Li, Bao, Hou, Sun, Wang and Gu59. ©2012, Wiley-VCH.

Optical limiting

Optical-limiting materials, or optical limiters, exhibit linear transmittance at low incident light fluences but become opaque at high incident light fluences.Reference Sun and Riggs^37, Reference Tutt and Boggess^69–Reference Wang and Blau⁷¹ Widely pursued limiting mechanisms have included nonlinear absorption (multiphoton, reverse-saturable, or free-carrier absorption) and nonlinear scattering.Reference Sun and Riggs^37, Reference Tutt and Boggess^69–Reference Riggs, Walker, Carroll and Sun⁷² Various carbon nanomaterials have been developed as optical limiters using both mechanisms, with examples of fullerenes for nonlinear absorption and carbon black suspensions for nonlinear scattering.Reference Sun and Riggs^37, Reference Sun, Riggs and Liu^73–Reference Vincent, Petit and Chin⁷⁸ The recent exploration of graphene-based materials for optical limiting can also be categorized in terms of these mechanisms.Reference Lim, Chen, Clark, Goh, Ng, Tan, Friend, Ho and Chua^35, Reference Wang, Hernandez, Lotya, Coleman and Blau^39, Reference Wang and Blau^71, Reference Zhao, Cao, Zhou, Li and Zhao^79–Reference Zhang, Zhao, Liu, Shi, Zhou, Tian, Xu and Chen⁸⁶

Excellent broadband (450–1064 nm) optical-limiting properties were found for graphene sheets prepared from substoichiometric GOs (sub-GOs, obtained by partially oxidizing graphite using a modified Staudenmaier method).Reference Lim, Chen, Clark, Goh, Ng, Tan, Friend, Ho and Chua³⁵ When dispersed in heavy-atom solvents such as chlorobenzene or film matrixes, these graphene sheets exhibited optical-limiting thresholds down to 10 mJ/cm² at 70% linear transmittance for nanosecond laser pulses. These thresholds are well below the pulse fluences required for microbubble or microplasma formation. Unlike fully oxidized stoichiometric GOs, sub-GOs contain a significant fraction of sp ² carbon atoms known to be responsible for bandgap opening and related optical properties and, thus, for the observed nonlinear absorption.Reference Lim, Chen, Clark, Goh, Ng, Tan, Friend, Ho and Chua³⁵ Mechanistically, this optical limiting was apparently related to the environment surrounding the graphene sheets rather than being an intrinsic property of the absorbing domains in the sheets, according to a comparison between two film matrixes, namely, poly(methyl methacrylate) and polycarbonate. The formation of localized and highly absorbing triplet-like states due to solvent/matrix effects in sub-GOs was proposed.Reference Lim, Chen, Clark, Goh, Ng, Tan, Friend, Ho and Chua³⁵

Graphene dispersions in organic solvents that were populated by single- and few-layer sheets were prepared for studies of their optical-limiting properties.Reference Wang, Hernandez, Lotya, Coleman and Blau³⁹ Using open-aperture Z-scan measurements, which show the transmittance decrease arising from nonlinear loss when the focus of a probe laser is moved through a sample, broadband optical-limiting responses to nanosecond laser pulses at 532 nm and 1064 nm were observed. The limiting mechanism was primarily nonlinear scattering associated with the formation of solvent bubbles and microplasma in the graphene dispersions, so the performance was affected by the solvent surface tension, with lower surface tension corresponding to higher scattering intensity and a lower limiting threshold. The solvent surface tension effect was similar to that reported previously for the optical-limiting performance of dispersed carbon nanotubes.Reference Wang and Blau⁷¹ Another study also suggested that the solvent polarity could affect the optical-limiting performance of graphene materials, by modifying their bonds to solvent molecules.Reference Zhao, Cao, Zhou, Li and Zhao⁷⁹

