APPLIED PHYSICS LETTERSVOLUME 75, NUMBER 1

5 JULY 1999

Nonresonant femtosecond second hyperpolarizabilities of intramolecularcharge-transfer molecules with great excited- and ground-state
dipole-moment differences
Mikio Yamashita,a) Shinji Kikuma, Yoshihisa Yamaoka,
Hidetoshi Murakami, and Ryuji Morita
Department of Applied Physics, Hokkaido University, Kita-13, Nishi-8, Kita-Ku, Sapporo 060-8628, Japanand CREST, Japan Science and Technology Corporation (JST)

Hidemi Shigekawa
Institute of Materials Science, University of Tsukuba and Center for Tsukuba Advanced Research Alliance(TARA), Tsukuba 305-8573, Japanand CREST, Japan Science and Technology Corporation (JST)~Received 3 December 1998; accepted for publication 23 April 1999!
The femtosecond second hyperpolarizability due to the nonresonant electronic polarization for two
intramolecular charge-transfer molecules, 6-propionyl-2-dimethylamino naphthalene and2-anilinonaphthalene-6-sulfonic acid which possess the great permanent dipole-moment difference
between the excited state and the ground state, is obtained from the measurement of the ultrafastchange in refractive index using a time-resolved interferometer. It is found that the second
hyperpolarizability increases parabolically from 5310234 to 4.3310232 esu with increasing the
dipole-moment difference from 7.7 to 40 D, and this quantitative relationship is well explained bya quantum-mechanical equation describing the electronic second hyperpolarizability of one
molecule with the permanent dipole-moment difference. © 1999 American Institute of Physics.
@S0003-6951~99!02025-2#

Recently, highly third-order nonlinear optical materials
with a femtosecond response and no absorption have come tobe desired for the development of the ultrafast opticalcontrol devices.1 One of the materials satisfying these opticalproperties is anticipated to be the organic compound having
the nonlinearity caused by intramolecular charge transfer~ICT! in the nonresonant region.2 However, the investigationof the femtosecond nonresonant dynamics of the third-order
optical nonlinearity for molecules possessing the large ICT
hardly has been carried out so far.
In this letter, we report that ICT molecules, with thegreat difference u D m u 5 u m ee 2 m gg u (>20 D) between thepermanent electric dipole moment of the excited state m ee
and that of the ground state m gg , have the highly nonlinear
electronic polarization even in the nonresonant region, andthe third-order nonlinearity responds instantaneously within
the duration of the femtosecond pump pulse. Furthermore, it
is found experimentally that the angular-averaged second hyperpolarizability ^g& of the molecule indicates a parabolic
dependence as an increasing function of the dipole-moment
difference uDmu over the wide range from u D m u >5 to 40 D.
The large ICT compounds studied in this investigation
are 6-propionyl-2-dimethylamino naphthalene ~PRODAN!
and 2-anilinonaphthalene-6-sulfonic acid ~2,6-ANS!. They
were obtained from Molecular Probes, Inc. Their ultrafast
third-order nonlinear optical responses were examined forthe sample solutions dissolved in ethanol ~EtOH! at the dilute concentration. The absorption peak of the PRODAN solution is at 360 nm with the long-wavelength absorption edgea!

Electronic mail: mikio@eng.hokudai.ac.jp

around 430 nm, where the molar absorption coefficient is
1.6% of the maximum one at 360 nm ~the maximum molar
absorption coefficient of 18 400 cm2/mM, the half width of2525 cm21 and the electronic transition dipole moment of
4.5 D!.3 The absorption peak of the 2,6-ANS solution is at
330 nm with the long-wavelength absorption edge around397 nm where the molar absorption coefficient is 1.6% of the
maximum one ~the maximum molar absorption coefficient of
50 880 cm2/mM!.
Since PRODAN has a good electron donor of the dimethyl amino group and a good electron acceptor of the propionyl group, attached to the 2 and 6 positions of the large
naphthalene ring, it shows a great charge-transfer character.
The dipole-moment difference uDmu between the first excitedelectronic state and the ground state is known to be 20 D on
the basis of the established measurement of the Stokes shiftof the absorption and emission spectra.3 Similarly, 2,6-ANS
has a good electron donor of the N-phenyl amino group anda good electron acceptor of the sulfonate group attached to
the 2 and 6 positions of the naphthalene ring, and hence
indicates a large u D m u 540 D. 4
The apparatus for the measurement of the femtosecond
time-dependent third-order nonlinearity using a timeresolved interferometer with a heterodyne pump and probe
technique is the same as the previously employed one, except for some points.5,6 100 fs pulses at 780 nm with theaverage power of 850 mW at a 100 MHz repetition rate weregenerated from a Kerr-lens mode-locked Ti:sapphire laser.
The linearly polarized laser output beam was split in a strong
pump-pulse beam and a weak pulse beam ~9:1!. The latter
beam, furthermore, was split in a probe pulse beam and areference pulse beam ~6:4! to compose of the time-division0003-6951/99/75(1)/28/3/$15.00
28© 1999 American Institute of Physics
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Appl. Phys. Lett., Vol. 75, No. 1, 5 July 1999

Yamashita et al.

