Large and ultrafast third-order optical non-linearity of single-wall carbon nanotubes at 820 nm

Article abstract of DOI:10.1016/S0009-2614(00)00261-X

Single-wall carbon nanotubes (SWCNT) of diameter 1.3 nm have been produced and cut into finite lengths centered at 160 nm. A solution of them in DMF has been prepared for third-order optical non-linearity measurements using the femtosecond optical Kerr effect at a wavelength of 820 nm. The ultrafast second-order hyperpolarizability, γ, of this SWCNT is estimated to be as large as 2.1×10^-28 esu.

Full text of DOI:10.1016/S0009-2614(00)00261-X

14 April 2000
Ž
.
Chemical Physics Letters 320 2000 411–414
www.elsevier.nlrlocatercplett
Large and ultrafast third-order optical non-linearity of single-wall
carbon nanotubes at 820 nm
Shufeng Wang a, Wentao Huang a, Hong Yang a, Qihuang Gong a,b,), Zujin Shi c,
Xihuang Zhou c, Di Qiang c, Zhennan Gu c
a
Department of Physics, Mesoscopic Physics Laboratory, Peking UniÕersity, Beijing 100871, China
b
Institute of Physics, Chinese Academy of Sciences, Beijing, 100080, China
c
Department of Chemistry, Peking UniÕersity, Beijing 100871, China
Received 9 November 1999; in final form 22 December 1999
Abstract
Ž
.
Single-wall carbon nanotubes SWCNT of diameter 1.3 nm have been produced and cut into finite lengths centered at
160 nm. A solution of them in DMF has been prepared for third-order optical non-linearity measurements using the
femtosecond optical Kerr effect at a wavelength of 820 nm. The ultrafast second-order hyperpolarizability, g, of this
28
SWCNT is estimated to be as large as 2.1=10y esu. q 2000 Elsevier Science B.V. All rights reserved.
Carbon nanotubes have attracted great attention
chemical properties. Many potential applications in-
cluding strong carbon fibers, molecular electrical
wires in nanometer electronic device and nanometer
semiconductors have been proposed for the nan-
otubes.
w x
since their discovery in 1991 1 and are regarded to
be the largest one-dimensional molecule with an
exotic structure consisting only of carbon atoms with
each atom connected to three neighboring atoms by
covalent bonds. The fourth valence electron of each
carbon atom is free to form a uniform p-bond over
the framework and can move freely along the hollow
nanotube. The size of the tubes is a few nanometers
in diameter and nano- to micrometers in length. With
developments in condition control, mass-production
The exotic electronic structure of the nanotubes is
w
x
also of great interest in nonlinear optics 11 . How-
ever, only few studies on this subject have been
reported. Theoretically, the extended Su–
Ž
.
Schrieffer–Heeger SSH model with the Coulomb
interaction included has been used by Xie and Jiang
w
x
w
x
w x
w
x
2–4 , purification 5–8 , tailoring 9 and improve-
12–14 to study the optical non-linearity of single-
w
x
Ž
.
ments in solubility 10 , researchers now have access
to sufficient quantities to test their physical and
wall carbon nanotubes SWCNT . They found the
magnitudes of the second-order hyperpolarizabilities,
g, for the two types of nanotubes, zigzag and arm-
2.98
Ž
.
chair, increased as gs 1qi=18r60 gC60 and
3.15
Ž
.
gs 1qi=10r60 gC60. This predicts that the
high third-order optical non-linearity of SWCNTs
increases strongly with i, the raw number of
)
Corresponding author. Fax: q86-10-62756567; e-mail:
qhgong@ibm320h.phy.pku.edu.cn
0009-2614r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved.
Ž
.
PII: S0009-2614 00 00261-X

