Today, one could not dismiss the pertinence of opt-ronics in the frame of modern observation systems.These notions of optronics directly refer to the useof an optical system able to visualize or detect a par-tially hidden object using its optical emission, eithervia reflection of ambient light or via its own emission.The usable optical radiations correspond to specific
spectral ranges where the atmosphere is transpar-ent: the visible–near-IR (so-called band I, 0:3 μm <
λ < 2 μm) and the mid-IR (band II, 3 μm < λ <5 μm, and band III, 8 μm < λ < 12 μm).
Besides the development of optical detection sys-tems, numerous studies have focused on the develop-ment of optronic countermeasure systems able todazzle or damage such optical detection systems.The concept and interest in optical limitation has in-creased since the early 1980s to face the danger ofdazzling or destruction of optical systems as lasersbecome more and more compact and powerful.
The active principle of an optical limiter consists ina diminution, down to a certain level, of the incidentlaser fluence reaching the detector to be protected.Consequently, the optical limiting device should be
optically transparent for incident laser light of lowfluence level. Instead of using additional shuttersor switches, the most efficient optical limitingmethod is to take advantage of the nonlinear opticalresponse of certain materials. There are two majormechanisms governing the optical limitation: the in-stantaneous nonlinearities related to the third-ordernonlinear susceptibility χð3Þ, responsible for two-photon absorption and the Kerr effect, and the cumu-lative nonlinearities covering thermal lensing andnonlinear scattering effects.One of the first optical limiters, reported by Leite
et al. [1] in 1967, was based on a thermal lensingeffect; this mechanism was studied for the first timeby Gordon et al. in 1964 [2]. Numerous optical limit-ing studies have been performed with nanomaterialsin the visible and near-IR ranges; see, for example,[3–8].To our knowledge, only very few optical limiting
studies have been performed in the IR band III at λ ¼10:6 μm [9–15]. Furthermore, the study of the opticallimiting performance of nanomaterial suspensions atλ ¼ 10:6 μm has never been reported.In this paper, we report on the optical limiting prop-
erties ofmultiwalled carbon nanotube (MWCNT) sus-pensions submitted to intense CO2 nanosecond laserpulses at λ ¼ 10:6 μm. In Section 2, the Z-scan andpump-probe methods, as well as the optimization ofthe one-dimensional (1D) carbon-based nanomaterialsuspension, will be presented in detail. A comparisonbetween the experimental and the theoretical non-linear refractive indices will further be given, andthe time constants for thermal lensing resulting frompump-probe experiments will also be discussed.
2. Experimental
In our experiments, the conventional Z-scan method,both in an open- and a closed-aperture scheme, wasused [9]. The experimental setup described in Fig. 1in the closed-aperture configuration is very close tothe one described by Sheik-Bahae et al. [10].The irradiation was carried out with a CO2 laser
(Lumonics 960 SSM) emitting at λ ¼ 10:6 μm and de-livering single pulses of τp ¼ 160ns pulse width(FWHM) from a Gaussian laser beam, with an en-ergy of Ep ¼ 30mJ. A 7mm thick CaF2 attenuatingplate was placed in the optical path to reduce the
pulse energy to its effective value of Ep ¼ 2mJ.The laser was used in a single-pulse mode to preventthermal accumulation effects. It is worth noting thatall the optics used in these experiments were espe-cially adapted to the emitting wavelength, i.e., AR-coated ZnSe lenses and optics, as well as gold-coatedmirrors and integrating spheres. After passingthrough a spatial filter (L1, f 1 ¼ 100mm; D, 3mmpinhole; L2, f 2 ¼ 200mm), the beam is focused intothe sample area with a converging lens L3, f 3 ¼125mm. The probe is mounted on a motorized trans-lating stage. The beam waist radius, w0, at the focalplane of L3, was experimentally determined to bew0 ¼ 120 μm (at 1=e2 intensity level). The trans-mitted beam was collected in an integrating spherewith a 10mm aperture. This latter was kept at a dis-tance of 310mm from lens L3. A calibrated photo-diode PD1 (model PVM-10.6 from Vigo System SArise time < 1ns) was selected to measure the trans-mitted pulse energy and the time profiles were mon-itored on a digital oscilloscope (Lecroy LT374L). Theinput pulse is characterized with the same method[integrating sphere and calibrated photodiode PD2(model PVM-10.6 from Vigo System SA), see Fig. 1].The beam is directed to the center of the integratingsphere aperture with the CaF2 attenuator, for whicha slight off-axis tilt was applied.
