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The saturated optical absorption of multi-walled carbon nanotube (MWNT)-doped hybrid-glass composites was studied at 1064 nm with nanosecond long pulses using the Z-scan technique. Increased transmission was demonstrated for high intensity pulses. The results were modeled for the limiting cases of a slow or a fast saturable absorber, both referring to a three-level system. The ground-state absorption cross section was estimated as 2.3x10−18 cm2, in good agreement with that of a single carbon atom. The excited state absorption cross section for carbon nanotubes (CNTs) was estimated for the first time as 6.9x10−19 cm3. The absorber's density of 2.8x1018 cm−3 is smaller by approximately a factor of 5 compared to the nominal density of carbon atoms incorporated into the glass. This could be a result of the broad band-like states formation in the MWNTs. The above figures were obtained by assuming that the excited state decay time was longer than the pulse duration of ~1 ns.
©2012 Optical Society of America
1. Introduction
Carbon nanotubes (CNTs) have been widely explored for their nonlinear optical properties. In the visible, specifically at 532 and 800 nm, enhanced absorption and/or scattering were observed at high light intensities, in liquid suspensions [1–8] as well as in solids [5,6,9–11]. These effects were termed “optical limiting” by virtually all workers. In the near infrared (NIR), mainly saturable absorption was observed [12–22], although several studies showed the occurrence of optical limiting at 1064 nm [2–5]. Saturable absorption was studied using single-walled carbon nanotubes (SWNTs), which exhibit discrete band transitions [19,23–25] and a controllable band-gap that depends on the tubes diameter [24]. Applications of the SWNTs for laser mode-locking [15–17,19–21] noise suppression [18,21] and pulse shaping [22] were demonstrated utilizing their fast saturable absorption property.
Any CNT composite production requires dispersion of the CNT species within the hosting matrix. It has been established, that dispersion of multi-walled carbon nanotubes (MWNTs) is achieved more easily and effectively than SWNTs [26–28]. Thus MWNTs are advantageous in terms of composite production ease, and not less importantly, in terms of price. However, the saturable absorption of MWNTs was studied only briefly [12]. In this work we present a study of saturable absorption of MWNT/hybrid organic-inorganic sol-gel glass composites prepared by a Fast-Sol-Gel (FSG) method [29]. Analysis of the nonlinear properties was performed by studying two limiting cases: the slow saturable absorber, analyzed by the modified Frantz-Nodvik equation, and the fast saturable absorber, analyzed by the steady-state solution of Hercher's rate equations [30]. The models allow estimation of ground-, and excited-state absorption cross sections, and respectively, the absorber's effective density N, and the excited state decay time .
The matrix in which the MWNTs were incorporated is a silica-based optically transparent material prepared by the FSG route. The process facilitates and shortens the production of organic-inorganic hybrid glassy materials. These hybrid glasses exhibit tunable properties that vary between those of a silicon rubber and those of a silica glass [29]. A variety of optical properties of the glasses, such as refractive index, thermo-optic coefficient, infrared absorption and humidity sensitivity, have been published [29,31,32]. The process is based on an accelerated sol–gel reaction of a combination of organically modified silicon alkoxides (ORMOSILs) with traditional alkoxides at elevated temperature and pressure. The composites were prepared by solution mixing [33], which is a common fabrication technique of CNT/polymer composites [34].
The composite MWNT/hybrid glasses were studied for their nonlinear optical properties at 1064 nm, using the Z-scan technique [35]. In this method, a sample in the form of a thin slab is moved along the converging axis (Z-direction) of a Gaussian beam emanating from a pulsed laser. This results in variation of the laser beam power density impinging the sample, reaching a maximum at the beam waist position. Analysis of the transmitted beam intensity as a function of the sample position Z reveals the nonlinear interactions between the light and the sample material.