Optical-limiting properties of various graphene nanostructures, including GO nanosheets (GONSs) and nanoribbons (GONRs) and graphene nanosheets (GNSs) and nanoribbons (GNRs), were investigated using an open-aperture Z-scan system with nanosecond laser pulses at 532 nm and 1064 nm.Reference Feng, Zhan and Chen⁸⁰ The optical-limiting performances of the GNSs, GONRs, and GNRs were exceptional, and chemical reduction of these nanostructures to enhance the integrated crystalline structure and electronic conjugation was found to improve their performances even further. The results were explained in terms of both two-photon absorption and nonlinear scattering in the graphene nanostructures.Reference Feng, Zhan and Chen⁸⁰

Graphene-based nanocomposites have also been explored for optical-limiting applications.Reference Feng, Zhan and Chen^80–Reference Zhang, Zhao, Liu, Shi, Zhou, Tian, Xu and Chen⁸⁶ For example, graphene–porphyrin composite materials were examined for their limiting responses toward nanosecond laser pulses at 532 nm, in comparison with those of porphyrin and of graphene.Reference Krishna, Kumar, Venkatramaiah, Venkatesan and Rao^81, Reference Krishna, Venkatramaiah, Venkatesan and Rao⁸² The improved performance in the nanocomposites was rationalized in terms of enhanced excited-state absorption and multiphoton absorption, as well as nonlinear scattering.Reference Krishna, Kumar, Venkatramaiah, Venkatesan and Rao^81, Reference Krishna, Venkatramaiah, Venkatesan and Rao⁸² In a pair of similar studies,Reference Xu, Liu, Zhang, Wang, Tian, Huang, Ma, Zhang and Chen^83, Reference Liu, Xu, Zhang, Zhang, Chen and Tian⁸⁴ optical-limiting properties of graphene–porphyrin and graphene–fullerene nanohybrids were probed using the open-aperture Z-scan technique. The results showed that both nanohybrids performed better than porphyrin, fullerene, or GOs alone, with the graphene–fullerene nanohybrid exhibiting the best performance (Figure 5).Reference Liu, Xu, Zhang, Zhang, Chen and Tian⁸⁴ The proposed optical-limiting mechanism in the nanohybrids was a combination of photoinduced electron and/or energy transfer, reverse saturable absorption, two-photon absorption, and strong nonlinear scattering (the fast growth of hot carbon vapor bubbles due to incandescence and sublimation of graphitic particles) (Figure 5).Reference Liu, Xu, Zhang, Zhang, Chen and Tian⁸⁴

Figure 5.

(a–b) Open-aperture Z-scan curves showing the transmittance decrease arising from nonlinear loss as the focus of a probe laser (532 nm, 5-ns pulses) is moved through the sample for (a) graphene–poly[2-(3-thienyl)ethoxy-4-butylsulfonate] (TPP), TPP–NH₂, graphene oxide (GO), and a controlled blend sample of TPP–NH₂ with graphene oxide (1:1 w/w) and (b) graphene–C₆₀, pyrrolidine fullerene, graphene oxide, and a controlled blend sample of pyrrolidine fullerene with graphene oxide (1:1 w/w). (c–d) Images of strong nonlinear scattering of light when samples of (c) graphene–C₆₀ and (d) graphene–TPP were fixed on the focus (z = 0 mm). Reproduced with permission from Reference Reference Liu, Xu, Zhang, Zhang, Chen and Tian84. ©2009, American Chemical Society.

In another study, GNSs were decorated with CdS quantum dots, and the resulting nanocomposites were investigated for their optical-limiting properties.Reference Feng, Sun, Zhan and Chen⁸⁵ Limiting thresholds of ∼0.88 J/cm² at 532 nm and >6.4 J/cm² at 1064 nm were obtained. Similarly, it has been reported that, in GO–Fe₃O₄ nanocomposites, the two-photon coefficients and nonlinear refraction coefficients were enhanced by about a factor of three in comparison with those in pristine GOs.Reference Zhang, Zhao, Liu, Shi, Zhou, Tian, Xu and Chen⁸⁶ The observed optical-limiting threshold of 3.7 J/cm² at 87% linear transmittance was also better than those of pristine GOs and C₆₀at high input fluence, which was attributed to strong nonlinear scattering in combination with negative nonlinear refraction and two-photon absorption.

