Near infrared nonlinear refractive index dispersion of metallic and semiconducting single-wall carbon nanotube colloids

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Near infrared nonlinear refractive index dispersion of metallic and semiconducting single-wall carbon nanotube colloids Antonio C. Branda˜o-Silva a, Roge´rio M.A. Lima b, Cristiano Fantini b, Alcenı´sio Jesus-Silva a, Ma´rcio A.R.C. Alencar c, Jandir M. Hickmann d, Rishabh M. Jain e, Michael S. Strano e, Eduardo J.S. Fonseca a,* a

Instituto de Fı´sica, Caixa Postal 2051, Universidade Federal de Alagoas, 57061-970 Maceio´, AL, Brazil Departamento de Fı´sica, Universidade Federal de Minas Gerais, Belo Horizonte, MG 30123-970, Brazil c Departamento de Fı´sica, Universidade Federal de Sergipe, Sa˜o Cristo´va˜o, SE 57072-970, Brazil d Instituto de Fı´sica, Universidade Federal do Rio Grande do Sul, Porto Alegre, RS 91501-970, Brazil e Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA b

A R T I C L E I N F O

A B S T R A C T

Article history:

Third-order nonlinear optical properties of different colloidal systems containing metallic

Received 20 March 2014

and semiconducting enriched single wall carbon nanotubes have been investigated. Ther-

Accepted 6 June 2014

mally managed Z-scan technique was performed to measure the nonlinear refractive index

Available online 14 June 2014

(n2) and estimate the absorption coefficient (b) of the colloidal systems. The n2 dispersion curve was obtained for both colloids in the range of 755–825 nm, showing a considerable increase on the nonlinear refractive index for laser tuned at 800 nm. The measurements also showed that the colloids nonlinear absorption coefficients were smaller than 8.5 · 1010 cm/W in this wavelength range. Analysis of the obtained figures of merit indicates that these systems are promising materials for all-optical switching applications.  2014 Elsevier Ltd. All rights reserved.

1.

Introduction

In the last decades, extensive researches have widely recognized that single-walled carbon nanotubes (SWCNTs) present a considerable potential which evolved from rather fundamental studies to applications, reaching from nanoelectronics [1] to biosensors [2] and nonlinear optics [3]. Especially, nowadays, with efficient methods that enable to separate metallic from semiconducting SWCNTs [4–6], new frontiers fundamental problems and applications can be investigated. Now it is possible to identify the direct influence of the

* Corresponding author: Fax: +55 8232141424. E-mail address: [email protected] (E.J.S. Fonseca). http://dx.doi.org/10.1016/j.carbon.2014.06.008 0008-6223/ 2014 Elsevier Ltd. All rights reserved.

SWCNTs nature on specific physical properties and to exploit the suitable nanotube electronic character for the development of applications. For instance, metallic SWCNTs could represent key building blocks in future nanoscale circuit [7], whereas semiconducting SWCNTs are under extensive studies as a candidate for replacement of silicon-based transistors [8,9]. Among a variety of applications, SWCNTs have emerged as an unique nanostructure which may be responsible for a new generation of nonlinear optical devices. For example, it can be used as an efficient optical limiting, possessing several

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advantages over other materials, such as broad wavelength range [10]. In addition, due to its chemical properties, SWCNT is a suitable material for functionalization, enabling it to be used as a versatile optical limiting composite [3]. All-optical devices based on saturable absorber incorporating SWCNTs may have a very fast nonlinear optical response. Q-switching or mode-locking for lasers are examples of such devices containing SWCNTs. In fact, SWCNTs have emerged as a promising candidate for ultrafast devices due to its large third-order nonlinearity and ultrafast electronic response as a consequence of delocalized p-electrons cloud along the tube axis [11–13]. In this regime, several papers have been published exploring the study of SWCNT composites where electronic contributions to the third-order nonlinear susceptibility take place [14–18]. On the other hand, few fundamental studies on the nonlinear optical properties of SWCNTs with well-defined chirality have been made [19,20]. Here, we explore the effect of electronic character, metal or semiconducting, on the nonlinear optical response of the SWCNTs. We measured the electronic contribution to the nonlinear refractive index (n2) of different colloidal systems of metallic and semiconducting

enriched SWCNT samples using the Z-scan technique managed thermally [21]. Dispersion curves for n2 as a function of laser wavelength in the range of 755–825 nm were obtained for both kinds of SWCNTs.

2.