In the past, analysis of saturable absorption in CNTs was performed using an empirical formula [36–38]
where is the input optical pulse intensity, is the intensity-dependent absorption coefficient, and are the limits of the linear saturable-, and non-saturable absorption coefficients, respectively, and is the saturation intensity (the intensity necessary to reduce the saturable absorption coefficient to a half). In our work, we present a refined analysis of the saturable absorption process based on solutions of the basic rate equations that describe the energy state population and the photon density kinetics in saturable absorbers [30]. These solutions consider two limiting cases: a slow saturable absorber yielding a modified Frantz-Nodvik equation, and a fast saturable absorber yielding a modified Hercher equation. A more detailed description of the models and the resulting solutions is presented in section 2.4.1.2. Experimental
2.1. Materials
The precursors used for the Fast-Sol-Gel reaction were tetramethylorthosilicate (TMOS), methyltrimethoxysilane (MTMS), and 0.1 N HCl as the catalyst. The precursors (98% purity) and HCl (99% purity) were purchased from Sigma–Aldrich. Ethanol absolute (dehaydrated, 99.9% purity) and tetrahydrofuran (THF) high performance liquid chromatography (HPLC)-grade were purchased from BioLab Ltd. MWNTs of 10-30 nm diameter, 1-10 μm long were purchased from Nanostructured and Amorphous Materials Inc. at 90% purity. All chemicals were used as purchased.
2.2. Sample preparation
A solution mixing approach was adopted [39] to achieve a homogeneous dispersion of the MWNTs in the composite. The MWNTs were dispersed in ethanol at a concentration of 1 mg/ml using a KUDOS model SK2210HP ultrasonic bath (frequency 53 kHz) for 1 hour. Correspondingly, a hybrid organic-inorganic glass, comprising 19.3 wt.% organic content, was prepared according to the process described in [29,32]. The resulting viscous gel was diluted with THF at a 1:1 weight ratio. When kept refrigerated below ~10°C, the diluted gel remained stable for several months. The composite gel was prepared by mixing 2 ml of MWNT/ethanol suspension with 20 g of a diluted gel at ambient temperature until evaporation of the solvents. The viscous composite gel was then poured into polystyrene cups and covered with perforated lids. The samples were cured for 48 hrs at ambient temperature, followed by an additional 48 hrs at 65°C. The resultant MWNTs concentration was 0.02 wt.%. Prior to optical characterization, the samples were polished to form thin slabs with thicknesses ranging between 1.0 and 1.6 mm.
2.3. Characterization
Environmental scanning electron microscopy (E-SEM) was used to study the morphology of different stages of the composite material formation. The E-SEM was equipped with Quanta 200 field-emission gun. For inspection of the MWNTs powder, several grains were deposited on a double-sided carbon tape; for inspection of MWNT/ethanol suspension, a drop was spread on a microscope slide and dried; inspection of the composite hybrid glass was performed by examining its cross section. All inspections were performed under vacuum (10−2 - 10−5 mbar). Optical transmission spectra were measured using a Jasco model V-570 spectrophotometer in the 400–2500 nm range with 2 nm resolution.
2.4. Nonlinear transmission
The samples were irradiated with 1 ns-long pulses at 1064 nm, ~10 kHz repetition rate, from a diode-pumped, passively Q-switched fiber-pumped microchip laser PULSELAS-P-1064-300-FC-CS model, manufactured by ALPHALAS GmbH. The average power output was approximately 200 mW. The power was measured with an OPHIR Laserstar model power meter. A reference beam for monitoring the pulse intensity was obtained using a 3.5% reflecting quartz beam-splitter. The sample was moved along the Z-axis using a Newport 426/431 series linear stage of 10 µm resolution. The beam waist radius was . The input and transmitted signals were measured with THORLABS PDA55 model Si detectors, with their output displayed on a TEXTRONIX TDS360 model digital real-time oscilloscope. To avoid overheating of the irradiated sample spot, the incident beam was blocked between successive transmission measurements. A schematic layout of the optical set-up is provided in Fig. 1 .
2.4.1. Analysis of the nonlinear transmission
Analysis of the Fresnel-reflection-corrected light transmission was performed according to expressions developed for slow and fast saturable absorbers [30]. These expressions relate to a three-level optical system as shown in Fig. 2 .
Fig. 2 Schematic diagram of a three-level system used for modeling of saturable absorption. Optical transitions are marked with solid arrows; non-radiative intra-band transitions are marked with a wiggled one.