The same laser as that mentioned above acted asan excitation source in pump-probe experiments(Fig. 2). The cw radiation of a He–Ne laser was usedas the probe beam; both radiations were combinedwith a dichroïc beam splitter, M, and focused on thesample using the converging lens L3, f 3 ¼ 125mm.To reach the perfect overlap between the pumpand the probe beams in the focus plane, lens L3was removed and the spatial overlap in the far field(a few meters) was adjusted. This operation was alsorepeated at the focal point of L3. The probe beam iscaptured by a fast photodiode (Osram BPX65, risetime 12ns) through an optical fiber that has alsobeen carefully axially positioned. On the other hand,the pump beamwas directed to an integrating spherein the means of previously mentioned CaF2 plate andmeasured with a calibrated photodiode PD2. Finally,both signals were monitored on a digital oscilloscope(Lecroy LT374L).
The materials used in this study are commerciallyavailable MWCNTs (Pyrography-III, type PR-24, XT-PS grade). For our optical measurements, 3mg of the
CO2 Laser
L1 L2D
CaF2
L3 Sample
-z +z
A
PD1
PD2Fig. 1. Z-scan experimental setup in a close aperture scheme.L1, D, and L2, spatial filter; L3 focusing lens, PD1 and PD2, photo-diodes. In the open-aperture Z-scan method, the pinhole A is re-moved and PD1 is placed right behind the sample.
CO2 Laser
L1 L2D CaF2 L3Sample
-z +z
PD2
to Photodiode
Optical FiberM
He-NeLaser
Fig. 2. Pump-probe experimental setup. M, dichroïc beam split-ter; L1, D, and L2, spatial filter; L3, focusing lens; PD1, photodiode.
1D nanomaterial were suspended ultrasonically for15 min in chloroform without the use of surfactant.The addition of chloroform was adjusted in order toset the total amount of the sample to 20 g. Chloro-form was selected for its excellent dispersant proper-ties for carbon nanotubes and also for its relativelygood transparency at λ ¼ 10:6 μm.1mm thick cells with KCl windows, which have
been chosen for their excellent transparency atλ ¼ 10:6 μm, were used. It has to be pointed out thatthe experimental cell thickness fulfills our statementthat the medium is considered to be thin. Indeed, ifwe assign L to the cell thickness and z0 to the diffrac-tion length, the condition z0 ≫ L has to be accountedfor. The characteristic diffraction length given byz0 ¼ πW0
2=λ is equal to 4:3mm; therefore, the thinmedium approximation is valid. Figure 3 displaysthe linear transmittance from Fourier transform in-frared spectroscopy measurements of the carbon-nanotube-based suspension compared to that of purechloroform. As seen from this graph, the linear trans-mittance at λ ¼ 10:6 μm is about 40%.
3. Results and Discussions
Hereafter, the third-order refractive nonlinearitieswill be considered, where η is expressed as
n ¼ n0 þn2
2jEj2 ¼ n0 þΔn: ð1Þ
Figure 4 shows the Z-scan signature of the MWCNTsample in a closed-aperture scheme. The observedpeak-to-valley curve, as interpreted as a self-defocusing effect [10], reveals a negative refractivenonlinearity [16]. In the following, we will exposethe evidence of the thermal origin of the nonlinearrefraction Δn.The precise determination of the on-axis phase dis-
tortion or phase shift, ΔΦ0, allows one to calculate
the nonlinear refractive index change,Δn. For calcu-lations of nonlinear parameters, equations of theZ-scan theory were used [17]:
ΔTp−v ≈ 0:406ð1 − SÞ0:25jΔΦ0j; ð2Þ
ΔΦ0 ¼ −2πλ n2I · Leff ¼ −
2πλ Δn · Leff : ð3Þ
ΔTp−v represents the difference between the peak-to-valley normalized transmittance, ΔTp−v ¼ Tp − Tv,whereas S is the aperture factor defined as [9]
S ¼ 1 − exp�−2
�rawa
�2�: ð4Þ
In the relation of Eq. (4), the aperture radius and thebeam radius in the plane of the integrating sphereare denoted ra andwa, respectively. It is to be pointedout that the relationship in Eq. (2) is valid as long asthe condition of the phase distortion jΔΦ0j ≤ π is ful-filled [9]. Our study is in good accordance with thishypothesis.
