ARTICLE IN PRESS

Optics & Laser Technology 42 (2010) 956–959

Contents lists available at ScienceDirect

Optics & Laser Technology

0030-39

doi:10.1

� Corr

Departm

E-m

journal homepage: www.elsevier.com/locate/optlastec

Nonlinear properties of polyurethane-urea/multi-wall carbon nanotubecomposite films

Jin Wang a, Ya-Xian Fan a, Jing Chen b, Bing Gu a, Hui-Tian Wang a,b,�

a Nanjing National Laboratory of Microstructures and Department of Physics, Nanjing University, Nanjing 210093, Chinab School of Physics, Nankai University, Tianjin 300071, China

a r t i c l e i n f o

Article history:

Received 28 October 2009

Received in revised form

1 January 2010

Accepted 7 January 2010Available online 25 January 2010

Keywords:

Z-scan technique

Nonlinear refraction

Nonlinear absorption

92/$ - see front matter Crown Copyright & 2

016/j.optlastec.2010.01.014

esponding author at: Nanjing National Labor

ent of Physics, Nanjing University, Nanjing 2

ail addresses: htwang@nju.edu.cn, htwang@n

a b s t r a c t

The third-order nonlinear optical properties of polyurethane-urea/multiwalled carbon nanotube

composites (PU/MWNT) films with different MWNT concentrations are investigated by the use of

the Z-scan technique at a wavelength of 532 nm with a pulse duration of 8 ns. The results reveal that the

nonlinear refraction and absorption coefficients are linearly dependent on the MWNT concentration.

The negative nonlinear refraction effect is validated from the closed-aperture Z-scan measurements. We

find that PU/MWNT films are promising nonlinear optical materials, and the nonlinear coefficients can

be controlled.

Crown Copyright & 2010 Published by Elsevier Ltd. All rights reserved.

1. Introduction

Nonlinear optical materials are always of considerable interestdue to their wide range of potential applications, such as in opticallimiting and in all-optical photonics devices. Therefore, a largenumber of materials have been synthesized and their nonlinearoptical properties have been explored. Some carboneous materi-als among them have been shown to be promising nonlinearoptical materials, such as fullerenes, carbon black suspensions(CBS), single-wall and multi-wall carbon nanotubes [1–4].Recently, the third-order nonlinear properties of the multi-wallcarbon nanotubes (MWNT) and single-wall carbon nanotubes(SWNT) suspensions (in water and chloroform) and solutions (inethylene glycol, DMF, and ethanol) have been investigated [5–12].For instance, Sun et al. [3] and Vivien et al. [4] have studied firstlythe nonlinear properties of MWNT and SWNT suspensions,respectively, and compared their optical limiting performanceswith those of CBS and C60fullerenes. Jin et al. [6] have measuredthe nonlinear optical properties of polymer–MWNT solutions inDMF by using the Z-scan technique with using nanosecond laserpulses at 532 nm, and showed that the polymer–MWNT compo-sites possess strong nonlinear optical properties. O’Flaherty et al.[7] explored the nonlinear optical extinction in PmPV/MWNTsuspension with the open aperture Z-scan using nanosecond laserpulses at 532 nm.

010 Published by Elsevier Ltd. All

atory of Microstructures and

10093, China

ankai.edu.cn (H.-T. Wang).

However, carbon nanotube suspensions and solutions havesome disadvantages, such as the bad solubility and the uncertainhomogeneity, which can cause the measurement of the nonlinearproperties to be unreliable. Therefore, it is necessary to find a moreappropriate method to improve the solubility of carbon nanotubesand produce more homogeneously dispersed carbon nanotubesolutions. Alternatively, solid-state samples such as the thin filmscan avoid these disadvantages and can often be used in practicaloptical systems. Up to now, there have been few reports of studies ofthe nonlinear optical properties of well-dispersed homogeneousnanotube films [13,14]. In the present work, we will investigate onthe third-order nonlinear optical properties of polyurethane-urea/multi-wall carbon nanotube (PU/MWNT) films by using the closed-aperture (CA) and open-aperture (OA) Z-scan techniques with thenanosecond laser pulses at a 532 nm with a pulse duration of 8 ns.The PU/MWNT composite, which is fabricated by the sol–gel method[15], is a homogeneously dispersed nanotube film with a smoothsurface. Firstly, the CA and OA Z-scan schemes are performed for PU/MWNT films with different MWNT concentrations. By fitting the OAZ-scan data, nonlinear absorption coefficients are extracted. Based onHuygens–Fresnel integral principle, we fit the CA Z-scan curves toestimate the nonlinear refraction coefficients with the knownnonlinear absorption coefficients. The results show that the nonlinearabsorption and refraction coefficients increase as the MWNTconcentration increases.