(
)
412
S. Wang et al.rChemical Physics Letters 320 2000 411–414
carbon-derived nanotube. A g value as large as
10y29 esu has been estimated for is10 for zigzag
The raw SWCNTs were made by the d.c. arc
discharge method with a Y–Ni alloy composite
graphite rod as the anode that has been reported by
w
x
and 18 for armchair nanotubes. The Margulis 15
w
x
w x
and Wan 16 groups have also predicted theoreti-
cally that g would be larger than 10y29 esu for
SWCNT with more than 200 carbon atoms. To date,
only one experimental measurement of the third-order
optical non-linearity of carbon nanotubes has been
Gu et al. 4 The soot was then washed with CS2 and
hydrochloric acid. This raw material was determined
to contain 40% of SWCNTs by HREM and Raman
w x
spectroscopy 4 . By HREM, the SWCNTs were
observed to be 1.3 nm in diameter and to exist in
w
x
w x
carried out by Ye et al. 17 . However, in their
report, multi-wall carbon nanotubes were dispersed
in mixing solution of polypyrrol and m-cresol with
ethanol. No real solution of carbon nanotubes was
obtained, resulting in a large absorption in the in-
frared region. Moreover, the technique of degenerate
four-wave mixing with pico- and nanosecond lasers
both at 1064 and 532 nm had limited ability to
bundles. After purification 8 a sample of more than
90% purity of SWCNTs was obtained. Thermogravi-
Ž
.
metric analysis TGA was undertaken and the SEM
image of purified SWCNTs has been published in
w x
Ref. 8 .
To cut the SWCNTs into certain lengths, the
method of oxidizing the SWCNTs in a mixture of
concentrated sulfuric and nitric acid with ultrasonic
Ž
.
w x
distinguish the nonlinear optical NLO contribution
from the p-conjugated electrons. In this Letter, we
first report a femtosecond time-resolved third-order
NLO investigation of SWCNTs with a finite length
of 160 nm in a real solution. An extremely large and
instantaneous NLO response was observed. The av-
erage magnitude of g for each SWCN was estimated
to be 2.1=10y28 esu, which suggests potential ap-
plications in optical information processes.
treatment developed by Smalley et al. 9 was em-
ployed. The final finite length SWCNTs are straight
one-dimensional molecules separate from the bundle
and open at both ends. Fig. 1 shows the length
distribution of SWCNTs in our sample, determined
by the laser scattering method. The lengths range
from 46 to 580 nm with the peak at 162.2 nm. To
prepare a single tube colloid solution, we used mixed
acids to oxidize the purified SWCNTs and to obtain
a dispersed colloid solution in N,N-dimethylform-
The NLO measurements were performed using
w
x
Ž
.
the femtosecond optical Kerr technique 18,19 , with
amide DMF with a concentration as high as 2
mgrml by ultrasonic treatment. In our experiment,
three solutions with concentrations of 0.33, 0.22 and
0.14 mgrml were used. The absorption spectrum of
sample solution is shown in Fig. 2. A slight absorp-
tion at a wavelength of 820 nm is observed.
Ž
.
a Ti:Sapphire laser Mira 900F, Coherent, USA .
The operating wavelength was centered at 820 nm.
The beam from the laser was divided into pump and
probe beams with an intensity ratio of 10:1. The
polarization of the probe beam was rotated 458 with
respect to the linear polarization of the pump beam.
The pump beam passed through a delay line driven
by a steper motor in order that the optical path length
difference between the pump and probe beams could
be adjusted during the measurement. Two beams
were focused to interact with a sample solution
filling a glass cell 1 mm thick. The orthogonal
optical Kerr signal generated passed through an ana-
lyzer and was detected by the photodiode. The signal
was then ArD converted and stored to a computer.
All the measurements were performed under the
control of a computer program. We replaced the
The ultrafast NLO response of SWCNTs solutions
is shown in Fig. 3 together with that for the reference
Ž
.
sample cell with a BBO crystal thickness, 0.3 mm
to determine the zero delay point and the autocorre-
lation signal of the laser beam. The pulse duration
was determined to be 120 fs.
Fig. 1. The length distribution of SWCNTs in water, determined
by the laser scattering method at wavelength of 514.5 nm.

