Experimental observation of low threshold optical bistability in exfoliated graphene with low oxidation degree

Optical Materials 53 (2016) 80–86

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Experimental observation of low threshold optical bistability in exfoliated graphene with low oxidation degree Morteza A. Sharif a,b,⇑, M.H. Majles Ara c, Bijan Ghafary a, Somayeh Salmani c, Salman Mohajer c a

Photonics Lab, School of Physics, Iran University of Science & Technology, Narmak, Tehran, Iran Optics & Laser Engineering Group, Faculty of Electrical Engineering, Urmia University of Technology, Band Road, Urmia, Iran c Photonics Lab, Kharazmi University, Mofatteh Ave., Tehran, Iran b

a r t i c l e

i n f o

Article history: Received 2 December 2015 Accepted 8 January 2016

Keywords: Optical bistability Exfoliated graphene Nonlinear Schrödinger Equation Nonlinearity Chaos

a b s t r a c t We have experimentally investigated low threshold Optical Bistability (OB) and multi-stability in exfoliated graphene ink with low oxidation degree. Theoretical predictions of N-layer problem and the resonator feedback problem show good agreement with the experimental observation. In contrary to the other graphene oxide samples, we have indicated that the absorbance does not restrict OB process. We have concluded from the experimental results and Nonlinear Schrödinger Equation (NLSE) that the nonlinear dispersion – rather than absorption – is the main nonlinear mechanism of OB. In addition to the enhanced nonlinearity, exfoliated graphene with low oxidation degree possesses semiconductors group III–V equivalent band gap energy, high charge carrier mobility and thus, ultra-fast optical response which makes it a unique optical material for application in all optical switching, especially in THz frequency range. Ó 2016 Elsevier B.V. All rights reserved.

1. Introduction Since the last decade, graphene has been proposed as an outstanding nonlinear optical material due to its single layer atomic structure in hexagonal lattice which causes zero band gap energy, independent group velocity, high charge carrier mobility, tunable nonlinear optical conductivity and intense optical nonlinearity [1–9]. These particular aspects have led to the recent researches seeking for the applications in ultra-fast saturable absorption, biochemical sensing, beam splitting, optical power limiting and optical switching [2,9–23]. Primarily, Han Zhang et al. have reported the experimental z-scan measurement of nonlinear refractive index of loosely stacked few-layer graphene to be of order 10
11 m2/W [24]. As well, Rui Wu et al. have experimentally studied the spatial self-phase modulation in graphene dispersion for the visible laser beam; this might imply the huge third order nonlinearity [9]. Subsequently, N. Liaros et al. have experimentally shown that graphene oxide dispersion can exhibit optical power limiting in the visible frequency range. They have deduced that saturable absorption and reverse saturable absorption can be provided by few layer graphene [19,22]. Optical Bistability (OB) ⇑ Corresponding author at: Photonics Lab, School of Physics, Iran University of Science & Technology, Narmak, Tehran, Iran. E-mail addresses: [email protected], [email protected] (M.A. Sharif). http://dx.doi.org/10.1016/j.optmat.2016.01.017 0925-3467/Ó 2016 Elsevier B.V. All rights reserved.

as the feasible approach to all optical switching have been also investigated in graphene-silicon waveguide resonator and graphene-silicon photonic crystal cavity [16,25]. Most recently, OB has been reported in graphene nanobubbles [26]. On the other hand, theoretical investigation of optical nonlinearity in graphene invokes precise calculation of nonlinear conductivity by the means of Dirac cone representation which will give an estimation of optical nonlinear susceptibility [7,27–32]. S.A. Mikhailov has proved that the electromagnetic response of graphene in collisionless system is strongly nonlinear, especially for THz frequencies [32–35]. E. Hendry et al. have demonstrated an estimation of remarkable third order optical susceptibility in graphene flakes in the near infrared frequency range [36]. VI. A. Margulis et al. have then theoretically calculated the nonlinear refractive index of moderately doped graphene in the range from mid-infrared to ultraviolet; the results have declared the very high nonlinearity [29]. Today, the universal perception denotes the huge nonlinear response of graphene in THz frequency range resulting from the intraband conductivity in highly doped graphene, decreasing for the higher frequencies due to the interband transitions in lowly doped-undoped graphene. On this base, N.M.R. Peres et al. have investigated OB of monolayer, bilayer and ABA stacked trilayer graphene in THz range by solving Boltzman equation. However, the results have revealed that the attainable OB needs extra-large optical power [37]. Meanwhile, J.B. Khurgin has inferred in his paper that the huge values of nonlinear coefficient

