OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 6 — Mar. 25, 2013
  • pp: 7511–7520
« Show journal navigation

Transient thermal effect, nonlinear refraction and nonlinear absorption properties of graphene oxide sheets in dispersion

Xiao-Liang Zhang, Zhi-Bo Liu, Xiao-Chun Li, Qiang Ma, Xu-Dong Chen, Jian-Guo Tian, Yan-Fei Xu, and Yong-Sheng Chen  »View Author Affiliations


Optics Express, Vol. 21, Issue 6, pp. 7511-7520 (2013)
http://dx.doi.org/10.1364/OE.21.007511


View Full Text Article

Acrobat PDF (1082 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The nonlinear refraction (NLR) properties of graphene oxide (GO) in N, N-Dimethylformamide (DMF) was studied in nanosecond, picosecond and femtosecond time regimes by Z-scan technique. Results show that the dispersion of GO in DMF exhibits negative NLR properties in nanosecond time regime, which is mainly attributed to transient thermal effect in the dispersion. The dispersion also exhibits negative NLR in picosecond and femtosecond time regimes, which are arising from sp2- hybridized carbon domains and sp3- hybridized matrix in GO sheets. To illustrate the relations between NLR and nonlinear absorption (NLA), NLA properties of the dispersion were also studied in nanosecond, picosecond and femtosecond time regimes.

© 2013 OSA

1. Introduction

Graphene, a new two-dimensional carbon nanomaterial with sp2-hybridized carbon atoms, has received tremendous interest in recent years owing to its various remarkable properties and potential applications in electronics and photonics [1

1. A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007). [CrossRef] [PubMed]

3

3. C. N. R. Rao, A. K. Sood, K. S. Subrahmanyam, and A. Govindaraj, “Graphene: the new two-dimensional nanomaterial,” Angew. Chem. Int. Ed. Engl. 48(42), 7752–7777 (2009). [CrossRef] [PubMed]

]. Graphene oxide (GO) can be synthesized by the oxidation of graphite, the presence of oxygen-containing groups in GO sheet makes it strongly hydrophilic and water soluble. GO sheets contain a mixture of electronically conducting sp2-hybridized carbon domains and insulating sp3-hybridized carbon matrix, with the heterogeneous atomic and electronic structure. Since materials with large π-conjugated structures usually show strong nonlinear optical properties, graphene has exhibited saturable absorption (SA) due to the large sp2-hybridized carbon π-conjugated and zero energy gap structure [4

4. Q. L. Bao, H. Zhang, Y. Wang, Z. H. Ni, Y. L. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19(19), 3077–3083 (2009). [CrossRef]

6

6. H. Z. Yang, X. B. Feng, Q. Wang, H. Huang, W. Chen, A. T. S. Wee, and W. Ji, “Giant two-photon absorption in bilayer graphene,” Nano Lett. 11(7), 2622–2627 (2011). [CrossRef] [PubMed]

], while GO has showed SA at low intensity, and photoinduced absorption (PA) including two photon absorption (TPA) at high intensity due to the coexistence of sp2 carbon domains and sp3 matrix in GO [7

7. Z. B. Liu, Y. Wang, X. L. Zhang, Y. F. Xu, Y. S. Chen, and J. G. Tian, “Nonlinear optical properties of graphene oxide in nanosecond and picosecond regimes,” Appl. Phys. Lett. 94(2), 021902 (2009). [CrossRef]

9

9. X. F. Jiang, L. Polavarapu, S. T. Neo, T. Venkatesan, and Q. H. Xu, “Graphene oxides as tunable broadband nonlinear optical materials for femtosecond laser pulses,” J. Phys. Chem. Lett. 3(6), 785–790 (2012). [CrossRef]

]. Nonlinear scattering (NLS) was also observed in graphene and GO dispersions in nanosecond time regime due to the heating of carbon atoms [10

10. J. Wang, Y. Hernandez, M. Lotya, J. N. Coleman, and W. J. Blau, “Broadband nonlinear optical response of graphene dispersions,” Adv. Mater. 21(23), 2430–2435 (2009). [CrossRef]

12

12. X. L. Zhang, X. Zhao, Z. B. Liu, S. Shi, W. Y. Zhou, J. G. Tian, Y. F. Xu, and Y. S. Chen, “Nonlinear optical and optical limiting properties of graphene oxide–Fe3O4 hybrid material,” J. Opt. 13(7), 075202 (2011). [CrossRef]

]. The excellent nonlinear absorption (NLA) and NLS properties enable their potential applications in saturable absorbers, optical switching and optical limiter.

Besides NLA and NLS processes, nonlinear refraction (NLR) can also plays an important role in the applications of optical switching and optical limiter, and NLR of graphene has attracted great interest because of its large sp2-hybridized carbon π-conjugated structure. Recently, Wu et al reported the spatial self-phase modulation in graphene dispersions arising from the NLR of graphene [13

13. R. Wu, Y. L. Zhang, S. C. Yan, F. Bian, W. L. Wang, X. D. Bai, X. H. Lu, J. M. Zhao, and E. G. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11(12), 5159–5164 (2011). [CrossRef] [PubMed]

]. Bourlinos et al reported the significant third-order nonlinear optical and NLR response of graphene fluoride in aqueous dispersions [14

14. A. B. Bourlinos, A. Bakandritsos, N. Liaros, S. Couris, K. Safarova, M. Otyepka, and R. Zboril, “Water dispersible functionalized graphene fluoride with significant nonlinear optical response,” Chem. Phys. Lett. 543, 101–105 (2012). [CrossRef]

]. Zhang et al reported Z-scan measurements of the nonlinear refractive index of loosely stacked graphene, and the results showed that graphene possesses a giant nonlinear refractive index [15

15. H. Zhang, S. Virally, Q. L. Bao, L. K. Ping, S. Massar, N. Godbout, and P. Kockaert, “Z-scan measurement of the nonlinear refractive index of graphene,” Opt. Lett. 37(11), 1856–1858 (2012). [CrossRef] [PubMed]

]. However, the reports about NLR properties of GO with sp2 carbon domains and sp3 matrix and the relations between NLR and NLA of GO in the regime from nanosecond to femtosecond are few [16

16. V. Nalla, L. Polavarapu, K. K. Manga, B. M. Goh, K. P. Loh, Q. H. Xu, and W. Ji, “Transient photoconductivity and femtosecond nonlinear optical properties of a conjugated polymer-graphene oxide composite,” Nanotechnology 21(41), 415203 (2010). [CrossRef] [PubMed]

].