Experimental procedure

Semiconducting and metallic SWCNTs samples dispersed in 2 wt% SDS aqueous solution and separated by the gel chromatography method described in [22] were used in this work. The samples were characterized by Raman and optical absorption spectroscopies. Fig. 1 shows the resonance Raman excitation map of the two samples obtained by measuring the radial breathing modes with 30 different excitation energies in the range of 1.90–2.30 eV of a dye laser. Families of metallic and semiconducting nanotubes can be clearly distinguished in the maps. From the analysis of the Raman data we observed that the samples present metallic or semiconducting nanotubes with more than 90% purity. The diameter distributions of the samples, 0.89–1.18 nm for metallic and 0.67–0.83 nm for semiconducting SWCNTs, were also obtained from the analysis of the Raman maps. The

Fig. 1 – Resonance Raman maps for the Radial breathing modes of the metallic (a) and semiconducting (b) enriched SWCNT suspensions. The color scale represents the Raman intensity increasing from blue to red. (c) Absorption spectra of metallic and (bottom spectrum) semiconducting (top spectrum) enriched SWCNT suspensions. (A color version of this figure can be viewed online.)

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concentration of nanotubes in each sample was determined from the optical absorption spectra measured by placing the solutions in cuvettes with different optical paths and by fitting the absorbance vs. optical path plot according the Beer–Lambert law. For this analysis the optical extinction coefficient was considered to be 21.4 mLÆmg1Æcm1 [23]. The values obtained were 7.85 · 103 and 8.53 · 103 mg/mL for metallic and semiconducting, respectively. Z-scan technique managed thermally [21,24] was performed to investigate the nonlinear optical properties of the colloids. This technique allows separating the instantaneous response from the cumulative thermal effect. The experimental setup is shown in Fig. 2(a). A mode-locked Ti:Sapphire laser, linearly polarized, delivering pulses of 200 fs (FWHM) at 76 MHz repetition rate, tuned between 755 and 825 nm, was used as excitation source. The laser beam was modulated by a chopper (14 Hz frequency and 0.09 duty cycle) and focused on to the sample by a convergent lens of 7.5 cm focal length. The samples consisted of 1 mm width quartz cell filled with colloids of different chirality carbon nanotubes, metallic and semiconducting. The cell was mounted on a translation stage and moved around the lens focal plane (z = 0). The light transmittance was then measured by a closed (without) aperture photodetector as a function of the sample position for nonlinear refraction (absorption) measurements. The detected signal was temporally analyzed by digital

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oscilloscope and then processed by a computer. Fig. 2(b) shows a typical 3D graph of a complete temporal evolution of the Z-scan curve. It is clear that the difference between the peak-valley transmittance increases with time, which indicates that the cumulative thermo-optical effect is present in this sample. One important point in this paper is to establish a criterion to separate thermal from electronic effects. Experimentally, a chopper was used, as a temporal window, to control the exposure time of the whole beam at the sample. Fig. 2(c) shows a typical temporal window. Between A–B and E–F, there is no light at the sample. B–C and E–D the beam is partially blocked, and between C and D window the sample is illuminated by the whole beam. Basically, all we need is to know the transmission signal, for each displacement z, from C to D. Fig. 2(d) represents a temporal window (C and D) of the prefocal and postfocal in some +z and –z positions, respectively. The red curve is an extrapolation for t = 0 (see Eq. (3)).

3.

Theoretical method

The refractive index and absorption coefficient of many materials can be modified due to their interaction with an intense optical radiation. Although different physical mechanisms can contribute to these modifications, for the majority of known systems, including carbon nanotubes, irrespective of

Fig. 2 – Sketch of steps used to separate thermal from electronic effects. Experimental setup (a), 3D graph of a temporal evolution of the Z-scan curve (b), temporal window (c), and temporal window of the prefocal and postfocal positions (d). (A color version of this figure can be viewed online.)

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the physical process, the dependence of the medium’s refractive index and the intensity of the interaction optical field can be described by the relation [25]. nðIÞ ¼ n0 þ n2 I;

ð1Þ

in which I is the laser beam intensity, n0 and n2 are the linear and nonlinear refractive index of the material respectively. A similar equation describes the behavior of the material optical absorption aðIÞ ¼ a0 þ bI;