Species at the S(0) ground state band are excited by the incident photons to the S(1) first excited state band. The probability for this process is given by the ground-state absorption cross section . Electrons at the first excited band level can non-radiatively decay to the S(1) lowest state level at a very fast rate. Subsequent photons may then induce further excitation to the S(2) higher lying band levels, with a cross section . The effective spontaneous decay time of S(1) may be assumed to be either very long or very short compared to the light pulse duration. Increased light intensity brings about a reduction in the ground-state species concentration. If , the pulsed light transmission increases. In practical saturable absorbers, the transmission never reaches 100%, which is a result of the photon absorption by species in their S(1) excited state.
2.4.1.1. Slow saturable absorber – the modified Frantz-Nodvik Solution
The term “slow absorber” is used for the case where the light pulse duration is very short compared to the excited state decay time . An analytical solution for the transmission of a real saturable absorber is given in a closed form [30] as
where is the sample thickness, is the transmission in the low pulse intensity limit, is the maximal transmission achieved at very high pulse intensities, is the absorbers density and is the transmission of an “ideal” saturable absorber where is the input beam fluence in units of photons per unit area. This expression is known as the Frantz-Nodvik equation [40]. In the case of a transversely Gaussian beam distribution, the half peak beam fluence should appear in Eq. (3) instead of [30].2.4.1.2. Fast saturable absorber – the modified Hercher Solution
This case occurs when the relaxation of excited atoms is very fast, namely the excited-state decay time is short compared to the pulse duration. The analytical solution for the photon flux density (photons per unit time per unit area) is given in a closed form [30] as
where is the input beam intensity in units of photons per unit area per unit time, and . This expression is known as Hercher’s equation [41]. In the case of a transversely Gaussian beam distribution, the half peak beam intensity should appear in Eq. (4) instead of [30]. Although Eq. (4) constitutes a closed equation for as a function of , this expression should be very useful for curve fitting of measured data, as one may readily swap between the and axes.3. Results and discussion
3.1. Morphology
MWNTs were imaged by E-SEM over several steps of the composite glass processing. Figure 3(a) shows a grain of the MWNTs powder along with two other particles. The grain appears as a very dense particle of an approximately 25 µm diameter, composed of tightly agglomerated nanotubes. The image is a typical micrograph of the as-purchased MWNTs powder. As such, the MWNTs cannot be directly used for the composite glass preparation. During the first processing step, the MWNTs are dispersed in ethanol with the aid of ultrasonication. During ultrasonication, vibrational energy is delivered to the system, inducing disentangling of the agglomerates. Dispersed nanotubes of the MWNT/ethanol suspension are shown in Fig. 3(b). The agglomeration of the nanotubes appears to have been reduced dramatically. The nanotubes appear quite isolated, with lengths ranging between approximately 1 and 6 µm. The large distribution of lengths implies that the nanotubes were also fractioned by the ultrasonication [42,43]. A cross-section of a MWNT/hybrid-glass is shown in Fig. 3(c). The smooth background demonstrates the uniform and nonporous glassy matrix surface, with some nanotube edges sticking out.
Fig. 3 E-SEM images of (a) a MWNTs powder grain, as purchased; (b) MWNT/ethanol suspension after drying; (c) a MWNT/hybrid-glass composite surface
In spite of the said dispersion process, occasionally, some inhomogeneous distribution of the MWNTs in the glasses was obtained. It manifested itself in the appearance of several “dark dots”, each 10-50 μm in diameter, across the uniform slab. Throughout our optical transmission experiments we verified that only optically uniform regions were used.
3.2. Vis-NIR spectroscopy
The effective absorption spectrum of the MWNTs’ suspension in ethanol is shown in Fig. 4 . The Nd:YAG 1064 nm laser wavelength is indicated on the abscissa for reference in our following experiments. The spectrum is entirely structureless, exhibiting a decrease in transmission with shortening wavelength. Light scattering is most likely the major factor causing the transmission reduction with wavelength shortening [24], thus bringing about the “effective” absorption coefficient to grow in that direction. The effective absorption spectrum for 0.3 mg/ml MWNT concentration in the 400-1500 nm range follows an empirical relation
where is the effective adsorption coefficient and is the wavelength. The lack of any pronounced structure is characteristic of MWNTs [2] as well as of long SWNTs; in the latter, pronounced absorption peaks in the vicinity of 1000 nm were observed for only very short (<1 µm) tubes [23]. The absorption of the composite glass compared to a pure hybrid glass is shown in Fig. 5 . As in Fig. 4, the Nd:YAG 1064 nm laser wavelength is indicated on the abscissa for reference in our following experiments. The composite glass exhibits the characteristic absorption bands of silica and its organic residues [32], superimposed on those of the MWNT background. The MWNT background spectrum exhibits a general agreement with that of the MWNT/ethanol suspension provided in Fig. 4, namely the absorption decreases with . However, the exact wavelength dependence is weaker than in Fig. 4; i.e. it does not follow the empiric relation of Eq. (5). We have not studied this behavioral difference further. We assume that light scattering at 1064 nm is negligible thus the absorption coefficient of the MWNTs/hybrid-glass is at 1064 nm for the particular MWNTs’ concentration in the measured sample.Fig. 5 Vis-NIR absorption spectrum MWNT/hybrid-glass containing 0.02 wt.% MWNT, compared to a pure hybrid glass. Both spectra corrected for Fresnel reflections.