In this paper, the NLR properties of GO sheets in N, N-Dimethylformamide (DMF) were studied in nanosecond, picosecond and femtosecond regimes, Thick quartz cell and small beam waist radius at focus were used to induce and enhance the NLR signal for picosecond and nanosecond pulses. Results show that the dispersion of GO in DMF exhibits negative NLR properties, mainly arising from transient thermal effect in nanosecond regime. In picosecond and femtosecond regime, the dispersion exhibits negative NLR properties arising from sp2 carbon domains and sp3 matrix of GO. To illustrate the relations between NLR and NLA, we also studied the NLA properties of the dispersion, results show that the transition from SA behaviors to reverse saturable absorption (RSA) of GO dispersion (also GO sheets) occurred as the energy (intensity) of input pulse increases, while the dispersion keeps the negative NLR behaviors in nanosecond, picosecond and femtosecond time regimes.

2. Experiments

GO was prepared by the modified Hummers method [17

17. W. S. Hummers Jr and R. E. Offeman, “Preparation of graphitic oxide,” J. Am. Chem. Soc. 80(6), 1339–1339 (1958). [CrossRef]

, 18

18. H. A. Becerril, J. Mao, Z. F. Liu, R. M. Stoltenberg, Z. N. Bao, and Y. S. Chen, “Evaluation of solution-processed reduced graphene oxide films as transparent conductors,” ACS Nano 2(3), 463–470 (2008). [CrossRef] [PubMed]

] and was dispersed in DMF, the presence of oxygen-containing groups in GO makes it dispersed in DMF very well. Nonlinear optical (NLO) properties of GO were measured by using Z-scan technique [19

19. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990). [CrossRef]

]. In Z-scan measurements, a Q-switched Nd:YAG laser (Continuum Surelite-II), a mode-locked Nd:YAG laser (Continuum model PY61) and a mode-locked Ti: sapphire laser (Spitfire pro, Spectra Physics) laser were used to generate 4.8~10.7 ns (FWHM) nanosecond pulses at 532 nm, 35 ps (FWHM) pulses at 532 nm and 120 fs (FWHM) pulses at 800 nm, respectively. The repetition rates of nanosecond and picosecond pulses are 10 Hz, and that of femtosecond pulses is 1 kHz. For nanosecond pulses Z-scan experiments, laser beam was focused by a 15-cm and 25-cm focal length lens and the beam waist radius ω0 at focus were 12 µm and 22 µm, respectively. For picosecond pulses Z-scan experiments, the beam waist radius is 16 µm. For femtosecond pulses Z-scan experiments, the beam waist radius is 31µm. The sample was filled in a 5-mm thick quartz cell for nanosecond and picosecond Z-scan experiments, while the sample was filled in a 2-mm thick quartz cell for femtosecond pulses experiments. The concentration of GO used in nanosecond and picosecond pulses Z-scan experiments is 0.5 mg/mL corresponding to a linear absorption coefficient α0 of 4.41 cm−1 at 532 nm, the concentration is 1 mg/mL corresponding to a linear absorption coefficient α0 of 2.95 cm−1 at 800 nm for femtosecond pulses experiments. The NLA properties of the samples was performed by open-aperture Z-scan experiments, all NLR Z-scan curves of the samples were obtained from closed-aperture Z-scan curves divided by corresponding open-aperture Z-scan curves.

It should be pointed out that the NLR signals of GO sheets dispersion filled in thin quartz cell were too weak and the signal to noise is quite low for nanosecond and picosecond pulses, even with the maximum concentration of GO of 1 mg/mL, so we have to use thick quartz cell with long pathlength to enhance NLR response [20

20. J. Wang and W. J. Blau, “Nonlinear optical and optical limiting properties of individual single-walled carbon nanotubes,” Appl. Phys. B 91(3–4), 521–524 (2008). [CrossRef]

], use small beam waist radius at focus to increase the input pulse intensity, and then a 5-mm thick quartz cell and a moderate concentration of GO of 0.5 mg/mL were selected. For femtosecond pulses, nonlinear scattering and damage of sample can take place easily for sample in thick quartz cell due to the long pathlength and high pulse intensity [21

21. X. Q. Yan, Z. B. Liu, Y. S. Chen, and J. G. Tian, “Polarization characteristics of nonlinear refraction and nonlinear scattering in several solvents,” J. Opt. Soc. Am. B 29(10), 2721–2728 (2012). [CrossRef]

23

23. L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowicz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89(18), 186601 (2002). [CrossRef] [PubMed]

]. To enhance the NLR response and avoid the nonlinear scattering and damage of sample, a moderate quartz cell of 2 mm-thick and the maximum concentration of GO of 1 mg/mL were selected. All the pulse intensity was controlled to be lower than the nonlinear scattering and damage threshold in the three regimes. Although the linear absorption coefficient α0 of the dispersion is 4.41cm−1 for nanosecond and picosecond pulses experiments at 532 nm, while α0 is 2.95 cm−1 for femtosecond pulse experiments at 800 nm, the differences in cell thickness, the concentration of GO and the value of α0 in the three regimes experiments did not cause confusions for our analysis of the nonlinear optical properties and nonlinear optical mechanisms of GO sheets.

3. Results and discussion

Figure 1
Fig. 1 Absorption spectra of GO in DMF. Inset shows the structure of GO.
gives the UV-visible absorption spectrum of GO in DMF and the absorption of DMF has been subtracted. Unlike common semiconductor with an optical absorption edge, the GO sheets show a maximum absorption at around 265 nm, and tailing to 1000 nm. The broadband absorption shown in Fig. 1 and the reported broadband fluorescence suggest a dispersion of energy gaps of GO [24

24. G. Eda, Y. Y. Lin, C. Mattevi, H. Yamaguchi, H. A. Chen, I. S. Chen, C. W. Chen, and M. Chhowalla, “Blue photoluminescence from chemically derived graphene oxide,” Adv. Mater. 22(4), 505–509 (2010). [CrossRef] [PubMed]

, 25

25. X. Zhao, Z. B. Liu, W. B. Yan, Y. P. Wu, X. L. Zhang, Y. S. Chen, and J. G. Tian, “Ultrafast carrier dynamics and saturable absorption of solution-processable few-layered graphene oxide,” Appl. Phys. Lett. 98(12), 121905 (2011). [CrossRef]

]. Since sp2 carbon domains and sp3 matrix are mixed and coexist in GO sheet as shown in the inset of Fig. 1, so the absorption spectrum of GO sheets include the absorption of sp2 carbon domains and sp3 matrix.

Figures 2(a)
Fig. 2 Open-aperture Z-scan curves (a) and NLR Z-scan curves (b) of the dispersion of GO in DMF for different input pulse energy with the same pulsewidth τp of 4.8 ns. Open-aperture Z-scan curves (c) and NLR Z-scan curves (d) of the dispersion of GO in DMF for different τp with the same pulse energy of 5.75µJ (2.54 J/cm2). △Tp-v (e) and n2eff (f) of dispersions for different τp and input pulse energy; Solid lines are theoretical fits. ω0 = 12µm for (a)- (f).
-2(d) show the open-aperture Z-scan curves and NLR Z-scan curves of GO dispersion with nanosecond pulses. As shown in Fig. 2(a), GO dispersion shows SA at lower input pulse energy (intensity), with larger pulse energy, RSA behavior occurred near focus and became dominant as pulse energy increases. Meanwhile, the NLR Z-scan curves of the dispersions are characterized by a prefocal peak followed by a valley as shown in Fig. 2(b), which indicates the negative NLR or self defocusing properties for different input pulse energy.