Considering our experimental case wherera=wa ¼ 1=2, an aperture factor of S ¼ 0:4 is ob-tained. Consequently, Eq. (2) can be written as
ΔTp−v ¼ 0:357 · jΔΦj: ð5Þ
As we can see from Eq. (5), the parameterΔTp−v is alinear function of the phase retardation, ΔΦ0. Thisparameter ΔTp−v, directly extracted from the experi-ment, allows an easy and qualitative estimation ofthe magnitude of the nonlinear refractive index var-iation, Δn, after the medium has been submitted toan intense electromagnetic wave. The combination ofEqs. (3) and (5) leads to the expression of Δn:
0
10
20
30
40
50
60
70
80
90
100
Chloroform MWCNTs in Chloroform
Tra
nsm
ittan
ce [
%]
3 4 5 6 7 8 9 10 11 12
Wavelength [µm]
Fig. 3. FTIR spectrum giving the linear transmittance of theMWCNT suspensions in chloroform (solid curves) compared topure chloroform (dashed curves). The linear transmittance at λ ¼10:6 μm is about 40%.
-20 -15 -10 -5 0 5 10 15 200,0
0,2
0,4
0,6
0,8
1,0
1,2
Tra
nsm
ittan
ce [
au]
Position Z [mm]
Fig. 4. Z-scan signature of the MWCNT/chloroform sample in aclosed-aperture scheme. The observed peak-to- valley curve,interpreted as a self-defocusing effect, reveals a negative refractivenonlinearity.
Leff , defined as the effective length of the sample, isobtained as follows:
Leff ¼1 − expð−αLÞ
α ; ð7Þ
where L and α represent the length of the sample andthe linear absorption coefficient, respectively. Usinga value of α ¼ 9:7 cm−1 (at λ ¼ 10:6 μm), determinedexperimentally, Leff ¼ 0:06 cm was obtained. There-fore, the quantitative application of Eq. (6) leads toa nonlinear index change of Δn ¼ −7:5 · 10−3. More-over, if the relation Δn ¼ n2 · I is applied with thepeak irradiance I ¼ 2:8 · 107 W=cm2, the nonlinearrefractive index, n2, can be deduced:
n2 ¼ −2:7 · 10−10 cm2=W:
If only the pure thermal contribution for the non-linear refraction is assumed, one can express thethermally induced refractive index change as [18,9]
hΔntheri ¼ −dndT
ΔT ¼ −dndT
Iτpα2ρCv
; ð8Þ
where ρ is the chloroform density (ρ ¼ 1:48 g · cm−3,Cp is its specific heat (Cp ¼ 1:45 J:g−1 · K−1 [18]),dn=dT is the thermo-optical coefficient (dn=dT ¼5:9 · 10−4 K−1 [18]), whereas the bracket stays forthe time-averaged quantity (factor 1=2 in Eq. (8)).In these conditions, hΔntheri ¼ −60 · 10−3 was ob-
tained. In the same manner, the pure thermal refrac-tive index, n2ther, can be deduced:
n2ther ¼ −2:1 · 10−10 cm2=W:
There is a good accordance between n2 and n2ther,suggesting that the major contribution to the non-linear response measured by Z-scan is of thermalorigin.
However, there still remains a minor discrepancybetween n2 and n2ther. This may be attributed, on onehand, to some doubts in the estimation of the laserirradiance and, on another hand, to an additionalphase distortion to the phase term of the sphericalwave due to lensing in the medium [19].