3.3. Nonlinear transmission
At high light power densities, the sample undergoes a “bleaching” process. This can be clearly seen from the Z-scan measurement shown in Fig. 6 . Here, the optical transmission is shown as a function of the sample position along the beam path. At low laser beam intensities, i.e. at distances beyond ± 10 mm from the beam waist (Z = 0), the sample transmission is approximately 46%. As the sample approaches the waist position, the beam intensity increases, which leads to an increased transmission. The nonlinear phenomenon of increased transmission at high laser intensities is attributed to a saturated absorption of the MWNTs in the glass. The overall behavior, however, is not solely related to saturable absorption. Particularly, in a fresh sample, starting from one side on the Z axis and scanning towards the waist position, some decrease in transmission is obtained at the very close vicinity of the waist. It is, however a relatively small effect, that may perhaps be related to enhancement of a two-photon absorption process [7]. Furthermore, on moving further away from the waist position, the transmission pattern is not symmetrical with that obtained while approaching the waist. This asymmetry is most likely related to some changes in the glass properties induced by the light pulses, that develop and persist during the measurement, and quite long afterwards. In our present work, we have not further explored the dynamics nor nature of these changes. Our analysis to be described below, considers in fact an average of the enhanced transmission between the two sides of the waist position.
Fig. 6 Z-scan measurement: Optical Transmission of MWNT/hybrid-glass containing 0.02 wt.% MWNT as function of sample position Z along the beam. Beam waist radius ; sample thickness. Scan direction from left to right.
The results of Fig. 6 were modeled by the limiting cases of a slow or a fast saturable absorber expression, and are shown in Figs. 7 and 8 respectively. The figures show the measured data of the composite hybrid glass transmission as function of the peak pulse fluence and the peak pulse intensity, and their fittings for each model. As the peak pulse fluence/intensity increases, the transmission exhibits an increase which is initially linear, but which then saturates. At the turn to saturation, most of the absorbing species in the glass have been excited to the S(1) state level by the first arriving photons. Later photons impinging the absorbing species exhibit a higher probability for traversing the sample. The fact that the saturated value never reaches 100% indicates that excited-state absorption by an transition sets in as a result of the enhanced population in the S(1) band (Fig. 2).
Fig. 7 Optical transmission of MWNT/hybrid-glass containing 0.02 wt.% MWNT as function of the peak beam fluence (same results as Fig. 6). Fit curve is by the modified Frantz-Nodvik model (Eqs. (2)-(3)) for a slow saturable absorber (SA).
Fig. 8 Transmission of MWNT/hybrid-glass containing 0.02 wt.% MWNT as function of peak beam power (same results as Fig. 6). Fit curve by Eq. (4) for a fast saturable absorber (SA).
In Fig. 7 we show the same experimental data of Fig. 6 and the calculated fit according to the slow saturable absorber model (Eqs. (2) and (3)), where the optical transmission is plotted vs. the peak beam fluence. Justification for attempting this model is based on excited state lifetimes of ~3-10 ns estimated by Miyauchi et al. [44], which are in fact quite longer than our pulse duration of only 1 ns. Moreover, Park et al. [45] have recently found that the triplet excited-state lifetime is even orders of magnitude longer, ~15 µs. As a word of caution, however, we should add that both latter values were estimated for SWNTs and not for MWNTs.