From Figs. 2(b) and 2(e) we can also see that the difference between normalized transmittance peak and valley (ΔTPV=TPeakTValley) increases as the pulse energy increases. For example, the value of ΔTPVincreases from 0.22 to 0.58 as pulse energy increases from 1.90 µJ (corresponds the input fluence at focus of F0 = 0.84 J/cm2) to 8.15 µJ (F0 = 3.60 J/cm2) under the same pulsewidth τp of 4.8 ns. As shown in Figs. 2(c) and 2(d) the RSA behavior of the dispersion keeps unchanged as τp increases with the same input pulse energy (or F0) at focus. However, the NLR was enhanced for longer pulsewidth. For example, the value of ΔTPV increases from 0.44 to 1.10 as τp increases from 4.8 to 10.7 ns with the same pulse energy of 5.75 µJ (F0 = 2.54 J/cm2).

Different mechanisms exist for NLR, such as electronic polarization, molecular reorientation effects, population redistribution (or excited states refraction), free carrier refraction, and thermal effect [26

26. R. L. Sutherland, Handbook of Nonlinear Optics, 2nd ed. (Dekker, 2003).

]. In the case of nanosecond pulses, considering the strong linear absorption of the pulse energy for the dispersion, the thermal effect should be generally taken into account for the measurements of NLR. The thermal effect arises from acoustic wave propagation caused by medium density change after local heating, and its buildup time τac is determined by the time required for a sound wave to propagate across beam size and τac = ω0/υs, where ω0 is the beam waist radius and υs is the velocity of sound in the medium. Velocity of sound in DMF is υs = 1439 m/s [27

27. J. Y. Yang, Y. L. Song, J. H. Gu, and H. G. Zheng, “determinations of the transient thermal lensing effect in metal cluster Polymer {WS4Cu4I2(bpe)3}n solution by the use of the Z-scan,” Opt. Commun. 282(1), 122–125 (2009). [CrossRef]

]. For ω0 = 12µm, the buildup time of the thermally induced optical nonlinearities τac is about 8.3 ns. Since τac is comparable to τp and the factor τp/τac is smaller than 1.6, so thermally induced optical nonlinearities is in the transient regime, and acoustic and electromagnetic wave equations must be solved simultaneously in the transient regime while the nonlinear process is simulated numerically [28

28. D. I. Kovsh, D. J. Hagan, and E. W. Van Stryland, “Numerical modeling of thermal refraction inliquids in the transient regime,” Opt. Express 4(8), 315–327 (1999). [CrossRef] [PubMed]

].

To evaluate the NLR coefficient, we fit the experimental data only by solving the propagation equation of electric field envelope E as Ref. 29

29. D. I. Kovsh, S. Yang, D. J. Hagan, and E. W. Van Stryland, “Nonlinear optical beam propagation for optical Limiting,” Appl. Opt. 38(24), 5168–5180 (1999). [CrossRef] [PubMed]

, The NLA coefficient and change of refraction index were written as α(I)=α0/(1+I/IS)0.5+βeffI and Δn(I)=n2effI, respectively [12

12. X. L. Zhang, X. Zhao, Z. B. Liu, S. Shi, W. Y. Zhou, J. G. Tian, Y. F. Xu, and Y. S. Chen, “Nonlinear optical and optical limiting properties of graphene oxide–Fe3O4 hybrid material,” J. Opt. 13(7), 075202 (2011). [CrossRef]

]. Where Iis the laser radiation intensity,IS is saturable intensity,βeff is the effective TPA coefficient. Here an effective NLR coefficient n2eff was used to simplify the multiple nonlinear refraction processes and n2eff values can be obtained by theoretical fitting. As shown in Fig. 2(f), we can see that n2eff is negative and the value of |n2eff| increases from 2.50×1013to1.70×1012cm2/W as τp increases from 4.8 to 10.7 ns with the same pulse energy of 5.75 µJ (F0 = 2.54 J/cm2). As the pulse energy increases, the value of |n2eff| decreases. For example, the |n2eff| value decreases from 3.52×1013 to 2.32×1013 cm2/W as input pulse energy from 1.90 µJ (F0 = 0.84 J/cm2) to 8.15 µJ (F0 = 3.60 J/cm2) with the same pulsewidth τp of 4.8 ns. Decreasing |n2eff| values with increasing input pulse energy indicates that the NLR responses are not arising from intrinsic third-order nonlinear optical response. This phenomenon was also studied in Ref. 30

30. M. Yüksek, T. Ceyhan, F. Bağcı, H. G. Yağlıoğlu, A. Elmali, and Ö. Bekaroğlu, “The nonlinear refraction and absorption dependence on the thermal effect for 4 ns pulse duration in binuclear Zn(II) phthalocyanine solution,” Opt. Commun. 281(14), 3897–3901 (2008). [CrossRef]

.

The NLR of nigrosine in DMF was also measured, we found that the NLR response and the value of |n2eff| for the dispersion of GO in DMF were comparable with that for the solution of nigrosine in DMF under the same condition. Since the NLR of nigrosine solution mainly originate from thermal effect [31

31. P. Brochard, V. G. Mazza, and R. Cabanel, “Thermal nonlinear refraction in dye solutions:a study of the transient regime,” J. Opt. Soc. Am. B 14(2), 405–414 (1997). [CrossRef]

] and no nonlinear optical signal for DMF was observed in our nanosecond experiments, so the strong pulsewidth influence on NLR indicates the thermal effect exists in the dispersion in nanosecond regime [32

32. Z. B. Liu, W. Y. Zhou, J. G. Tian, S. Q. Chen, W. P. Zang, F. Song, and C. P. Zhang, “characteristics of co-existence of third-order and transient thermally induced optical nonlinearities in nanosecond regime,” Opt. Commun. 245(1–6), 377–382 (2005). [CrossRef]

]. To further confirm the thermal origin of the NLR, we also measured the NLR of GO under the conditions of two different beam waist radius ω0 of 12 µm and 22 µm with the same input fluence F0 at focus. As shown in Figs. 3(a)
Fig. 3 NLR Z-scan curves of the dispersion of GO in DMF for two different beam waist radius ω0 for τp = 4.8 ns, F0 = 2.54 J/cm2. (b) τp = 10.7 ns, F0 = 1.22 J/cm2. Solid lines are theoretical fits.
and 3(b), when ω0 changes from 12 µm to 22 µm, τac increases from 8.3 to 15.3 ns. For τp = 10.7 ns, the value of |n2eff| decreases from 2.26×1012cm2/W (ΔTPV=0.76) to 8.80×1013 cm2/W (ΔTPV=0.54), with a decreased factor of 2.57 (the ratio of ΔTPVis 1.41), while for τp = 4.8 ns, the value decreases from 2.5 × 10−14 cm2/W (ΔTPV=0.42) to 1.3×1014 cm2/W (ΔTPV=0.4), with a decreased factor of 1.92 (1.05). So |n2eff| (or ΔTPV) decreases greatly for larger beam waist, which also indicates the existence of thermal effect [31

31. P. Brochard, V. G. Mazza, and R. Cabanel, “Thermal nonlinear refraction in dye solutions:a study of the transient regime,” J. Opt. Soc. Am. B 14(2), 405–414 (1997). [CrossRef]

].