Indeed, it seems obvious that during the propaga-tion of the 160ns pulse, a given amount of the totalenergy is absorbed by the MWCNTs, followed by ahighly transient thermal coupling with the surround-ing medium. Subsequently, the heat is transferredinto the solvent, resulting in a variation of the refrac-tive index through density reduction. The occurrenceof such thermal lens effects in carbon nanotubes/chloroform suspensions have already been reportedby Vivien et al. in the nanosecond time scale for thevisible and near-IR spectral ranges [20,21].
The illustration of the thermal lens observed in asuspension of MWCNTs in chloroform is given inFigs. 5. The picture in Fig. 5(a) results from high-speed digital video imaging (HSDVI) using a PhotronFastcam APX-RS and has been recorded along theoptical axis at a frame rate of 4200Hz. This pictureclearly shows the laser-induced sound wave propa-gating across the beam area (circled zone). TheHSDVI picture of Fig. 5(b) has been obtained nor-mally to the optical axis at a frame rate of 6000Hz;one can clearly see the beam caustic during thepropagation, as well as the gradient of the nonlinearrefractive index change.
What is also clearly evidenced in Fig. 4 is thestrong asymmetry in the peak-to-valley behaviorwith respect to the zero transmittance line. Suchan effect has already been reported by Brochardet al. [18] and Vivien et al. [21]. The occurrence ofa further process, such as nonlinear scattering inaddition to nonlinear refraction, is most probably re-sponsible for this asymmetry. Indeed, open-apertureZ-scan experiments have been performed to check forthis contribution, and the results are shown and com-pared in Fig. 6 in the cases of pure chloroform andMWCNT suspension. As compared to the purechloroform, one can observe a strong transmittanceloss around z ¼ 0 for the MWCNT suspension, whichis the signature of a nonlinear scattering effect.
Fig. 5. (Color online) (a) HSDVI picture of the laser-induced sound wave propagating across the beam area (circled zone) recorded alongthe optical axis at a frame rate of 4200Hz. (b) HSDVI picture obtained perpendicularly to the optical axis at a frame rate of 6000Hz. Thebeam caustic during the propagation can be observed clearly.
Furthermore, it is to be pointed out that scatteringcenters, in the form of microbubbles, can be visual-ized in appropriate conditions, therefore, confirmingthe latter assumption.The pump-probe method is well adapted to have a
quantitative assessment of the temporal behavior inthe 160ns regime. As mentioned above, after absorp-tion of the laser pulse, the medium starts to expandand the phenomenon propagates further as an acous-tic wave. The buildup time of the thermal lens is di-rectly related to the time necessary for the acousticwave to spread across the beam area. In a first ap-proximation, this latter time, τr, is estimated as
τr ¼w0
vs; ð9Þ
where vs denotes the sound velocity in the medium,i.e., chloroform in the present case: vs ¼ 990m · s−1.Thus, taking the waist radius w0 ¼ 120 μm, onecan easily deduce a rise time τr ¼ 121ns. Actually,the rise time of the thermal lens, τr, is of the sameorder of magnitude as the first intense part of thepulse shape with a pulse width, τp, shown in Fig. 7.However, the condition τr < τp still holds, meaningthat the occurrence of the thermal lens can be consid-ered as instantaneous [22]. The probe intensitydecay is also shown in Fig. 7. The signal decay exhi-bits two regions separated with a discontinuity or abump. The early probe decay well overlaps with thepump peak power density profile, whereas the sec-ond part of the probe decay occurs with the trailingpart of the pump signal. Figure 8 is a local view of theearly probe decay shown in Fig. 7; in an attempt toestimate the relaxation time τ1, we applied a simplefirst-order exponential decay model and fitted the ex-perimental probe signal. As shown in the enclosedwindow of Fig. 8, a value of τ1 ¼ 149ns is obtained,which is, in a first approximation, in good agreementwith the theoretical expansion time for the acoustic
wave, τr. The discontinuity or bump displayed inFig. 7 is thought to arise from the solvent vapor cav-itation bubbles that scatter the probe beam [20]. In-deed, this latter fact is in good accordance with ourexperimental model where, right after the expansionof the thermal lens, solvent microbubbles start togrow, scatter the laser beam, and, consequently, leadto a further drop of the probe signal, as shown in thesecond part of the decay in Fig. 7. This transmittanceloss occurs with the trailing part of the pump beamand finds a place on a microsecond time scale. Thesame type of fit as previously mentioned yields arelaxation time of τ ¼ 1:8 μs. The transmittancerecovers its initial level in a much longer time scalesince the thermodynamic equilibrium has to bereached via thermal conduction, on one hand, andthe coalescence of microbubbles has to disappearfrom the medium, on the other hand. This recovery
-30 -20 -10 0 10 20 30 40
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
1,1
Nor
mal
ized
Tra
nsm
ittan
ce
Position Z [mm]
Fig. 6. Compared open Z-scan signature of pure chloroform (opencircles) and MWCNT/chloroform suspension (filled circles). Com-pared to the pure chloroform, a strong transmittance loss aroundz ¼ 0 can be observed for the MWCNT suspension, which is thesignature of a nonlinear scattering effect.