Other nonlinear optical properties

Beyond their use for optical limiting, nonlinear optical absorption and scattering in graphene-based materials have also been investigated with respect to other nonlinear optical phenomena, including nonlinear refraction, spatial self-phase modulation, four-wave mixing, and second-harmonic generation.Reference Liu, Zhao, Zhang, Yan, Wu, Chen and Tian^36, Reference Nalla, Polavarapu, Manga, Goh, Loh, Xu and Ji^87–Reference Glazov⁹² For example, GOs synthesized from graphite with a controlled degree and location of oxidation were found to have spatially heterogeneous nonlinear optical responses.Reference Liu, Zhao, Zhang, Yan, Wu, Chen and Tian³⁶ In Z-scan measurements, the increased pump power resulted in enhanced two-photon absorption of the sp ³ domains in the GOs. It was suggested that the nonlinear optical properties could be altered by changing the relative sp ² and sp ³ fractions in the GO sheets.Reference Liu, Zhao, Zhang, Yan, Wu, Chen and Tian³⁶ Composites of GOs with the sodium salt of poly[2-(3-thienyl)ethoxy-4-butylsulfonate] (TPP) were also studied for their nonlinear optical response to femtosecond laser pulses at 800 nm in Z-scan measurements.Reference Nalla, Polavarapu, Manga, Goh, Loh, Xu and Ji⁸⁷ The results suggested enhanced nonlinear absorption (20 cm³/GW²) and nonlinear refraction coefficients (0.05 cm²/GW) in the GO–TPP composite films. Negative nonlinear refraction due to the self-defocusing effect was also observed. These nonlinear optical enhancements in the GO–TPP films were attributed to multiphoton absorption, excited-state absorption, and charge transfer.Reference Nalla, Polavarapu, Manga, Goh, Loh, Xu and Ji⁸⁷

Spatial self-phase modulation (SSPM) was observed in a dispersion of exfoliated graphene sheets in organic solvents using various laser sources (ultraviolet, visible, and near-infrared).Reference Wu, Zhang, Yan, Bian, Wang, Bai, Lu, Zhao and Wang⁸⁸ The apparently coherent light-scattering phenomenon was attributed to the large broadband and ultrafast third-order nonlinearity (χ⁽³⁾) originating from the Dirac-cone band structure in graphene sheets.

Four-wave mixing measurements were performed to study the coherent nonlinear response of single- and few-layer graphene flakes.Reference Hendry, Hale, Moger, Savchenko and Mikhailov⁸⁹ An exceptionally large third-order optical susceptibility (|χ⁽³⁾| ≈ 10^–7 esu) was observed in the near-infrared region, which might be due to interband electron transitions in the graphene sheets, as in SSPM. In a comparison of optical microscopy images of graphene flakes by reflection and four-wave mixing, the nonlinear optical contrast increased with the number of layers (up to six, Figure 6), which was explained in terms of constructive interference of the radiated fields from different graphene layers. Dark nonlinear images were also obtained for graphene flakes with many more layers (≫20), which can be ascribed to the reflection of the incident light and the reabsorption of the nonlinear signals in the thick graphene flakes.

Figure 6.

(a) Standard green-light (550-nm) reflection images of two graphene flakes. (b) Nonlinear optical images of the same flakes measured with pump wavelengths of 969 nm and 1179 nm. (c) Measured contrast in four-wave mixing images as a function of the number of graphene layers. Reproduced with permission from Reference Reference Hendry, Hale, Moger, Savchenko and Mikhailov89. ©2010, American Physical Society.

Finally, graphene-based materials have also been explored both theoretically and experimentally for second-harmonic generation (SHG).Reference Dean and van Driel^90–Reference Glazov⁹² For example, SHG signals (400-nm light) were observed from exfoliated graphene and multilayer graphite films on an oxidized silicon surface when an incident pump pulse laser (800 nm, 150 fs) was applied.Reference Dean and van Driel⁹⁰