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for interband transitions of graphene are due to the huge absorption coefficient and thus never lead up to the improvement in all optical switching. He has also deduced that all optical switching for intraband transitions requires 1000 doped graphene layers to be realized; but the act of doping will confront a breakdown [38]. In this paper, we show that the sufficient nonlinearity can be achieved in exfoliated graphene with low oxidation degree inside a resonator which will result in low threshold dispersive OB and multi-stability – rather than absorptive – at low optical input power. Performing the experimental results in the visible range, a coincidence will be unfolded as the paraphrase of tunable OB in dielectric/graphene/dielectric heterostructures in THz range proposed by Xiaoyu Dai et al. through their inspiration from the ‘‘nonlinearity enhancement via stacking several layers of graphene separated by a dielectric medium” implicated by N.M.R. Peres et al. in their paper [37,39]. To provide a theoretical justification, we admit E. Hendry’s estimation of graphene third order nonlinearity and the modification presented by J.L. Cheng et al. [36,40]. We start with N-layer problem in which the nonlinearity enhancement and the mechanism of OB are expressed by the nonlinear conductivity in N-separated graphene flakes dispersed in a dielectric medium; we proceed with a numerical solution of Nonlinear Schrödinger Equation (NLSE) in order to analyze the resonator effect of N-separated graphene layers and the nonlinear dispersion/nonlinear absorption contribution in OB and multi-stability process. Then, we result an agreement of the theoretical predictions with our experimental results. Finally we propose exfoliated graphene with low oxidation degree for all optical switching.

8 > I: > > > > > > > > > > > > > > > > > > > > > > II : > > > > > > > > > < > > > > > > > > > > > > III : > > > > > > > > > > > > > > > > > > > > :

A system composed of N sequential separated graphene layers, dispersed in a dielectric medium is assumed. The system is illuminated by a visible laser beam with TE polarization as the optical input signal. The graphene flakes are not necessarily normal to the incident beam – which are exaggeratedly illustrated in Fig. 1 by the symbol G; D denotes the dielectric medium containing graphene flakes. Also, we note that the graphene layers are not equally displaced; Having recognized three different zones labeled with I, II & III in Fig. 1, the output electric field can be obtained starting from Maxwell equations and introducing the related boundary conditions through the following Eq. (1); where EI;II;III and EI;II;III T i stands for the incident and transmitted electric fields in three zones I, II & III respectively [39].

Ι

ΙΙ,1

ΙΙ,2

ΙΙ,i

z

z

II dII

KI ¼ 2e
ikz 2



II dII

2 



z

EIT ¼ EII;1 i ; EII;i i

¼

II;iþ1 EII;i ; T ¼ Ei

1 II;i E 4 T


ikIIz 2d

He


ikIIz 2d

K ¼ 2e II

i ¼ 1; 2; . . . ; N þ 1

II

II



 2  



HII ¼ 4e
ikz 2
lk0IIx r0 þ 14 r3 EIIT  jKj2 K II dII

z

EII;Nþ1 T EIII i

¼

¼

EIII i

1 III E 4 T




II dII

He
ikz 2

 II
 II III III KIII ¼ kkzII þ 1 e
ikz d þ 1
kkzII eikz d z z  2
 II dII   kIII l0 x III
ikz 2 z H ¼ 2 1 þ kII e
kII ðr0 þ 14 r3 EIIT  jKj2 ÞK z

ð1Þ I;II;III

kz

¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 k0 eI;II;III
k0 eI sin h; where k0 ¼ 2kp0 and k0 is the free space

laser beam wavelength; eI;II;III pertains to the medium dielectric conII

stant; h is the incident beam angle. d is the mean dielectric slab distance between flakes; l0 is the free space permeability; x ¼ 2pc=k0 in which c is the light velocity in free space. r0 is the isotropic surface conductivity and can be written as the sum of interband rinter and intraband rintra expressions given in Eqs. (2) and (3) respectively [32–36,40].

rinter ¼

  2 2EF
ðx þ is
1 Þh ie ; ln  2EF þ ðx þ is
1 Þh 4ph

rintra ¼

E EF
k FT B þ 1Þ : þ 2 lnðe ph2 ðx þ i=sÞ kB T 2

ie kB T

ð2Þ



ð3Þ

On the other side, r3 is the nonlinear conductivity of grahene flakes which can be obtained by Eq. (4) for interband transitions over the visible frequency range [32–36,40].