2. Theory

We assume that the TEM00 Gaussian laser beam propagatesalong the +z direction. The incident electric field Ein at the input

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ARTICLE IN PRESS

J. Wang et al. / Optics & Laser Technology 42 (2010) 956–959 957

plane of the sample can be written as

Einðz; rÞ ¼ffiffiffiffiI0

p o0

oðzÞ exp �r2

oðzÞ2�

ikr2

2RðzÞ

" #ð1Þ

where oðzÞ ¼o0½ð1þz2=z20Þ�

1=2 is the beam radius at the z position(the focal plane is located at the z=0 plane), o0 is the waist radiusof Gaussian beam, R(z)=z[1+(z0/z)2] is the radius of curvature ofthe wave front at the z plane, z0 ¼ ko2

0=2 is the Rayleigh length ofthe focused beam, and k=2p/l is the wave number and l denotesthe wavelength of the laser in free space, I0 is on-axis intensity atthe focal plane. Considering the linear and nonlinear absorption ofsample, the transmitted intensity at the exit surface of the samplecan be expressed as

Ioutðz; rÞ ¼Iinðz; rÞexpð�a0LÞ

1þDfðz; rÞð2Þ

where the incident intensity Iin(z, r) is

Iinðz; rÞ ¼ jEinðz; rÞj2 ð3Þ

and the nonlinear absorption phase shift Df(z, r) is

Dfðz; rÞ ¼Df0

1þz2=z20

exp �2r2

oðzÞ2

" #ð4Þ

Here Df0=bI0Leff is the on-axis nonlinear absorption phase shift atthe focal plane and Leff=[1�exp(�a0L)]/a0 is the effective samplelength. a0 and b are the linear and nonlinear absorptioncoefficients, respectively. The normalized transmittance TOA(z)for the OA Z-scan can be calculated as

TOAðzÞ ¼

R10 Ioutðz; rÞdr

expð�a0LÞR1

0 Iinðz; rÞdrð5Þ

Based on the Huygens–Fresnel integral principle [17,18], thenormalized transmittance of the CA Z-scan, TCA(z), can beobtained. When a material exhibits nonlinear absorption andrefraction simultaneously, the total nonlinear phase shift from thecontribution of both effects can be expressed as follows:

Dfðz; rÞ ¼kgb

ln½1þDfðz; rÞ� ð6Þ

Here Df(z, r) is the nonlinear absorption phase shift described byEq. (4) and g is the nonlinear refraction coefficient. Then, theelectric field of the exit surface of the sample is

Eoutðz; rÞ ¼ Einðz; rÞexpð�a0L=2Þ½1þDfðz; rÞ�ðikg=b�1=2Þ ð7Þ

By applying the Huygens–Fresnel integral method [17,18]under the Fresnel approximation, the complex electric field Ea atthe far-field aperture plane can be obtained by

Eaðz; raÞ ¼k

ilðd�zÞexp

ipr2a

lðd�zÞ

� �Z 10

Eout expipr2

lðd�zÞ

� �J0

2prra

lðd�zÞ

� �rdr

ð8Þ

where d is the distance between the focal plane and the far-fieldaperture plane and ra is the polar coordinate in the far-fieldaperture plane. J0[ � ] is the Bessel function of zero order. Under thefar field condition (in general, dZ20z0), the normalized transmit-

Table 1Linear absorption coefficient a0 and the thickness L of the PU/MWNT films with differ

N 0.0% 0.1% 0.2% 0

a0 (cm�1) 5.54 27.55 50.13 5

L (mm) 0.3070.01 0.2370.02 0.2270.01

tance, TCA(z), can be expressed as

TCAðzÞ ¼

R Ra

0 jEaðz; raÞj2radra

expð�a0LÞR1

0 jEinðz; rÞj2rdr

ð9Þ

where Ra is the radius of the far-field aperture.