The physical parameters used for the fit curve in Fig. 7 (see inset in the figure frame) exhibit reasonable agreement with those obtained by several other researchers, at least in the order of magnitude. Particularly, the estimated ground state absorption cross section is , in good agreement with that of a single carbon atom, , measured at [46]. However, our value is still an order of magnitude smaller than the value measured at [47]. Both latter values were reported per single carbon atom in SWNTs. In MWNTs, Ni and Bandaru [48] measured per carbon atom at 473 and 633 nm, which is approximately a factor of 5 larger than their measured value per single atom in SWNTs. Thus the value we have estimated by the slow saturable absorber model is within the range of previously reported values per carbon atom in CNTs. The excitation wavelength and the embedding matrix [49] may play an important role in determining CNTs’ absorption cross sections.
For the excited state absorption cross section we have further obtained (within the slow absorber model) the value . To the best of our knowledge, this is the first time an estimation of is reported for CNTs. With respect to other carbon-nanotube species, the singlet excited state absorption cross section of fullerenes at 532-540 nm was reported to be in the range of [50], which is larger than their ground state absorption cross section. Thus their samples exhibit a reverse saturable absorption phenomenon.
Another issue to consider is the fact that the estimated absorbers density is about a factor of 5 smaller than the nominal density of carbon atoms incorporated into the glass, . This discrepancy may perhaps be rationalized by assuming that band formation in the MWNTs causes a reduction in the effective density of states.
In Fig. 8 we show the experimental data shown in Fig. 6 and the calculated fit according to the fast saturable absorber model (Eq. (4)), where the optical transmission is plotted vs. the peak beam power. Justification for attempting this alternative model is based on numerous reported excited state recovery lifetimes in SWNTs [15,17–19,51,52] as well as in MWNTs [12], which are usually at least two orders of magnitude shorter than our pulse duration of 1 ns. The fit parameters indicated in Fig. 8 are based on assuming the value which is the nominal carbon atoms concentration incorporated into the glass. The ground and excited-state absorption cross-sections estimated by the fit curve are and , respectively. The estimated excited-state lifetime is ns, consistent with the assumption of a fast absorber, yet not very much shorter than the pulse duration of 1 ns. Notably, the two sets of fit parameters related to the diametrically opposite assumptions of a slow or a fast absorber are quite similar, and physically plausible. We may thus conclude that our absorber is neither slow nor fast under the 1 ns long pulses at 1064 nm; namely the excited state lifetime is also of the order of 1 ns, yielding reasonable fits for both model assumptions. Obviously, direct measurement of for every studied sample is of critical importance, both for obtaining accurate estimates of the absorption cross-sections, and for properly assessing the material suitability in any technological application. We intend to perform direct measurement of in our future studies.
It should be noted, that fitting attempts of our data to a dielectric function of a constant, obviously negative Im(χ(3)), always failed. This strongly supports our modeling approach of excited state absorption. Still, for the benefit of researchers who are used to assessment of nonlinear optical properties through the Im(χ(3)) parameter, we should indicate that its order of magnitude is around |10−10| esu, similar to values obtained by others [15].
With respect to technological applications, it should be mentioned that saturable absorption allows applications for Q-switching, mode-locking, pulse-shaping and noise suppressing in fast pulsing lasers [13,15–22].
4. Conclusions
Novel MWNT/hybrid-organic-inorganic glass composites containing 0.02 wt.% MWNTs were prepared by solutions mixing in a fast-sol-gel route. The composites had an approximately 50% visible light transmission along with a strong “bleaching” effect when irradiated with high intensity, 1 ns-long pulses at 1064 nm. This nonlinear phenomenon is attributed to saturated absorption of the MWNTs, and is analyzed using both slow and fast saturable absorber models of a three-level energy scheme. Both models yield very good fits with reasonable physical parameters. Quite arbitrarily, we choose the slow absorber model as representative. The ground state absorption cross section was estimated as , which is in good agreement with the known value per single carbon atom. The cross section for excited state absorption was estimated as , and is reported for the first time for CNTs. The saturable absorption phenomenon allows possible applications of the MWNT/hybrid-glass composites as promising candidates for applications in fast laser passive mode lockers and limiters. Obviously, direct measurement of the excited-state decay time for every studied sample is of critical importance, both for obtaining accurate estimates of the absorption cross-sections, and for properly assessing the material suitability in any technological application.
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