r3 ¼


2

ie  h



eV F hx2

2

ð1 þ iaT Þ

ð4Þ

In Eqs. (2)–(4), e is the electron charge,  h is the reduced Planck’s constant, kB is the Boltzmann constant, EF is the Fermi energy, s is the electron-photon relaxation time, T is the temperature. aT is two

ΙΙ,N

x y

 

HI ¼ 4e
ikz 2
lk0IIx r0 þ 14 r3 EIIT  jKj2 K

z

2. Theory 2.1. N-layer problem



 II II II II II II EIi ¼ 18 EIT 1 þ kkzI He
ikz d þ 18 EIT 1
kkzI ð2K
HÞeikz d

z

Fig. 1. Schematic illustration of graphic layers dispersed in dielectric system.

ΙΙI

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photon absorption coefficient which is negligible in Eq. (4) for the following calculations according to our experimental results, given in Section 3. For simplicity, we assume that h ¼ 0 . Optical roundtrip travelling wave between the graphene layers will cause a resonating effect in our problem which can be emulated by introducing the feedback depth and considering a Fabry–Perot resonator with mirrors M as given in Fig. 1. Nonetheless, we initially ignore the resonator effect to investigate purely the N-layer problem effect on the nonlinearity enhancement. I Eq. (1) generate solutions for EIII T in terms of Ei , given in Fig. 2 as

the OB S-shape for 2, 20 and 200 layers of graphene dispersed in N,N-Dimethylformamide (DMF) with eII ¼ 36:7 which is the dielectric medium taken in our experimental observation. We assume d ¼ 8:5  10
6 m, k0 ¼ 532:8 nm and II

s ¼ 1 ps. We already know

that v F ¼ 10 m=s. Three cases of Fig. 2a–c in comparison with each other states that the threshold input electric field for a primary OB is reduced by the order of 1 as the layer number increases 10 times. This implies that the threshold intensity will be lowered N2 times; an interpretation that is in agreement with the experimentally acquired relation by Rui Wu et al. represented in Eq. (5) to describe the nonlinear susceptibility enhancement for N-layer graphene [9]. 6

ð3Þ ð3Þ vTotal ¼ N2 vmonolayer :

ð5Þ

For the future consideration, we depict a nonlinear refractive index-wavelength dependence diagram of N = 1000 layers graphene according to Eqs. (5)–(8), given in Fig. 3 [36,40]. ð1Þ vmonolayer ¼ r0 =ð
ixe0 lgr Þ; ð3Þ vmonolayer ¼ r3 =ð
ixe0 lgr Þ; ð3Þ ð1Þ n2 ¼ 3vmonolayer =½4e0 cð1 þ vmonolayer ;

ð6Þ ð7Þ ð8Þ

In these equations, vmonolayer and vmonolayer are the linear and nonð1Þ

ð3Þ

linear susceptibility of graphene monolayer, e0 is the vacuum permittivity and lgr is the effective thickness of graphene monolayer. n2 is the nonlinear refractive index. The estimation of n2 for k0 ¼ 532 nm is
1:285  10
10 m2 =W which is 6 orders higher than that of the momolayer graphene. 2.2. Resonator feedback problem Particularly, if we introduce a Fabry–Perot resonator in our problem to emulate resonating effect due to the roundtrip travelling of optical wave between graphene layers, the feedback depth inside the cuvette will be intensified and the transition toward instability will then be inevitable. To investigate this effect, we present a numerical solution to NLSE which will also yield an approach to evaluate both the nonlinear dispersion and absorption contribution in OB process. Our problem is now summarized to a propagating wave in a nonlinear medium placed inside a Fabry– Perot resonator with the feedback depth q. This can be described by NLSE as given in Eq. (5) in which t means time and z is the propagation direction [41].

  @E @E x00 @ 2 E þV þ 0 2 þ cjEj2 E ¼ 0; i @t @z 2 @z

Fig. 2. OB and muti-stability for (a) 2 layers, (b) 20 layers, and (c) 200 layers of dispersed graphene.

Fig. 3. Nonlinear refractive index of 1000 layer graphen vs. wavelength.

ð9Þ

M.A. Sharif et al. / Optical Materials 53 (2016) 80–86

83

E is the slowly varying complex electric field, V is the group velocity, x000 is the dispersion parameter and c ¼ b þ ia is the nonlinearity parameter in which b and a measure the nonlinear refractive index and nonlinear absorption coefficient as given in Eqs. (10) and (11) [41].

b ¼ 2k0 cne0 n2 V;

a ¼ 4cne0 aT V;

ð10Þ ð11Þ

c is the light velocity in free space and n is the linear refractive index. Stationary solution of Eq. (9) – i.e. while the electric field amplitude is assumed time independent – leads to Eq. (12).