SA of the dispersion is attributed to band filling effect of sp2 domains and RSA can be mainly arising from TPA of sp3 matrix of GO sheets [7

7. Z. B. Liu, Y. Wang, X. L. Zhang, Y. F. Xu, Y. S. Chen, and J. G. Tian, “Nonlinear optical properties of graphene oxide in nanosecond and picosecond regimes,” Appl. Phys. Lett. 94(2), 021902 (2009). [CrossRef]

, 8

8. Z. B. Liu, X. Zhao, X. L. Zhang, X. Q. Yan, Y. P. Wu, Y. S. Chen, and J. G. Tian, “Ultrafast dynamics and nonlinear optical responses from sp2-and sp3-hybridized domains in graphene oxide,” J. Phys. Chem. Lett. 2(16), 1972–1977 (2011). [CrossRef]

, 12

12. X. L. Zhang, X. Zhao, Z. B. Liu, S. Shi, W. Y. Zhou, J. G. Tian, Y. F. Xu, and Y. S. Chen, “Nonlinear optical and optical limiting properties of graphene oxide–Fe3O4 hybrid material,” J. Opt. 13(7), 075202 (2011). [CrossRef]

]. By fitting, ISwas obtained to be ~107 W/cm2, βeffto be 3~11.5×108 cm/W, as τp increases from 4.8 to 10.7 ns with the same pulse energy of 5.75 µJ (F0 = 2.54 J/cm2), while βeffis near a constant as pulse energy increases with the same τp.

Since GO exhibited SA arising from the sp2 domains, and RSA from the sp3 matrix in nanosecond, picosecond and femtosecond regime, respectively [7

7. Z. B. Liu, Y. Wang, X. L. Zhang, Y. F. Xu, Y. S. Chen, and J. G. Tian, “Nonlinear optical properties of graphene oxide in nanosecond and picosecond regimes,” Appl. Phys. Lett. 94(2), 021902 (2009). [CrossRef]

9

9. X. F. Jiang, L. Polavarapu, S. T. Neo, T. Venkatesan, and Q. H. Xu, “Graphene oxides as tunable broadband nonlinear optical materials for femtosecond laser pulses,” J. Phys. Chem. Lett. 3(6), 785–790 (2012). [CrossRef]

, 12

12. X. L. Zhang, X. Zhao, Z. B. Liu, S. Shi, W. Y. Zhou, J. G. Tian, Y. F. Xu, and Y. S. Chen, “Nonlinear optical and optical limiting properties of graphene oxide–Fe3O4 hybrid material,” J. Opt. 13(7), 075202 (2011). [CrossRef]

], NLR from π electrons and free carriers of sp2 carbon domains, bound electrons and free carriers of sp3 matrix may be involved, similar to the case in some semiconductors [33

33. A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, “Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B 9(3), 405–414 (1992). [CrossRef]

], so NLR response from GO sheets should not be excluded. However, it is difficult to observe the NLR of GO sheets in nanosecond regime due to strong thermal effect.

To measure the intrinsic NLR of GO sheets, shorter pulses (35 ps) were used. For ω0 = 16 µm, τac = 11.1ns, τp/τac = 0.003, thus thermal effect can be ignored for the 35 ps pulse. From Figs. 4(a)
Fig. 4 For 35 ps pulse at 532nm: (a) Open-aperture Z-scan curves of the dispersion of GO in DMF (GO + DMF). (c) NLR Z-scan curves of the dispersion of GO in DMF (GO + DMF) and DMF, solid icons stand for the dispersion (GO + DMF), hollow icons stand for the solvent of DMF. Solid lines are theoretical fits. (b) Effective TPA coefficient βeff of GO as a function of incident intensity. (d) Effective NLR coefficient n2eff of DMF, the dispersion and GO sheets as functions of incident intensity.
and 4(b) we can see that GO dispersion shows SA at lower intensity (9.0 GW/cm2), with further increasing in the intensity, RSA takes place near focus. Since no NLA response of DMF was observed during the open-aperture Z-scan experiments, the SA and RSA behavior should be arising from GO sheets in the dispersion. The fits were obtained by using IS=3.2GW/cm2 and βeff~3.7×1010cm/W.

For NLR experiments, the NLR properties of solvent DMF cannot be ignored due to the strong peak on-axis intensity I0 in the sample under picosecond pulse, so the refraction index change Δn (dispersion) for the dispersion can be expressed as Δn(dispersion)=Δn(GO)+Δn(DMF), where Δn (GO) is the refraction index change of GO sheets and Δn (DMF) is that of the solvent DMF. Results show that DMF has an intensity-independent positive NLR coefficient n2 of 1.8×1015 cm2/W, while GO dispersion (GO + DMF) show negative NLR behaviors arising from GO sheets. As shown in Figs. 4(c) and 4(d), we found that n2eff is negative and the value of |n2eff| of dispersion decreases from 3.5×1015 cm2/W to 1.4×1015 cm2/W, as the intensity increases from 9.0 GW/cm2 to 36.7 GW/cm2. The value of |n2eff| of GO sheets from calculation decreases from 5.3×1015 cm2/W to 3.2×1015cm2/W. Comparing the open-aperture Z-scan curves in Fig. 4(a) with NLR curves in Fig. 4(c), we note that GO dispersion (and then GO sheets) keeps the negative NLR behaviors though the SA behavior to RSA transition.