(
)
S. Wang et al.rChemical Physics Letters 320 2000 411–414
413
carbon atom in the SWCNT using following equa-
tion
gc sx Ž3.rNrL
2
Ž .
where N is the number density of carbon atoms in
our sample and r is the purity of SWCNTs, L is the
wŽ
local field correction factor which is equal to 2q
2
4
.
x
n r3 . The magnitude of gc for each atom is then
calculated to be 7.7=10y33 esu. In our previous
results for C60 , measured under the same conditions,
the contribution of each carbon atom is less than
1.5=10y36 esu. It is three orders smaller than the
contribution in SWCNT. The contribution in SWCNT
is also three orders larger than the value of 5.9=
Fig. 2. Normalized absorption spectrum of SWCNTs in DMF,
from 270 to 1000 nm.
10y36 esu reported by Ye et al. 17 as multi-wall
carbon nanotubes were used in their measurement.
With the value of gc for each carbon atom, the g
for the SWCNT molecule with a diameter of 1.3 nm
w
x
sample of CS2 under identical experimental condi-
tions. The instantaneous response proves that the
NLO signal is contributed from the conjugated p-
electrons. The signals for solutions with different
concentrations indicate a quadratic dependence of
the signal on concentration. We use the following
Ž
and a length of 160 nm the corresponding carbon
.
atom number N is about 27 100 is deduced to be
about 2.1=10y28 esu. This is quite a large value
that could be appropriate for applications in optical
information processes. However, this result contra-
dicts the theoretical prediction of 10y28 esu for the
tube containing only about 200 carbon atoms. This
may be caused by an overestimate of gC60. While
using a value of gC60 (9=10y35 esu, which has
w
x
equation 20 to calculate the third-order optical
non-linearity susceptibility, x Ž3., of the sample solu-
tions at a particular concentration:
1r2
2
IS
nS
al
1yeya l eya lr2
xSŽ3. sxRŽ3.
1
Ž .
w
x
ž n /
obtained 23 under the same conditions as this ex-
periment, the theoretical prediction of g f
gC60 Nr60 for SWCNT may give a magnitude of
g(8.3=10y27 esu for the SWCNT with a length
of 160 nm. This value is still one order larger than
our result. We may attribute this to the saturation
ž /
IR
Ž
.
R
3
Ž
.
in which, S and R represent sample solution and
reference sample, I is the OKE signal intensity and
n is the refractive index. The x Ž3. for CS2 is taken
to be 1=10y13 esu 21 . The last term in the
equation is responsible for the sample absorption and
a is the absorption coefficient and l is the length of
sample cell which is 1 mm in our experiment. In this
experiment, ey a l is 0.83 at a concentration of 0.33
mgrml and the last term is 1.2. So we obtain the
x Ž3. as 4=10y13 esu for SWCNTs solution at 0.33
mgrml. In this measurement, the contribution of the
solvent DMF is justifiably ignored because the x Ž3.
for DMF is nearly 10 times smaller than that of CS2
w
x
w
x
22 and the signal of sample solution is 10 times
larger than that of CS2.
From Fig. 1, the lengths of SWCNT show a wide
distribution. It would be difficult to assign directly
the magnitude of g for the SWCNT. However, we
may calculate the average contribution from each
Fig. 3. The ultrafast OKE signals of SWCNTs DMF solutions
together with reference sample of CS2.