ð2Þ

In this case, similarly, a0 is the linear absorption coefficient, while b is known as the nonlinear absorption coefficient of the material. Ideally, materials for ultra-fast nonlinear applications must present a large and fast nonlinear refractive response in comparison with the medium’s linear and nonlinear absorptions. For all kind of materials, large nonlinear refraction can be achieved exploiting the thermo-optical effect. This phenomenon has a nonlocal character and it is defined as the change on the material’s refractive index due a laser induced increase of the medium’s temperature. However, the time response of this optical effect is very large, typically in the range of 10 ns to tens of milliseconds. On the other hand, laser induced electronic polarization may provide a very fast, femtosecond time scale, and large enough change on the material’s refractive index, which would be more suitable for all-optical switching applications. Therefore, the separation of these effects is a key point during the characterization of the medium’s nonlinear response. Up to this moment, the more effective separation techniques for thermal and electronic nonlinear refractions are based on modified approaches of the Z-scan technique [26], which exploit the distinct temporal dynamics that those physical mechanisms exhibit [21,24,27–29]. It must be emphasized that, usually, both contributions are present when an intense laser beam interacts with a nonlinear medium. However, while the electronic contribution to the medium’s nonlinear refractive index is instantaneously turned on, the thermal response can only be observed if the medium absorbs enough energy from the laser beam, convert it into heat and it is diffused along the medium due to the heat conduction. This process takes some time to be significant and stabilize, which depends on the medium acoustic and thermal properties [28]. In other words, irrespective if a CW or a pulsed laser is used in the nonlinear refractive index measurements, for time instants just a few femtoseconds after the interaction between the light beam and the medium began, the thermooptic effect is negligible and only the electronic contribution to the nonlinear refraction can be observed. On the other hand, if this interaction holds for a long time (longer than few nanoseconds), due to the use of a CW or a nanosecond pulsed laser the thermal effect can overcome the electronic polarization and the measurement will reveal only the thermal contribution to the refractive index change. The thermo-optical phenomena can be also very relevant even when a high repetition rate short-pulsed laser is employed, whose temporal pulse spacing is shorter than the material’s thermal characteristic time tc. In this case, if the measurement is performed just after a single pulse interacts with the medium, the electronic

nonlinear refraction can be accurately characterized. However, it is important to point out here that at a 76-MHz repetition rate regime, the cumulative thermo-optical effect dominates the refractive response of the medium after some time of the sample being irradiated. Following [24], the thermo-optical contribution is completely described by the Z-scan measurement, 2 3 Iðn; tÞ 2qn 1 4 5; h i ¼ 1 þ h Tan Tðn; tÞ ¼ Iðn; 0Þ ð2q þ 1Þ2 þ n2 tc ðnÞ þ 2q þ 1 þ n2 2qt

ð3Þ where h is the thermal induced phase-shift, n = z/z0 is the normalized distance, z0 corresponds to the Rayleigh range of the laser beam, q is the order of the multiphoton process and tc(n) is the characteristic thermal lens time. The time t = 0 is defined as instant that the chopper begins to unblock the laser beam (point C in Fig. 2(c)). During the time period between t = 0 and the chopper risetime (B–C temporal window in Fig. 2(c)), the laser beam is partially blocked in such a way that the beam power on the sample varies with time. Therefore transmittance measurements within this period cannot be described by the Eq. (3) and are disregard at the analysis procedure. However, the temporal evolution of the Z-scan traces can be followed from the opening risetime onwards (C–D temporal window in Fig. 2(c)) [24]. Ideally, the electronic contribution to the observed nonlinear refraction gives an instantaneous response. Although we could not measure the normalized transmittance at t = 0, we can reconstruct this curve extrapolating the time evolution curves of the measured normalized transmittance, at all sample positions, using Eq. (3) [21]. Hence, the value of n2 can be obtained fitting the normalized transmittance curve at t = 0 employing the standard equation of Z-scan method [26]: 4DU0 n ; ð4Þ ðn2 þ 9Þ ðn2 þ 1Þ pffiffiffi where DU0 ¼ 2kn2 I0 Leff , k is the modulus of the beam wave vector, I0 is the maximum laser intensity, Leff ¼ ð1  ea0 L Þ=L and L is the sample length. If the light beam induces a negative refraction, the value of n2 is negative and the profile of the transmittance curve displays a maximum for a sample position n ’ 1.7 and a minimum when the sample is placed at the n ’ +1.7. On the other hand, if the medium presents a positive nonlinear refraction, n2 > 0 and the maximum (minimum) occurs at n ’ +1.7 (n ’ 1.7). Removing the aperture, the measured transmittance provides information about the material’s nonlinear absorption. In this configuration, the change on the transmitted signal is related to the nonlinear absorption coefficient by [25] TðnÞ ffi 1 þ

TðnÞ ¼

1 X ½q0 ðn; 0Þm m¼0

ðm þ 1Þ3=2

;

ð5Þ

where q0(n,t) = bI0(t)Leff/(1 + n2) and I0(t) is the laser intensity at the focal plane.

4.