29

TABLE I. Third-order nonlinear optical parameters and permanent electric
dipole-moment differences between excited and ground states for different
ICT molecules.

FIG. 1. Phase-change signals from 7.04 mM PRODAN solution ~solid line!,
1.14 mM 2,6-ANS solution ~thick solid line!, flint glass as a reference ~dotted line! and ethanolic solvent ~dashed line!.

interferometer. The carrier frequency of the probe pulse was
up-shifted by 39.0 MHz using an acousto-optic modulator,
and that of the reference pulse was also up-shifted by 40.0
MHz using another modulator. Their diffraction efficiencies
were 60%–65%, and their linear polarizations were parallel
to each other. Both the pulse durations were broadened to
385 fs due to group-velocity dispersion of the materials of
acousto-optic modulators. The probe pulse was time delayed~t! with respect to the 1.14 kHz chopped pump pulse by adisplacementmeter-attached stepping motor. After the advanced reference pulse ~330 ps ahead of the probe pulse! andthe probe pulse were copropagated, these pulses and thepump pulse were noncollinearly focussed on the sample solution in a 1-mm-thick quartz cell ~or a reference sample of ahigh-refractive-index flint glass with a 1.2 mm thickness! by
a 10 cm focusing lens. Passing through the sample, thepump-pulse-induced phase-change probe pulse and the reference pulse were collimated by another 10 cm focusing lens,and overlapped in space and time at a fast response photodiode. The 1 MHz beat signal of the probe-reference pulses
was detected by an FM ham-radio receiver. The output
yields an electric signal proportional to the derivative of theprobe-pulse phase change with respect to the time. Since thepump pulse was chopped at 1.14 kHz, the receiver output
was modulated at the same frequency. By integrating themodulated output through a lock-in amplifier, the probepulse phase change was measured at each delay time t.
Figure 1 shows the typical signal S I/E ( t ) of the femtosecond time-dependent phase change ~solid line! in the nonresonant region for the 7.04 mM dilute solution of PRODAN
and the signal S I/E ( t ) ~thick solid line! for the 1.14 mM
dilute solution of 2,6-ANS. In addition, the signal S R ( t )~dotted line! for the reference flint glass and the signal S E ( t )~dashed line! for the ethanolic solvent are shown. The reference signal was measured two times before and after themeasurements of the sample signal and the solvent signal,
and its averaged result is shown in Fig. 1. Both the signals of
the two ICT-molecule solutions respond instantaneously
within 385 fs durations of the probe and reference pulses, aswell as the case of the reference glass which is alreadyknown to indicate the instantaneous response.5,7,8 This resultof the instantaneous change in refractive index in the femtosecond time region suggests that the nonlinear response measured for the two ICT-molecule solutions originates fromonly the nonlinear electronic polarization in the off-resonant
region ~not from the polarization due to the molecular motion and/or the intermolecular interaction such as thethiophene solution!.7,9,10 The third-order nonlinear electronicsusceptibility u x (3)I u of only ICT molecules at the measured
concentration is evaluated from the following equation for
the nonlinear response faster than the pulse employed for themeasurement:5,7,11,122
u x ~I 3 ! u 5 $ n 0I/E
L R u x ~R3 ! u / ~ n 20R L I/E ! % 3 ~ S TI /S TR ! ,~1!