Ii ¼ IT =ð1 þ q2
2q cosðIi þ uÞÞ;

ð12Þ

where Ii ¼ bL=VE2i and IT ¼ bL=VE2T ; u is the total phase shift induced by the feedback loop; L is the nonlinear medium length. We take our experimental measurement – as we will see in the next section – jbj ¼ 15:7 and jaj ¼ 0:08 which is negligible. Eq. (12) returns OB and multi-stability S shapes for different values of L, q and u. These parameters are correlated. With increasing one or more, the switching-up threshold of the input electric field will be considerably lowered as given in Fig. 4. Furthermore, it can be obviously seen that multi-stability will be also attainable. Nevertheless, for the criterion cjEi j2 > V 2 =2x000 þ x, the solution of Eq. (9) is unstable i.e. for an input intensity, there will not the single/bi-stable output. Instead, the output will fluctuate between two or more values. The fluctuations will become unstable and grow in amplitude intricately. This procedure is known as modulation instability which is shown in Fig. 5 as a result of numerical solution of NLSE (9) [41]. Here, the bifurcation diagram implies

Fig. 5. Illustration of unstable solution to NLSE for u ¼ p2 , L ¼ 3 mm, q ¼ 0:1.

the unstable behavior as a route to chaos. The corresponding input intensity to Ei is given by  i ¼ 12 e0 cnjEi j2 . Although we have shown this procedure as a consequence of the external feedback, but, for a highly doped graphene flakes, especially in THz frequency range, the nonlinearity will be intensely enhanced due to its cubic reversal dependence on the frequency and the internal feedback will be present resulting from the surface Plasmon resonance. Therefore, instability threshold will be lowered; this will break down the OB process [32–36,40,42–47].

Fig. 4. OB and muti-stability for (a) u ¼ p2 ; L ¼ 1 mm; q ¼ 0:25, (b) u ¼ p; L ¼ 1 mm; q ¼ 0:25, (c) u ¼ p2 ; L ¼ 3 mm; q ¼ 0:1, and (d) u ¼ p2 ; L ¼ 3 mm; q ¼ 0:25.

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0.9 nm which is in good agreement with the typical thickness of the few layer graphene [32–36,40]. The absorption spectra of the sample over a wavelength range 200–800 nm has been recorded by double beam Shimadzu UV2450 Scan UV–Visible spectrophotometer combined with a cell temperature controller (Fig. 7). Accordingly, the band gap energy is 3.5 eV which is equal to the band gap energy of semiconductors group III–V in contrary to the insulator graphene oxide nanosheets. 3.2. Z-scan measurement Fig. 6. AFM image of graphene sheets.

A 532.8 nm Nd:YAG laser with 300 mW power and 1 mm spot size is used. The Gaussian beam is focused by a lens with 80 mm focal length on the sample of graphene ink contained in a 3 mm cuvette. In the close z-scan set up which is used to determine the nonlinear refractive index, a power meter (Coherent, Lab master) is placed behind the aperture. In order to indicate the optical limiting behavior (Fig. 9), we measure the output power that is related to input power when the sample is placed in the fix point (e.g., focal point). The close z-scan plot (Fig. 8a) shows a peak–valley which implies the negative sign of the nonlinear refraction. The magnitude of nonlinear refractive index is obtained n2 ¼ 2:51  10
10 m2 =W. Meanwhile, Fig. 8b shows the open aperture measurement. As a result, the sign of nonlinear absorption coefficient is negative and its magnitude is aT ¼ 2:5  10
6 m=W. In Fig. 8, the solid curve is the theoretical prediction [24,50] and dotted curve indicates the experimental data. From Eqs. (10) and (11) one can easily obtain jbj ¼ 15:7 and jaj ¼ 0:08.

Fig. 7. UV–Vis spectrum of graphene ink.

3. Experimental results and discussion 3.1. Preparation In this study, we have prepared few layer graphene nanosheets dispersed in N,N-Dimethylformamide (DMF) at SHARIF SOLAR Co. Ltd. by exfoliation of graphite according to Khaled Parvez et al. [48]. As well, this highly concentrated graphene ink (10 mg/mL) possesses large flakes, few oxidation degree and remarkable charge carrier mobility. The latter will provide ultra-fast optical response which is crucial for all optical switching [5,9,12,49]. Fig. 6 shows AFM image of the prepared graphene sheets with a nearly smooth planar structure clearly distinguishable. The height profile diagram of the AFM image indicates that the height of the graphene sheet is

Fig. 8. Z-scan measurement data.