Figures 5(a)
Fig. 5 For 120 fs pulse at 800 nm: (a) Open-aperture Z-scan curves of the dispersion of GO in DMF (GO + DMF). (c) NLR Z-scan curves of the dispersion of GO in DMF (GO + DMF) and DMF, solid icons stand for the dispersion (GO + DMF), hollow icons stand for the solvent of DMF. Solid lines are theoretical fits. (b) Effective TPA coefficient βeff of GO as a function of incident intensity. (d) Effective NLR coefficient n2eff of DMF, the dispersion and GO sheets as functions of incident intensity.
and 5(c) show the open-aperture Z-scan and NLR curves of the dispersion of GO in DMF under femtosecond pulse laser at 800 nm with different intensity. The results are similar to the case of picosecond experiments although the laser wavelength and pulse width are different. GO dispersion exhibits SA at lower intensity (82.1 GW/cm2), with further increase in the intensity, RSA occurs near focus. IS=17.5 GW/cm2 and βeff was about 2.5×1011 cm/W from fitting, as shown in Fig. 5(b). In Fig. 5(d) the results of fits show that DMF has an intensity-independent positive NLR coefficient n2 of 6.3×1016cm2/W. There is a basic agreement with n2 of DMF in Ref. 21

21. X. Q. Yan, Z. B. Liu, Y. S. Chen, and J. G. Tian, “Polarization characteristics of nonlinear refraction and nonlinear scattering in several solvents,” J. Opt. Soc. Am. B 29(10), 2721–2728 (2012). [CrossRef]

taking into account the NLR of the quartz cell. We also can see that GO dispersion (GO + DMF) keeps the negative NLR behaviors and the value of |n2eff| decreases from 5.3×1016 cm2/W to 4.3×1016 cm2/W, the calculated value of n2eff of GO sheets nearly keeps a constant of 1.1×1015cm2/W, as intensity increases from 82.1 GW/cm2 to 224 GW/cm2. We also should note that GO dispersion (and then GO sheets) keeps the negative NLR behaviors though the SA behavior to RSA transition, similar to the case in picosecond time regime.

In femtosecond time regime, electronic polarization, population redistribution (or excited states refraction), free carrier refraction would contribute to the NLR of GO sheets. However, there may be additional molecular reorientation contribution in picosecond and nanosecond time regime. For GO sheets, since the negative NLR were accompanied by SA and RSA in picosecond and femtosecond time regime, the mechanism of NLR from GO sheets can be explained by the schematic drawing shown in Fig. 6
Fig. 6 A schematic drawing of NLA and NLR arising from sp2 domains and sp3 matrix of GO sheets.
. As shown in Fig. 6, the sp2 domain with a diameter of ~3 nm, has an narrow energy gaps of ~0.5eV [24

24. G. Eda, Y. Y. Lin, C. Mattevi, H. Yamaguchi, H. A. Chen, I. S. Chen, C. W. Chen, and M. Chhowalla, “Blue photoluminescence from chemically derived graphene oxide,” Adv. Mater. 22(4), 505–509 (2010). [CrossRef] [PubMed]

,34

34. G. Eda and M. Chhowalla, “Chemically derived graphene oxide: towards large-area thin-film electronics and optoelectronics,” Adv. Mater. 22(22), 2392–2415 (2010). [CrossRef] [PubMed]

36

36. C. Mattevi, G. Eda, S. Agnoli, S. Miller, K. A. Mkhoyan, O. Celik, D. Mostrogiovanni, G. Granozzi, E. Garfunkel, and M. Chhowalla, “Evolution of electrical, chemical, and structural properties of transparent and conducting chemically derived graphene thin films,” Adv. Funct. Mater. 19(16), 2577–2583 (2009). [CrossRef]

], the optical absorption of electrons in sp2 domains can be saturable easily and SA occur due to valence depletion and conduction band filling. Meanwhile, the π electrons and free carrier refraction in the conduction band of sp2 domains may contribute to NLR properties.

For sp3 matrix, the energy gaps are large (typically 2.7~3.1 eV) [37

37. C. Mathioudakis, G. Kopidakis, P. C. Kelires, P. Patsalas, M. Gioti, and S. Logothetidis, “Electronic and optical properties of a-C from tight-binding molecular dynamics simulations,” Thin Solid Films 482(1–2), 151–155 (2005). [CrossRef]

], when the intensity of laser pulse increases, the bound electrons in the valence band in sp3 matrix will transit to conduction band and become free carriers through TPA mechanism for 532nm or 800 nm pulse laser. Since the relaxation time of free carriers are in the order of hundreds of femtosecond, and a few picoseconds to scores of picoseconds [8

8. Z. B. Liu, X. Zhao, X. L. Zhang, X. Q. Yan, Y. P. Wu, Y. S. Chen, and J. G. Tian, “Ultrafast dynamics and nonlinear optical responses from sp2-and sp3-hybridized domains in graphene oxide,” J. Phys. Chem. Lett. 2(16), 1972–1977 (2011). [CrossRef]

], the bound electron NLR in the valence band and free carrier refraction in the conduction band of sp3 matrix will also contribute to the NLR response of GO sheets. In GO sheets, sp2 domains and sp3 matrix are coexistence, so SA, TPA and possible free carrier absorption (FCA) are coexistence in a GO sheet. In femtosecond time regime, the NLR from π electrons, bound electrons in the valence band and free carriers in the conduction band will contribute to the NLR of the whole GO sheets. What’ more, in the time regime of picosecond or longer, molecular reorientation effects of GO sheets may be also involved. While in nanosecond time regime, the contribution of these processes can be neglected because of the dominant transient thermal effect.

It should be pointed out that there are many differences in NLR mechanisms between the graphene layer on a substrate, graphene sheets in solution dispersions and GO sheets in dispersions. For single layer or few-layer graphene on a substrate, the NLR from π electrons is dominant and NLR are not affected by cumulative thermal effect due to the very high thermal diffusion coefficient of graphene [15

15. H. Zhang, S. Virally, Q. L. Bao, L. K. Ping, S. Massar, N. Godbout, and P. Kockaert, “Z-scan measurement of the nonlinear refractive index of graphene,” Opt. Lett. 37(11), 1856–1858 (2012). [CrossRef] [PubMed]

]. For graphene sheets in solution dispersions, both π electrons and the reorientation and alignment of the graphene sheets can contribute to the NLR [13

13. R. Wu, Y. L. Zhang, S. C. Yan, F. Bian, W. L. Wang, X. D. Bai, X. H. Lu, J. M. Zhao, and E. G. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11(12), 5159–5164 (2011). [CrossRef] [PubMed]

, 14

14. A. B. Bourlinos, A. Bakandritsos, N. Liaros, S. Couris, K. Safarova, M. Otyepka, and R. Zboril, “Water dispersible functionalized graphene fluoride with significant nonlinear optical response,” Chem. Phys. Lett. 543, 101–105 (2012). [CrossRef]

], thermal effect from solution dispersions can also contribute to NLR under continuous wave or long pulse laser. For GO sheets in dispersions, free carriers, π electrons and bound electrons of sp2 domains and sp3 matrix can contribute to the NLR. Reorientation effects of the GO sheets and thermal effect should be considered according to the duration of pulse.