0 2 4 6 8 10
0,0
0,2
0,4
0,6
0,8
1,0
Region 2
Region 1
Probe intensity
Pump intensity
Tra
nsm
ittan
ce [
a.u]
Time [µs]
Fig. 7. Pump and probe beam intensity decays in a MWCNT/chloroform suspension. The discontinuity or bump shown isthought to arise from the solvent vapor cavitation bubbles thatscatter the probe beam.
0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35
0,0
0,2
0,4
0,6
0,8
1,0
Probe signal (acoustic)
Pump signal (partly)
Tra
nsm
ittan
ce [a
.u]
Time [µs]
Fig. 8. Local view of the early probe intensity decay shown inFig. 7. A part of the pump signal is also displayed.
time or, as elsewhere reported as, decay time is ex-pressed as [23]
τd ¼ ρw20Cp
4K; ð10Þ
where K represents the thermal conductivity ofchloroform (K ¼ 0:119W ·m−1 · K−1). In the presentcase, one can easily deduce τd ¼ 65ms, which is ingood concordance with the experimental probe signalrecovery time depicted in Fig. 9.
4. Conclusions
The optical limiting behavior of MWCNT suspen-sions in chloroform exposed to IR laser irradiationat λ ¼ 10:6 μm has been reported. The pure thermalorigin of the optical limiting has been demonstratedfor the 160ns time scale under study. The Z-scanmethod has been revealed to be an excellent andhighly sensitive tool for the experimental assessmentof the nonlinear refractive index. Also, this techniqueallowed us to show evidence for the contribution ofnonlinear scattering in the process. An experimentalmodel for the optical limiting behavior of MWCNTsuspensions in chloroform is proposed, in close agree-ment with related activities published in the litera-ture. The occurrence of a laser-induced thermal lensthrough the absorption of energy from the MWCNTsand subsequent heat transfer to the solvent, followedby solvent vapor bubble growth, is the main factorgoverning the observed drop in the transmittance.Pump-probe experiments have been performed to ob-tain some quantitative estimation of the rise timeand decay time of the thermal lensing phenomenon.It was found that the early probe signal decay,τ1 ¼ 149ns, was of the same order of magnitude asthe rise time of the thermal lens, τ1 ¼ 149ns.Furthermore, when the nonlinear scattering is ac-counted for, a total decay time of τ ¼ 1:8 μs was ob-tained. A recovery time for the thermal lens of
several tens of milliseconds has been experimentallydetermined, which well overlaps with the value cal-culated from the theory.
The authors thank Y. Suma and Y. Boehrer fortheir expertise in HSDVI. The contribution ofF. Lacroix and M. Christen for the design of theexperimental setup is also gratefully acknowledged.
References1. R. C. C. Leite, S. P. S. Porto, and T. C. Damen, “The thermal
lens effect as a power-limiting device,” Appl. Phys. Lett. 10,100 –101 (1967).
2. J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, andJ. R. Whinnery, “Long-transient effects in lasers with insertedliquid samples,” J. Appl. Phys. 36, 3–8 (1965).
3. L. W. Tutt and T. F. Boggess, “A review of optical limitingmechanisms and devices using organics, fullerenes, semicon-ductors and other materials,” Prog. Quantum Electron. 17,299–338 (1993).
4. D. Vincent, S. Petit, and S. L. Chin, “Optical limiting studies ina carbon-black suspension for subnanosecond and subpico-second laser pulses,” Appl. Opt. 41, 2944–2946 (2002).