S Ti 5 * `2` S i ( t )d t

for thewhere the integral signals are
sample solutions @ i5I/E for S I/E ( t )], the ethanolic solvent@ i5E for S E ( t )] and the reference glass @ i5R for S R ( t )],T
S TI 5S I/E
2S TE , the linear refractive indices are n 0I/E 51.362
for the sample solutions and n 0,R 52.148 for the reference
glass, and the sample and reference lengths are L I/E
51.0 mm and L R 51.2 mm. The optical density ~OD! of the
1 mm sample solution at the measured wavelength of 780
nm is unmeasurably small (OD,0.01). The subscripts I/E,
E and R refer to the sample solution, the ethanolic solvent
and the reference glass, respectively. The third-order nonlinear susceptibility u x (3)R u of the reference flint glass with isotropic structure is 10.3310213 esu in the nonresonant
region.5,7,8
The use of the equation relating the u x (3)I u to the molecu2
larsecondhyperpolarizability,u x (3)I u 5N $ (n 0I/E
412)/3% ^ g I & , enables us to determine the angular-averaged
second hyperpolarizability ^ g I & of the single ICT molecule.10
Here, N is the number density which is obtained from themeasured dilute concentration.
(3)
Table I summarizes the susceptibility u x PR
u 55.7310214 esu obtained for the 7.04 mM PRODAN after thesubtraction of the ethanolic contribution, the susceptibility(3)
u x ANS
u 58.1310214 esu for the 1.14 mM 2,6-ANS, and theircorresponding second hyperpolarizabilities ^ g PR& 54.9
310233 esu and ^ g ANS& 54.3310232 esu, as well as theirdipole-moment differences D m PR520 D and D m ANS540 D.
In addition, the result of the ^ g DE& 55310234 esu and the
D m DE57.7 D obtained by other measurements in the nonresonant region for another ICT molecule, 4-~N,Ndiethylamino!- b -nitrostyrene ~DEANST!, is given.13,14 The
former value is the one obtained for DEANST dissolved in
N-dimethylformamide in the nonresonant region using a

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30

Yamashita et al.

Appl. Phys. Lett., Vol. 75, No. 1, 5 July 1999

FIG. 2. Dependence of second hyperpolarizability ( ^ g l & ) on permanentelectric dipole-moment difference between excited and ground states ~Dm!
for different ICT molecules. Inset, (D m ) 2 plot of ^ g l & .

femtosecond time-resolved degenerate four-wave mixing
spectroscopy.13 The latter value is the one obtained for
DEANST doped in poly~methyl methacrylate! using an electroabsorption spectroscopy,14 which is slightly smaller than
the already known one of a similar ICT molecule, 4-~N,Ndimethylamino!- b -nitrostyrene.15 Figure 2 shows the Dm
dependence of the ^ g I & for different ICT molecules. It isdefinitely found from Fig. 2 that second hyperpolarizabilities
of ICT molecules increase parabolically ~solid line! as theirdipole-moment differences between the excited state and theground state increase.
There is a theoretical equation describing the relationship between the second hyperpolarizability and the permanent dipole-moment difference for the third-order nonlinearity originating from the electronic polarization in thenonresonant region.2,16 That is, the following equation obtained quantum mechanically for a quasi-two-level modelusing the density matrix formalism in perturbation theory is:^g&}1
u m u 2 @~ D m ! 2 2 u m ge u 2 # ,~ DE eg ! 3 ge

~2!

where u m ge u and DE eg represent an electronic transition dipole moment and transition energy between the excited state
and the ground state, respectively. Setting Eq. ~2! as ^ g &5a(D m ) 2 2b, where b/a5 u m ge u 2 , permits us to fit the experimental values in Fig. 2 to a solid line ~in Fig. 2! by aleast-squares method, and to evaluate u m ge u 57.0 D. Thisvalue is reasonably compared with the transition dipole moment measured from the absorption spectrum for the typical

ICT-molecule solution ~3–7 D!.2,17 For example, thePRODAN/EtOH solution indicates u m ge u 54.5 D. 3 This deviation may be because the u m ge u and the DE eg have been
assumed to be not dependent on each ICT molecule. It
should be noted that the quantitative result obtained by themacroscopic femtosecond experiment directly gives a clean
evidence over the wide range of the dipole-moment difference for the microscopic prediction from the quantummechanical Eq. ~2! for noncentrosymmetric molecules. In
addition, this experimental finding provides good guidelines
on the practical selection of optical materials possessing an
ultrafast response ( t R ), a highly third-order nonlinearity( x (3) ) and no absorption ~a!, that is, a large figure of meritof x (3) / at R . 1
In conclusion, the second hyperpolarizability due to thenonresonant electronic polarization of the ICT molecule possessing the great permanent dipole-moment difference between the excited state and the ground state has been evaluated through the measurement of the ultrafast change inrefractive index for the two ICT-molecule ~PRODAN and
2,6-ANS! solutions using the femtosecond time-resolved interferometer. It has been found that the second hyperpolarizability measured in the femtosecond time region rapidly increases from 5310234 to 4.3310232 esu with a parabolic
character as the dipole-moment difference increases over thewide range from 7.7 to 40 D. Furthermore, it has been confirmed that the quantitative relationship of this experimental
finding is well explained by the quantum-mechanically derived equation which describes the electronic second hyperpolarizability of one molecule possessing the permanent
dipole-moment difference.
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