3. Experiments and analysis

The laser source used in experiment is a Q-switchedfrequency-doubled Nd:YAG laser operating at 532 nm with arepetition rate of 10 Hz and a pulse duration of 8 ns. The spatialprofile of the beam is of nearly Gaussian distribution. The beam isfocused by a 300-mm focal length lens to produce a focused beamwith the beam waist radius of about 20mm at the focal plane (theRayleigh length z0 is 2.4 mm). The OA and CA Z-scan experimentalsetups are the same as that used in Ref. [16]. The film is movedalong the z axis in the vicinity of the focal plane (the +z directionis the laser propagation direction). The transmitted intensity iscollected and then detected by a detector (J3S-10, Molectron Inc.).The linear transmittance of the far-field aperture, S, is constant at0.07 for the CA Z-scan measurements. We labeled the samples ofthe PU/MWNT composite films by concentration of MWNT, usingN to indicate the concentration. The diameter and the length ofMWNT are 15–30 nm and 0.5–50mm, respectively [15]. The filmthickness L is measured with a square caliper, and is listed inTable 1. It can be seen that the thickness for any film sample isconsiderably smaller than the Rayleigh length z0. In the presentwork, therefore, the thin-sample approximation can be usedsafely. The linear absorption coefficients, a0, for different films aremeasured by Spectrophotometer, as displayed in Table 1.

We measure the nonlinear properties of PU/MWNT compositefilms with different concentrations of MWNT by the OA and CAZ-scan schemes, respectively. As an example, Fig. 1 shows the OAZ-scan curves for the PU/MWNT films with differentconcentrations of MWNT at I0=1.55 GW/cm2. Fig. 2 shows theCA Z-scan curves for the corresponding PU/MWNT films atI0=1.55 GW/cm2 with S=0.07. For comparison, the film withoutMWNT, namely 0.0% MWNT in the film, is also measured by theuse of the OA and CA Z-scan schemes, respectively. Its OA and CAtraces are also plotted in Figs. 1 and 2, respectively. It is clear thatthe OA and CA signals of the 0.0% film sample are much lowerthan the other curves in Figs. 1 and 2. In the PU/MWNT films,therefore, the contribution of PU to the nonlinearity can beignored; that is to say, the nonlinearity in the PU/MWNT filmsoriginates from the MWNT only. In Fig. 1, the valley depth (1–TV)in the OA Z-scan trace enlarges gradually as the concentration ofMWNT increases. On the other hand, it can be seen in Fig. 2 that,with the increase of the concentration of MWNT in the films, thepeak height (TP–1) and the valley depth (1–TV) increasesynchronously, where TP and TV are the normalized peak andvalley transmittance in the Z-scan trace, respectively. The CAZ-scan traces exhibit the peak-to-valley configuration, implyingthat the PU/MWNT films possess the negative nonlinear refractioneffect.

In order to evaluate the nonlinear absorption and refractioncoefficients, b and g, we simulate numerically the measured

ent MWNT concentrations.

.3% 0.4% 0.5% 0.6%

8.91 91.24 104.47 106.45

0.2470.01 0.2170.01 0.2570.02 0.2470.01

ARTICLE IN PRESS

0.7

0.8

0.9

1.0

T(z)

z (mm)

A B C D

-15 -10 -5 0 5 10 15

Fig. 1. Open-aperture Z-scan traces for PU/MWNT films with different MWNT

concentrations at the on-axis peak intensity I0=1.55 GW/cm2. A, B, C, and D curves

correspond to the PU/MWNT film samples with the MWNT concentrations of 0.0%,

0.2%, 0.4%, and 0.6%, respectively.

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

T(z)

z (mm)

A B C D

-15 -10 -5 0 5 10 15

Fig. 2. Closed-aperture Z-scan traces for PU/MWNT films with different MWNT

concentrations at the on-axis peak intensity I0=1.55 GW/cm2 and S=0.07. A, B, C,

and D curves correspond to the PU/MWNT film samples with the MWNT

concentrations of 0.0%, 0.2%, 0.4%, and 0.6%, respectively.

0.7

0.8

0.9

1.0

Theory Experiment

T(z)

z (mm)

0.2

0.6

1.0

1.4 Theory Experiment

T(z)

z (mm)-15 -10 -5 50 10 15

-15 -10 -5 50 10 15

Fig. 3. Open-aperture (a) and closed-aperture (b) Z-scan curves for PU/MWNT film

with the MWNT concentration of 0.6% at I0=1.55 GW/cm2 and S=0.07. The circles

stand for the experimental data, while the lines represent the fitting data for the

experiments.