5. G. L. Fischer, R. W. Boyd, T. R. Moore, and J. E. Sipe, “Non-linear-optical Christiansen filter as an optical power limiter,”Opt. Lett. 21, 1643–1645 (1996).
6. L. W. Tutt and A. Kost, “Optical limiting performance of C60
and C70 solutions,” Nature 356, 225–226 (1992).7. V. Joudrier, P. Bourdon, F. Hache, and C. Flytzanis, “Nonlinear
light scattering in a two-component medium: optical limitingapplication ,” Appl. Phys. B 67, 627–632 (1998).
8. O. Durand, V. Grolier-Mazza, and R. Frey, “Temporal andangular analysis of nonlinear scattering in carbon-blacksuspensions in water and ethanol,” J. Opt. Soc. Am. B 16,1431–1438 (1999).
9. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W.Van Stryland, “Sensitive measurement of optical nonlineari-ties using a single beam,” IEEE J. Quantum Electron. 26,760–769 (1990).
10. M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, “High-sensitivity, single-beam n2measurements,” Opt. Lett. 14,955–957 (1989).
11. M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, and E.W. Van Stryland, “Nonlinear refraction and optical limiting inthick media,” Opt. Eng. 30, 1228–1235 (1991).
12. M. O. Baumgartner, D. P. Scherrer, and F. K. Kneubühl, “Time-dependent thermal lensing and Kerr nonlinearity in CS2 withCO2-laser radiation,” Appl. Phys. B 62, 473–477 (1996).
13. A. C. Walker, A. K. Kar, W. Ji, U. Keller, and S. D. Smith,“All-optical power limiting of CO2laser pulses using cascadedoptical bistable elements,” Appl. Phys. Lett. 48, 683–685(1986).
14. E. K. Kolobkova, A. A. Lipovskii, V. G. Melehin, V. D. Petrikov,A. M. Malayarevich, and V. G. Savitski, “PbSe quantum-dot-doped phosphate glasses as material for saturableabsorbers for 1- to 3-μm spectral region,” Proc. SPIE 5449,184–187 (2004).
15. F. Lacroix, J. P. Moeglin, M. Comet, D. Spitzer, and M. R.Schäfer, “Protection optique en bandes II and III,” ISL Inter-nal Report (2006).
16. S. R. Mishra, H. S. Rawat, M. P. Joshi, S. C. Mehendale, and K.C. Rustagi, “Optical limiting in C60 and C70 solutions,” Proc.SPIE 2284, 220–229 (1994).
17. R. A. Ganeev, A. I. Ryasnyansky, S. R. Kamalov, M. K. Kodirov,and T. Usmanov, “Nonlinear susceptibilities, absorption coef-ficients and refractive indices of colloidal metals,” J. Phys. D34, 1602–1611 (2001).
Fig. 9. Probe signal intensity recovery time of a MWCNT/chloroform suspension. From this graph, one can easily deducea recovery time of τd ¼ 65ms.
18. P. Brochard, V. Grolier-Mazza, and R. Cabanel, “Thermalnonlinear refraction in dye solutions: a study of the transientregime,” J. Opt. Soc. Am. B 14, 405–414 (1997).
19. M. Born and E. Wolf, Principles of Optics 7th ed. (CambridgeU. Press, 1999).
20. L. Vivien, D. Riehl, E. Anglaret, and F. Hache, “Pump-probeexperiments at 1064nm in singlewall carbon nanotubesuspensions,” IEEE J. Quantum Electron. 36, 680–686(2000).
21. L. Vivien, P. Lançon, D. Riehl, F. Hache, and E. Anglaret, “Car-bon nantubes for optical limiting,” Carbon 40, 1789–1797(2002).
22. D. I. Kovsh, D. J. Hagan, and E. W. Van Stryland, “Numericalmodeling of thermal refraction inliquids in the transient re-gime,” Opt. Express 4, 315–327 (1999).
23. B. Yu, C. Zhu, F. Gan, Y. Huang, “Optical limiting properties ofIn2O3 nanoparticles under cw laser illumination,” Opt. Mater.7, 103–107 (1997).