Results and discussion

Fig. 1(c) shows the absorption spectra of the investigated samples. In both cases, the colloids present a strong broadband

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absorption in the ultra-violet region and narrower absorption bands in the visible and near infrared region associated with excitonic transitions ES11 and ES22 for semiconducting nanotubes and EM 11 for the metallic ones. As expected, the different electronic characters of the tubes compounding these colloids can be detected in the measured spectra. For instance, it can be observed that the semiconducting SWCNTs sample displays a stronger absorption band between 650 and 700 nm, and 900–1200 nm, which are not present in the metallic sample spectrum. Fig. 3 presents the typical results of the reconstructed Zscan curves at t = 0 s for metallic and semiconducting SWCNTs colloids for light excitation tuned at 800 nm. As can be observed, both samples presented an intense negative nonlinear refraction of electronic origin, while the nonlinear absorption could not be detected. Indeed, the nonlinear absorption coefficient of these colloids must be smaller than our experimental limit, which was equal to 8.5 · 1010 cm/ W, in modulus. Using Eq. (4), the experimental curves were fitted and the values of the colloids’ n2 obtained. The same measurements were performed employing the surfactant aqueous solution without nanotubes. In this case, it was not possible to detect a measurable nonlinear refraction, nor absorption at any used experimental conditions. This indicates that the nonlinear response can be attributed only to the SWCNTs presence in the colloids.

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Similar results were observed for aqueous solution containing less selective mixes of metallic and dielectric carbon nanotubes [18]. As in this previous work, the self-defocusing nature of the observed nonlinearity can be attributed to one-photon non resonant transitions of the nanotubes. Negative nonlinear refraction was also observed varying the laser wavelength in the near infrared region, between 755 and 825 nm. In Fig. 4, it is shown the measured n2 values, in modulus, as a function of the excitation wavelength for both SWCNTs samples. For both cases, the value of |n2| increases significantly when the laser was tuned around 800 nm. A resonance-like behavior for the third-order nonlinear susceptibility of carbon nanotubes has been predicted and observed previously, in particular for the tensor element ð3Þ viiii ð3x; x; x; xÞ, which is related to the third-harmonic generation phenomenon [11,30–32]. However, a direct experimental evidence of this effect on the real part of the ð3Þ viiii ðx; x; x; xÞ element, which is related to the nonlinear refraction, has not been reported yet. As described in [30], several resonance peaks can be observed on the third-order nonlinear response of carbon nanotubes due to multiphoton transitions between the Van Hove singularities. For third-harmonic generation, three photon transitions play the most important role, however, from their theoretical calculations, one photon and two photon transitions may also contribute to this effect, but in distinct

Fig. 3 – Z-scan curves at t = 0 for the (a) metallic and (b) semiconducting SWCNTs colloids measured at 800 nm. Black squares correspond to the closed aperture experimental data and the red lines are the fittings. Opens circles corresponds to the open aperture measurements results. (A color version of this figure can be viewed online.)

Fig. 4 – |n2| dispersion curves for (a) metallic and (b) semiconducting SWCNTs colloids. Black squares are the experimental data and the dashed lines are guides to the eyes.

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ð3Þ

spectral ranges. Indeed, for the viiii ðx; x; x; xÞ, two photon transitions would also give an important contribution to the generation of spectral peaks on the nonlinear responses related to this tensor element. In order to verify this statement, we estimate the energy of the excitonic transition for the carbon nanotubes investigated in this work using the approximation proposed in [33]:   bp cos 3h p c Eii ðp; dt Þ ¼ þa 1 þ b log ; ð6Þ 2 dt p=dt dt where p is an integer number equals to 1, 2, 3, 4,. . . for ES11, ES22, S EM 11, E33,. . . optical transitions, respectively, dt is the nanotube diameter and h is the nanotube chiral angle. The empirical constants a = 1.049 eVÆnm, b = 0.456, c = 0.819 nm1, and the bp values for different values of p are given in [33]. Considering the average diameter 0.90 and 1.1 nm for the semiconducting and metallic enriched SWCNT samples, respectively, as obtained from the resonance Raman characterization, we estimate the values for ES33 and EM 22. The values obtained are = (3.3 ± 0.2) eV, where the variation in ES33 = (3.2 ± 0.2) and EM 22 the values is because the chiral angle dependence of the energies. These values correspond to wavelengths intervals 365–415 nm and 355–400 nm, respectively. Thus, the results observed in Fig. 4 may be associated with two photon transition processes. It is worth mentioning that due to the spectral characteristics of the employed femtosecond pulsed laser, it was not possible to measure the spectral behavior of the colloid’s nonlinear refractive index with a better resolution to obtain a well defined resonance peak. Indeed, as can be observed in Tables 1 and 2, the addition of intermediary points within 785 and 815 nm region would provide points with significant spectral overlap among them. Therefore, although it was not possible to completely characterize this expected resonance, the observed results suggest that this enhancement on the system’s negative nonlinear refraction may be related