Moreover, unlike the case of single layer or few-layer graphene on a substrate, the NLR response and n2eff value of graphene sheet or GO sheets dispersions is the sum of NLR signals from a large amount of sheets interacting with laser pulse. The NLR response or n2eff value of single graphene sheet or GO sheet cannot be obtained accurately, only can be obtained by roughly qualitative estimation [13

13. R. Wu, Y. L. Zhang, S. C. Yan, F. Bian, W. L. Wang, X. D. Bai, X. H. Lu, J. M. Zhao, and E. G. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11(12), 5159–5164 (2011). [CrossRef] [PubMed]

], because the sheets are dispersed and the sheets sizes are not uniform. So the values of n2eff (or n2) in the three cases, cannot be compared directly, because the duration of laser pulse and wavelength, the samples and the mechanisms contributing to NLR are different.

4. Conclusions

Acknowledgments

The authors thank Xiao-Qing Yan of Nankai University for the helpful discussion. This work was supported by the Program for New Century Excellent Talents in University (NCET-09-0484), Youth Foundation of Taiyuan University of Technology (No. 2012L085), and the Scientific Research Starting Foundation from Taiyuan University of Technology.

References and links

1.

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007). [CrossRef] [PubMed]

2.

D. Li and R. B. Kaner, “Materials science. graphene-based materials,” Science 320(5880), 1170–1171 (2008). [CrossRef] [PubMed]

3.

C. N. R. Rao, A. K. Sood, K. S. Subrahmanyam, and A. Govindaraj, “Graphene: the new two-dimensional nanomaterial,” Angew. Chem. Int. Ed. Engl. 48(42), 7752–7777 (2009). [CrossRef] [PubMed]

4.

Q. L. Bao, H. Zhang, Y. Wang, Z. H. Ni, Y. L. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19(19), 3077–3083 (2009). [CrossRef]

5.

G. C. Xing, H. C. Guo, X. H. Zhang, T. C. Sum, and C. H. A. Huan, “The Physics of ultrafast saturable absorption in graphene,” Opt. Express 18(5), 4564–4573 (2010). [CrossRef] [PubMed]

6.

H. Z. Yang, X. B. Feng, Q. Wang, H. Huang, W. Chen, A. T. S. Wee, and W. Ji, “Giant two-photon absorption in bilayer graphene,” Nano Lett. 11(7), 2622–2627 (2011). [CrossRef] [PubMed]

7.

Z. B. Liu, Y. Wang, X. L. Zhang, Y. F. Xu, Y. S. Chen, and J. G. Tian, “Nonlinear optical properties of graphene oxide in nanosecond and picosecond regimes,” Appl. Phys. Lett. 94(2), 021902 (2009). [CrossRef]

8.

Z. B. Liu, X. Zhao, X. L. Zhang, X. Q. Yan, Y. P. Wu, Y. S. Chen, and J. G. Tian, “Ultrafast dynamics and nonlinear optical responses from sp2-and sp3-hybridized domains in graphene oxide,” J. Phys. Chem. Lett. 2(16), 1972–1977 (2011). [CrossRef]

9.

X. F. Jiang, L. Polavarapu, S. T. Neo, T. Venkatesan, and Q. H. Xu, “Graphene oxides as tunable broadband nonlinear optical materials for femtosecond laser pulses,” J. Phys. Chem. Lett. 3(6), 785–790 (2012). [CrossRef]

10.

J. Wang, Y. Hernandez, M. Lotya, J. N. Coleman, and W. J. Blau, “Broadband nonlinear optical response of graphene dispersions,” Adv. Mater. 21(23), 2430–2435 (2009). [CrossRef]

11.

M. Feng, H. B. Zhan, and Y. Chen, “Nonlinear optical and optical limiting properties of graphene families,” Appl. Phys. Lett. 96(3), 033107 (2010). [CrossRef]

12.

X. L. Zhang, X. Zhao, Z. B. Liu, S. Shi, W. Y. Zhou, J. G. Tian, Y. F. Xu, and Y. S. Chen, “Nonlinear optical and optical limiting properties of graphene oxide–Fe3O4 hybrid material,” J. Opt. 13(7), 075202 (2011). [CrossRef]

13.

R. Wu, Y. L. Zhang, S. C. Yan, F. Bian, W. L. Wang, X. D. Bai, X. H. Lu, J. M. Zhao, and E. G. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11(12), 5159–5164 (2011). [CrossRef] [PubMed]

14.

A. B. Bourlinos, A. Bakandritsos, N. Liaros, S. Couris, K. Safarova, M. Otyepka, and R. Zboril, “Water dispersible functionalized graphene fluoride with significant nonlinear optical response,” Chem. Phys. Lett. 543, 101–105 (2012). [CrossRef]

15.

H. Zhang, S. Virally, Q. L. Bao, L. K. Ping, S. Massar, N. Godbout, and P. Kockaert, “Z-scan measurement of the nonlinear refractive index of graphene,” Opt. Lett. 37(11), 1856–1858 (2012). [CrossRef] [PubMed]

16.

V. Nalla, L. Polavarapu, K. K. Manga, B. M. Goh, K. P. Loh, Q. H. Xu, and W. Ji, “Transient photoconductivity and femtosecond nonlinear optical properties of a conjugated polymer-graphene oxide composite,” Nanotechnology 21(41), 415203 (2010). [CrossRef] [PubMed]

17.

W. S. Hummers Jr and R. E. Offeman, “Preparation of graphitic oxide,” J. Am. Chem. Soc. 80(6), 1339–1339 (1958). [CrossRef]

18.

H. A. Becerril, J. Mao, Z. F. Liu, R. M. Stoltenberg, Z. N. Bao, and Y. S. Chen, “Evaluation of solution-processed reduced graphene oxide films as transparent conductors,” ACS Nano 2(3), 463–470 (2008). [CrossRef] [PubMed]

19.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990). [CrossRef]

20.

J. Wang and W. J. Blau, “Nonlinear optical and optical limiting properties of individual single-walled carbon nanotubes,” Appl. Phys. B 91(3–4), 521–524 (2008). [CrossRef]

21.

X. Q. Yan, Z. B. Liu, Y. S. Chen, and J. G. Tian, “Polarization characteristics of nonlinear refraction and nonlinear scattering in several solvents,” J. Opt. Soc. Am. B 29(10), 2721–2728 (2012). [CrossRef]

22.

G. L. Mao, Y. H. Wu, and K. D. Singer, “Third harmonic generation in self-focused filaments in liquids,” Opt. Express 15(8), 4857–4862 (2007). [CrossRef] [PubMed]

23.

L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowicz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89(18), 186601 (2002). [CrossRef] [PubMed]

24.

G. Eda, Y. Y. Lin, C. Mattevi, H. Yamaguchi, H. A. Chen, I. S. Chen, C. W. Chen, and M. Chhowalla, “Blue photoluminescence from chemically derived graphene oxide,” Adv. Mater. 22(4), 505–509 (2010). [CrossRef] [PubMed]

25.