Fig. 9. Optical limiting behavior of graphene.

M.A. Sharif et al. / Optical Materials 53 (2016) 80–86

85

This step will yield the experimental data marked with red dots in Fig. 10a. As the next step, the incident power is reversely decreased. This will give the experimental data marked with blue cubes given in Fig. 10a. Overall, the obtained result seems to be an OB hysteresis diagram. However, if we use a 3 mm cuvette containing the same 10 mg/mL graphene ink, the OB hysteresis diagram will be obtained with an optimized feature, as given in Fig. 10b. For a constant graphene ink concentration (10 mg/mL), an increase in the cuvette length can be interpreted as increasing the number of graphene flakes. Hence, analogous to the theoretical representation in Section 2.1, the nonlinearity enhancement is anticipated. Finally, multi-stability diagram can be also achieved as given in Fig. 10c, if the laser power range is raised up to 300 mW. 3.4. Discussion A 3 mm sample of the graphen ink used in our experimental observation contains 1000 layers of graphene flakes. This means that the theoretical estimation of n2 in Section 2.1 is in good agreement with our experimental z-scan measurement (also refer to Eqs. (6)–(8)). Although introducing the other factors like creation of nanobubbles induced by laser heating and the variation of local graphene sheets concentration induced by the non-axissymmetrical thermal convections [9,51,52] – which have not been considered through the theoretical calculations – can cause the difference between our experimental measurement and theoretical estimation, but such discrepancy is not expected to be higher than the order of agreement. Experimental results given in Fig. 10 indicate that despite the large number of graphene flakes/high concentration of graphene ink, absorption will not overshadow the OB process even if one considers the peak of the absorption spectra at 530 nm (refer to Fig. 7). This implies that the situation can be further improved for the higher wavelengths. Moreover, these highly concentrated graphene flakes possess enhanced nonlinearity and present the extremely low threshold OB and multi-stability in accordance with theory (if we reconsider the relation  i ¼ 12 e0 cnjEi j2 and remind that the spot size is 1 mm, then, the experimental results match with theoretical calculations as previously given in Section 2.2). This observed threshold is even lower than that has been theoretically predicted in THz ranges given in previous studies [46]. On the other hand, according to NLSE (Eq. (9)) and the experimental values obtained for jbj and jaj in Eqs. (10) and (11), the dispersion – rather than absorption – is the main nonlinear mechanism that contributes in OB process. As a result, exfoliated graphene with low oxidation degree opens the practical ideas based on its outstanding trait of ultra-fast optical response, especially in THz frequency range where, the nonlinearity can be further enhanced by the surface Plasmon resonance [32–36,40,42–47]. 4. Conclusion

Fig. 10. Experimental observation of OB & multi-stability for (a) 1 mm cuvette length, (b) 3 mm cuvette length, and (c) Maximum input power 300 mW.

3.3. OB and multi-stability The 532.8 nm Nd:YAG laser beam with TE polarization is illuminated to a 1 mm quartz cuvette containing 10 mg/mL graphene ink placed inside a Fabry–Perot resonator in a similar manner given in Fig. 1. Some attenuator is also used to control increasing and decreasing procedure of the incident power. At first, the incident power is gradually increased from a minimum value to 100 mW.

Nonlinearity enhancement and consequently low threshold OB and multi-stability have been theoretically investigated by proposing N-layer problem and the resonator feedback problem in exfoliated graphene ink with low oxidation degree and high concentration. Experimental results of OB and multi-stability have shown good agreement with the theoretical predictions. This includes the experimental obtained value for the nonlinear refractive index and the low threshold value of OB. It has been indicated that the absorbance does not limit OB process. It has been also concluded that dispersion – rather than absorption – is the main nonlinear mechanism of OB. On this base, exfoliated graphene with low oxidation degree has been proposed as a unique optical

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material for all optical switching application. In addition to the enhanced nonlinearity, this nanomaterial possesses semiconductors group III–V equivalent band gap energy, high charge carrier mobility and thus, ultra-fast optical response.

Acknowledgement The authors should appreciate SHARIF SOLAR Co. Ltd. for facilitating the preparation of exfoliated graphene with low oxidation degree.

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