J. Wang et al. / Optics & Laser Technology 42 (2010) 956–959958

Z-scan traces. Firstly, the nonlinear absorption coefficient b of thePU/MWNT films is estimated by fitting the OA Z-scan tracewith Eq. (5). Then, in combination with the known nonlinearabsorption coefficient b, the nonlinear refraction coefficient g canbe calculated through simulating the CA Z-scan trace with Eq. (9).As an example, Fig. 3 (a) shows the experimental (circles) andtheoretical (line) OA Z-scan traces of the PU/MWNT film with 0.6%MWNT at I0=1.55 GW/cm2. The corresponding CA Z-scan tracesare shown in Fig. 3 (b), where the experimental and theoreticalresults are shown as circles and line, respectively. The nonlinearabsorption coefficient b and the nonlinear refraction coefficient gare �53 cm/GW and �2.8�10�3 cm2/GW, for the 0.6% PU/MWNT film sample, respectively. We explore the dependencesof the nonlinear refraction and absorption coefficients, b and g, onthe concentration of MWNT in the PU/MWNT films, as shown inFigs. 4 and 5, respectively. We can find that when the MWNTconcentration is less than or equal to 0.5%, b and g increase

linearly as the MWNT concentration increases. In the case of thePU/MWNT film with the MWNT concentration of 0.6%, b and gdeviate both from the linear growth; in particular, g has the morelarge deviation. The deviation may originate from the followingfactors: (i) the actual MWNT concentration is greater than 0.6%;(ii) the strong scattering induced by the relatively high MWNTconcentration leads to the enhancement of the OA and CA Z-scantraces, and then resulting in that the values of b and g areoverestimated with respect to the true values. We deem that thelatter has the larger contribution, because the strong scatteringphenomenon was observed in our experiments when thePU/MWNT film has the MWNT concentration of 0.6%.

The results indicate that MWNT makes the dominantcontribution to the nonlinear properties of the PU/MWNT films.Thus, we can control the nonlinear coefficients of the PU/MWNTfilm to satisfy the requirements of the practical applications, bychanging the MWNT concentration. The PU/MWNT film is apromising candidate for application in real optical systems.However, due to the presence of the scattering phenomenon,the scattering influence on the Z-scan data should be considered

ARTICLE IN PRESS

0

10

20

30

40

50

60

β (c

m/G

W)

MWNT Concentration (%)0.1 0.2 0.3 0.4 0.5 0.6

Fig. 4. Dependence of the nonlinear absorption coefficient b on the MWNT

concentration in the PU/MWNT films. The circles are the experimental results and

the solid line is the linear fitting results from the five experimental values except

for the case that the MWNT concentration is 0.6%.

0

5

10

15

20

25

30

γ (c

m2 /

MW

)

MWNT Concentration (%)0.1 0.2 0.3 0.4 0.5 0.6

Fig. 5. Dependence of the nonlinear refraction coefficient g on the MWNT

concentration in the PU/MWNT films. The circles are the experimental results and

the solid line is the linear fitting results from the five experimental values except

for the case that the MWNT concentration is 0.6%.

J. Wang et al. / Optics & Laser Technology 42 (2010) 956–959 959

under the high MWNT concentration. In addition, as the MWNTconcentration increases, the PU/MWNT film sample is easy to bedamaged. Therefore, the PU/MWNT film should have an appro-priate MWNT concentration for practical application. The resultssuggest that 0.3–0.4% may be a suitable concentration. Taking PU/MWNT film with 0.3% as an example, we compared the nonlinearcoefficients of PU/MWNT film with the solution of PEO/MWNT [6]and PmPV/MWNT [7], which are excited by the nanosecond laserwith a wavelength of 532 nm, and discovered that the nonlinearcoefficients of PU/MWNT film is larger than the values reported inRefs. [6,7]. Thus, PU/MWNT film with larger nonlinear coefficientsis a promising nonlinear material, and its nonlinear coefficientscan be controlled.

4. Conclusion

We investigated the nonlinear optical properties of a carbonnanotube composite films with different MWNT concentrationsby the use of the single beam CA and OA Z-scan techniques withnanosecond laser pulse at 532 nm. The nonlinear absorptioncoefficient was acquired by simulating the OA Z-scan curvesnumerically, and a nonlinear refraction coefficient was deter-mined by fitting the CA Z-scan curves using Huygens–Fresnelintegral principle. A self-defocusing refraction effect is demon-strated when the PU/MWNT films are excited by a nanosecondlaser pulse at 532 nm. The results indicate that the PU/MWNT filmwith the higher MWNT concentration has the larger nonlinearabsorption and refraction coefficients. Thus, it is possible tocontrol the nonlinear coefficients for real applications by regulat-ing the concentration of MWNT in PU/MWNT composite films.

Acknowledgements

This work was in part supported by the 973 Program of China(Grant no. 2006CB9211805) and by NSFC (Grant no. 60608006).

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