(
)
414
S. Wang et al.rChemical Physics Letters 320 2000 411–414
w x
4
Z. Shi, Y. Lian, X. Zhou, Z. Gu, Y. Zhang, S. Lijima, L.
effect known for p-conjugated one-dimensional
Ž
.
Zhou, K. Yue, S. Zhang, Carbon 37 1999 1449.
w
x
polymers 24 . This could be further investigated
with SWCNTs of different length.
w x
5
A.G. Rinzler, J. Liu, H. Dai, P. Nikolaev, C.B. Huffman, F.J.
Rodriguez-Macias, P.J. Boul, A.H. Lu, D. Heymann, D.T.
Colbert, R.S. Lee, J.E. Fischer, A.M. Rao, P.C. Eklund, R.E.
In conclusion, a solution of SWCNT with definite
length in DMF was prepared. Its third-order optical
non-linearity was studied using transient OKE mea-
surements. The value of the instantaneous response g
is estimated to be on the order of 10y28 esu for the
SWCNT with a diameter of 1.3 nm and a length of
160 nm. This is a remarkably large non-resonant and
instantaneous NLO response for p-conjugated
molecules. The contrast between the experimental
results and the theoretical predictions has also been
discussed. To improve NLO performance of
SWCNT, it would be of interest to test the optical
non-linearity of SWCNTs of various lengths.
Ž
.
Smalley, Appl. Phys. A 67 1998 29.
w x
6
K. Tohji, T. Goto, H. Takahashi, Y. Shinoda, N. Shimizu, B.
Jeyadevan, I. Matsuoka, Y. Saito, A. Kasuya, T. Ohsuna, H.
Ž
.
Hiraga, Y. Nishina, Nature 383 1996 679.
w x
7
H. Takahashi, T. Goto, K. Akiyama, B. Jeyadevan, K. Tohji,
Ž
.
I. Matsuoka, Mater. Sci. Eng. A 217 1996 42.
w x
8
Z. Shi, Y. Lian, F. Liao, X. Zhou, Z. Gu, Y. Zhang, S.
Ž
.
Lijima, Solid State Comm. 112 1999 35.
w x
9
J. Liu, A.G. Rinzler, H. Dai, J.H. Hafner, R.K. Bradley, P.J.
Boul, A.H. Lu, T. Iverson, K. Shelimov, C.B. Huffman, F.J.
Rodriguez-Macias, Y.S. Shon, T.R. Lee, D.T. Colbert, R.E.
Ž
.
Smalley, Science 280 1998 1253.
w
w
x
10 J. Chen, M.A. Hamon, H. Hu, Y. Chen, A.M. Rao, P.C.
Ž
.
Eklund, R.C. Haddon, Science 282 1998 95.
x
11 J. Jiang, J. Dong, X. Wan, D. Xing, J. Phys. B: At. Mol. Opt.
Ž
.
Phys. 31 1998 3079.
w
w
w
w
w
w
x
Ž
.
Ž
12 R. Xie, J. Jiang, J. Appl. Phys. 83 1998 3001.
Acknowledgements
x
.
13 R. Xie, J. Jiang, Chem. Phys. Lett. 280 1997 66.
x
Ž
.
14 R. Xie, J. Jiang, Appl. Phys. Lett. 71 1997 1029.
x
Ž
.
15 V. Margulis, T. Sizikova, Physica B 245 1998 173.
The work was supported by the National Science
Foundation of China Grants No.19525412 and
x
Ž
.
16 X. Wan, J. Dong, D. Xing, Phys. Rev. B 58 1998 6756.
Ž
x
17 X. Liu, J. Si, B. Chang, G. Xu, Q. Yang, Z. Pan, S. Xie, P.
.
19884001 and National Climbing Projects of China.
Ž
.
Ye, J. Fan, M. Wan, Appl. Phys. Lett. 74 1999 164.
w
w
w
w
w
w
w
x
18 Q. Gong, J. Li, T. Zhang, H. Yang, Chin. Phys. Lett. 15
Ž
.
1998 30.
x
19 T. Zhang, F. Wang, H. Yang, Q. Gong, X. An, H. Chen, D.
References
Ž
.
Qiang, Chem. Phys. Lett. 301 1999 343.
x
20 Q. Gong, Y. Sun, Z. Xia, Y. Zou, Z. Gu, X. Zhou, D. Qiang,
w x
Ž
.
1
w x
2
S. Iijima, Nature 354 1991 56.
Ž
.
J. Appl. Phys. 71 1992 3025.
A. Thess, R. Lee, P. Nikolaev, H. Dai, P. Petit, J. Robert, C.
Xu, Y. Hee Lee, S. Gon Kim, A.G. Rinzler, D.T. Colbert,
G.E. Scuseria, D. Tomanek, J.E. Fischer, R.E. Smalley,
x
Ž
.
21 R. Minoshima, M. Taija, T. Kobayashi, Opt. Lett. 16 1991
1683.
x
22 Q. Gong, J. Li, T. Zhan, H. Yang, Chin. Phys. Lett. 15
Ž
.
Science 273 1996 483.
Ž
.
1998 30.
w x
3
C. Journet, W.K. Maser, P. Bernier, A. Loiseau, M.L. de la
Chapelle, S. Lefrant, P. Deniard, R. Lee, J.E. Fischer, Nature
x
23 J. Li, S. Wang, H. Yang, Q. Gong, X. An, H. Chen, D.
Ž
.
Qiang, Chem. Phys. Lett. 288 1998 175.
Ž
.
388 1997 756.
x
Ž
.
24 H.S. Nalwa, Adv. Mater. 5 1993 341.