X. Zhao, Z. B. Liu, W. B. Yan, Y. P. Wu, X. L. Zhang, Y. S. Chen, and J. G. Tian, “Ultrafast carrier dynamics and saturable absorption of solution-processable few-layered graphene oxide,” Appl. Phys. Lett. 98(12), 121905 (2011). [CrossRef]

26.

R. L. Sutherland, Handbook of Nonlinear Optics, 2nd ed. (Dekker, 2003).

27.

J. Y. Yang, Y. L. Song, J. H. Gu, and H. G. Zheng, “determinations of the transient thermal lensing effect in metal cluster Polymer {WS4Cu4I2(bpe)3}n solution by the use of the Z-scan,” Opt. Commun. 282(1), 122–125 (2009). [CrossRef]

28.

D. I. Kovsh, D. J. Hagan, and E. W. Van Stryland, “Numerical modeling of thermal refraction inliquids in the transient regime,” Opt. Express 4(8), 315–327 (1999). [CrossRef] [PubMed]

29.

D. I. Kovsh, S. Yang, D. J. Hagan, and E. W. Van Stryland, “Nonlinear optical beam propagation for optical Limiting,” Appl. Opt. 38(24), 5168–5180 (1999). [CrossRef] [PubMed]

30.

M. Yüksek, T. Ceyhan, F. Bağcı, H. G. Yağlıoğlu, A. Elmali, and Ö. Bekaroğlu, “The nonlinear refraction and absorption dependence on the thermal effect for 4 ns pulse duration in binuclear Zn(II) phthalocyanine solution,” Opt. Commun. 281(14), 3897–3901 (2008). [CrossRef]

31.

P. Brochard, V. G. Mazza, and R. Cabanel, “Thermal nonlinear refraction in dye solutions:a study of the transient regime,” J. Opt. Soc. Am. B 14(2), 405–414 (1997). [CrossRef]

32.

Z. B. Liu, W. Y. Zhou, J. G. Tian, S. Q. Chen, W. P. Zang, F. Song, and C. P. Zhang, “characteristics of co-existence of third-order and transient thermally induced optical nonlinearities in nanosecond regime,” Opt. Commun. 245(1–6), 377–382 (2005). [CrossRef]

33.

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, “Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B 9(3), 405–414 (1992). [CrossRef]

34.

G. Eda and M. Chhowalla, “Chemically derived graphene oxide: towards large-area thin-film electronics and optoelectronics,” Adv. Mater. 22(22), 2392–2415 (2010). [CrossRef] [PubMed]

35.

K. Erickson, R. Erni, Z. Lee, N. Alem, W. Gannett, and A. Zettl, “Determination of the local chemical structure of graphene oxide and reduced graphene oxide,” Adv. Mater. 22(40), 4467–4472 (2010). [CrossRef] [PubMed]

36.

C. Mattevi, G. Eda, S. Agnoli, S. Miller, K. A. Mkhoyan, O. Celik, D. Mostrogiovanni, G. Granozzi, E. Garfunkel, and M. Chhowalla, “Evolution of electrical, chemical, and structural properties of transparent and conducting chemically derived graphene thin films,” Adv. Funct. Mater. 19(16), 2577–2583 (2009). [CrossRef]

37.

C. Mathioudakis, G. Kopidakis, P. C. Kelires, P. Patsalas, M. Gioti, and S. Logothetidis, “Electronic and optical properties of a-C from tight-binding molecular dynamics simulations,” Thin Solid Films 482(1–2), 151–155 (2005). [CrossRef]

OCIS Codes
(190.0190) Nonlinear optics : Nonlinear optics
(190.4710) Nonlinear optics : Optical nonlinearities in organic materials
(190.7110) Nonlinear optics : Ultrafast nonlinear optics

ToC Category:
Nonlinear Optics

History
Original Manuscript: December 20, 2012
Revised Manuscript: February 22, 2013
Manuscript Accepted: February 28, 2013
Published: March 19, 2013

Citation
Xiao-Liang Zhang, Zhi-Bo Liu, Xiao-Chun Li, Qiang Ma, Xu-Dong Chen, Jian-Guo Tian, Yan-Fei Xu, and Yong-Sheng Chen, "Transient thermal effect, nonlinear refraction and nonlinear absorption properties of graphene oxide sheets in dispersion," Opt. Express 21, 7511-7520 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-6-7511