to the two-photon processes. Moreover, due to experimental limitations, such as linear scattering, it was not possible to verify if the imaginary part of the colloid’s third-order nonlinear response also presents an enhancement for excitation near 800 nm. Finally, we also investigated these SWCNTs potential for ultrafast all-optical switching applications, evaluating the figures of merit W ¼ Dnmax =ka0 and T ¼ 2a2 k=n2 , where Dnmax is the maximum refractive index change achievable, limited by saturation [34]. Suitable materials for all-optical switching devices, in a nonlinear Fabry-Pe´rot configuration, should satisfy the conditions |W| > 0.27 and |T| < 1. The fulfill of those means that the medium have large enough nonlinear refractive index to perform optical switching operations in thicknesses comparable to the absorption length. As in this present work we did not reach the saturation limit for the change on the medium refractive index, neither could measure the colloids nonlinear absorption coefficient, we could only estimate these figures of merit values. Indeed, for the W calculations the value of Dnmax was taken as the change on the material refractive index for laser intensity equal to 8.33 · 108 W/cm2. On the other hand, the figures of merit T could not be accurately evaluated due to the fact that the nonlinear absorption coefficients of the studied SWCNTs were much smaller than our system resolution (|a2| < 8.5 · 1010cm/W). These results are summarized in Tables 1 and 2. As can be observed, both SWCNTs kinds satisfy the figures of merit W condition. These results indicate that these materials have a good potential for the development of switching applications in femtosecond regime. It is worth mentioning that both W and T figures of merit can only evaluate a medium’s potential for all-optical switching applications. Naturally, the larger (smaller) the value of |W| (|T|), the better performance a material would present for this end. A comparison between the obtained results displayed in Tables 1 and 2 suggests that, among the investigated

Table 1 – Optical properties of the studied metallic SWCNTs colloid. k (nm)

Pulse’s linewidth (nm)

Pulse’s time duration (fs)

a0 (cm1)

n2 (1014 cm2/W)

|W|

755 775 785 800 815 825

2.9 3.8 3.9 4.1 6.5 6.9

286 231 231 227 151 145

0.097 0.087 0.055 0.058 0.044 0.028

1.4 0.5 1.5 5.5 1.0 0.9

1.6 0.6 3 6.2 2.3 2.5

Table 2 – Optical properties of the studied semiconducting SWCNTs colloid. k (nm)

Pulse’s linewidth (nm)

Pulse’s time duration (fs)

a0 (cm1)

n2 (1014 cm2/W)

|W|

755 775 785 800 815 825

2.9 3.8 3.9 4.1 6.5 6.9

286 231 231 227 151 145

0.006 0.002 0.002 0.002 0.002 0.002

1.3 0.6 3.1 4.2 0.4 0.3

23 28 143 190 18 13.2

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samples, the semiconducting SWCNT presented slightly superior features than the metallic systems. Indeed, although both colloids presented almost the same carbon nanotubes concentration, both samples possess comparable nonlinear refractive indexes values, but the semiconducting displayed lower linear absorption coefficient in this wavelength region. Nevertheless, other uninvestigated parameters, such as the surfactant or dispersant choices, different tubes diameters and wavelength regions should be yet exploited aiming the development of improved carbon nanotubes systems for ultra-fast optical devices.

5.

Conclusion

We investigate the nonlinear response of aqueous colloids containing metallic and semiconducting SWCNTs. We observed that both tubes nature displays a self-defocusing behavior. Due to experimental limitations, we could only estimate that the modulus of the colloids’ nonlinear absorption coefficients were smaller than 8.5 · 1010 cm/W in the near infrared region. The n2 dispersion curves were obtained and a significant enhancement of this quantity was observed around 800 nm for both samples. Our results indicate that both semiconducting and metallic SWCNTs are promising materials for ultra-fast nonlinear optical applications. However, nonlinear optical studies of single-chirality carbon nanotube samples are necessary to map the dependence of the nonlinear refractive index on the nanotube diameter and chirality.

Acknowledgements The authors thank the financial support from CNPq, Pronex/ FAPEAL, CAPES Pro´-equipamentos/PROCAD/PROCAD-NF, Nanofoton Network, INCT-Nanocarbono, FAPEMIG and PADCT.

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