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater.6(3), 183–191 (2007). [CrossRef] [PubMed]
  2. D. Li and R. B. Kaner, “Materials science. graphene-based materials,” Science320(5880), 1170–1171 (2008). [CrossRef] [PubMed]
  3. C. N. R. Rao, A. K. Sood, K. S. Subrahmanyam, and A. Govindaraj, “Graphene: the new two-dimensional nanomaterial,” Angew. Chem. Int. Ed. Engl.48(42), 7752–7777 (2009). [CrossRef] [PubMed]
  4. Q. L. Bao, H. Zhang, Y. Wang, Z. H. Ni, Y. L. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater.19(19), 3077–3083 (2009). [CrossRef]
  5. G. C. Xing, H. C. Guo, X. H. Zhang, T. C. Sum, and C. H. A. Huan, “The Physics of ultrafast saturable absorption in graphene,” Opt. Express18(5), 4564–4573 (2010). [CrossRef] [PubMed]
  6. H. Z. Yang, X. B. Feng, Q. Wang, H. Huang, W. Chen, A. T. S. Wee, and W. Ji, “Giant two-photon absorption in bilayer graphene,” Nano Lett.11(7), 2622–2627 (2011). [CrossRef] [PubMed]
  7. Z. B. Liu, Y. Wang, X. L. Zhang, Y. F. Xu, Y. S. Chen, and J. G. Tian, “Nonlinear optical properties of graphene oxide in nanosecond and picosecond regimes,” Appl. Phys. Lett.94(2), 021902 (2009). [CrossRef]
  8. Z. B. Liu, X. Zhao, X. L. Zhang, X. Q. Yan, Y. P. Wu, Y. S. Chen, and J. G. Tian, “Ultrafast dynamics and nonlinear optical responses from sp2-and sp3-hybridized domains in graphene oxide,” J. Phys. Chem. Lett.2(16), 1972–1977 (2011). [CrossRef]
  9. X. F. Jiang, L. Polavarapu, S. T. Neo, T. Venkatesan, and Q. H. Xu, “Graphene oxides as tunable broadband nonlinear optical materials for femtosecond laser pulses,” J. Phys. Chem. Lett.3(6), 785–790 (2012). [CrossRef]
  10. J. Wang, Y. Hernandez, M. Lotya, J. N. Coleman, and W. J. Blau, “Broadband nonlinear optical response of graphene dispersions,” Adv. Mater.21(23), 2430–2435 (2009). [CrossRef]
  11. M. Feng, H. B. Zhan, and Y. Chen, “Nonlinear optical and optical limiting properties of graphene families,” Appl. Phys. Lett.96(3), 033107 (2010). [CrossRef]
  12. X. L. Zhang, X. Zhao, Z. B. Liu, S. Shi, W. Y. Zhou, J. G. Tian, Y. F. Xu, and Y. S. Chen, “Nonlinear optical and optical limiting properties of graphene oxide–Fe3O4 hybrid material,” J. Opt.13(7), 075202 (2011). [CrossRef]
  13. R. Wu, Y. L. Zhang, S. C. Yan, F. Bian, W. L. Wang, X. D. Bai, X. H. Lu, J. M. Zhao, and E. G. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett.11(12), 5159–5164 (2011). [CrossRef] [PubMed]
  14. A. B. Bourlinos, A. Bakandritsos, N. Liaros, S. Couris, K. Safarova, M. Otyepka, and R. Zboril, “Water dispersible functionalized graphene fluoride with significant nonlinear optical response,” Chem. Phys. Lett.543, 101–105 (2012). [CrossRef]
  15. H. Zhang, S. Virally, Q. L. Bao, L. K. Ping, S. Massar, N. Godbout, and P. Kockaert, “Z-scan measurement of the nonlinear refractive index of graphene,” Opt. Lett.37(11), 1856–1858 (2012). [CrossRef] [PubMed]
  16. V. Nalla, L. Polavarapu, K. K. Manga, B. M. Goh, K. P. Loh, Q. H. Xu, and W. Ji, “Transient photoconductivity and femtosecond nonlinear optical properties of a conjugated polymer-graphene oxide composite,” Nanotechnology21(41), 415203 (2010). [CrossRef] [PubMed]
  17. W. S. Hummers and R. E. Offeman, “Preparation of graphitic oxide,” J. Am. Chem. Soc.80(6), 1339–1339 (1958). [CrossRef]
  18. H. A. Becerril, J. Mao, Z. F. Liu, R. M. Stoltenberg, Z. N. Bao, and Y. S. Chen, “Evaluation of solution-processed reduced graphene oxide films as transparent conductors,” ACS Nano2(3), 463–470 (2008). [CrossRef] [PubMed]
  19. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron.26(4), 760–769 (1990). [CrossRef]
  20. J. Wang and W. J. Blau, “Nonlinear optical and optical limiting properties of individual single-walled carbon nanotubes,” Appl. Phys. B91(3–4), 521–524 (2008). [CrossRef]
  21. X. Q. Yan, Z. B. Liu, Y. S. Chen, and J. G. Tian, “Polarization characteristics of nonlinear refraction and nonlinear scattering in several solvents,” J. Opt. Soc. Am. B29(10), 2721–2728 (2012). [CrossRef]
  22. G. L. Mao, Y. H. Wu, and K. D. Singer, “Third harmonic generation in self-focused filaments in liquids,” Opt. Express15(8), 4857–4862 (2007). [CrossRef] [PubMed]
  23. L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowicz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett.89(18), 186601 (2002). [CrossRef] [PubMed]
  24. G. Eda, Y. Y. Lin, C. Mattevi, H. Yamaguchi, H. A. Chen, I. S. Chen, C. W. Chen, and M. Chhowalla, “Blue photoluminescence from chemically derived graphene oxide,” Adv. Mater.22(4), 505–509 (2010). [CrossRef] [PubMed]
  25. X. Zhao, Z. B. Liu, W. B. Yan, Y. P. Wu, X. L. Zhang, Y. S. Chen, and J. G. Tian, “Ultrafast carrier dynamics and saturable absorption of solution-processable few-layered graphene oxide,” Appl. Phys. Lett.98(12), 121905 (2011). [CrossRef]
  26. R. L. Sutherland, Handbook of Nonlinear Optics, 2nd ed. (Dekker, 2003).
  27. J. Y. Yang, Y. L. Song, J. H. Gu, and H. G. Zheng, “determinations of the transient thermal lensing effect in metal cluster Polymer {WS4Cu4I2(bpe)3}n solution by the use of the Z-scan,” Opt. Commun.282(1), 122–125 (2009). [CrossRef]
  28. D. I. Kovsh, D. J. Hagan, and E. W. Van Stryland, “Numerical modeling of thermal refraction inliquids in the transient regime,” Opt. Express4(8), 315–327 (1999). [CrossRef] [PubMed]
  29. D. I. Kovsh, S. Yang, D. J. Hagan, and E. W. Van Stryland, “Nonlinear optical beam propagation for optical Limiting,” Appl. Opt.38(24), 5168–5180 (1999). [CrossRef] [PubMed]
  30. M. Yüksek, T. Ceyhan, F. Bağcı, H. G. Yağlıoğlu, A. Elmali, and Ö. Bekaroğlu, “The nonlinear refraction and absorption dependence on the thermal effect for 4 ns pulse duration in binuclear Zn(II) phthalocyanine solution,” Opt. Commun.281(14), 3897–3901 (2008). [CrossRef]
  31. P. Brochard, V. G. Mazza, and R. Cabanel, “Thermal nonlinear refraction in dye solutions:a study of the transient regime,” J. Opt. Soc. Am. B14(2), 405–414 (1997). [CrossRef]
  32. Z. B. Liu, W. Y. Zhou, J. G. Tian, S. Q. Chen, W. P. Zang, F. Song, and C. P. Zhang, “characteristics of co-existence of third-order and transient thermally induced optical nonlinearities in nanosecond regime,” Opt. Commun.245(1–6), 377–382 (2005). [CrossRef]
  33. A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, “Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B9(3), 405–414 (1992). [CrossRef]
  34. G. Eda and M. Chhowalla, “Chemically derived graphene oxide: towards large-area thin-film electronics and optoelectronics,” Adv. Mater.22(22), 2392–2415 (2010). [CrossRef] [PubMed]
  35. K. Erickson, R. Erni, Z. Lee, N. Alem, W. Gannett, and A. Zettl, “Determination of the local chemical structure of graphene oxide and reduced graphene oxide,” Adv. Mater.22(40), 4467–4472 (2010). [CrossRef] [PubMed]
  36. C. Mattevi, G. Eda, S. Agnoli, S. Miller, K. A. Mkhoyan, O. Celik, D. Mostrogiovanni, G. Granozzi, E. Garfunkel, and M. Chhowalla, “Evolution of electrical, chemical, and structural properties of transparent and conducting chemically derived graphene thin films,” Adv. Funct. Mater.19(16), 2577–2583 (2009). [CrossRef]
  37. C. Mathioudakis, G. Kopidakis, P. C. Kelires, P. Patsalas, M. Gioti, and S. Logothetidis, “Electronic and optical properties of a-C from tight-binding molecular dynamics simulations,” Thin Solid Films482(1–2), 151–155 (2005). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited