Jpn. J. Appl. Phys. Vol. 38 (1999) pp. 4056–4064
Part 1, No. 7A, July 1999c
°1999
Publication Board, Japanese Journal of Applied Physics

Aggregation Effect on the Third-Order Optical Nonlinearity
in 4-(N,N-Diethylamino)-β-Nitrostyrene-Doped Polymer Films
Hidetoshi M URAKAMI1,∗ , Ryuji M ORITA1,3 , Mikio YAMASHITA1,3 and Hidemi S HIGEKAWA2,3
1 Department of Applied Physics, Hokkaido University, Kita-13, Nishi-8, Kita-ku, Sapporo 060-8628, Japan
2 Institute of Materials Science, Center for Tsukuba Advanced Research Alliance, University of Tsukuba, 1-1-1 Tennodai, Tsukuba 305-8573, Japan
3 CREST, Japan Science and Technology Corporation (JST)(Received November 16, 1998; revised manuscript received April 1, 1999; accepted for publication April 22, 1999)

The absorption and electroabsorption (EA) spectra for 4-(N,N-diethylamino)-β-nitrostyrene (DEANST)-doped poly(methyl
methacrylate) (PMMA) films in the dopant concentration range of 0.1–40 wt% were measured. Dispersion of the third-ordernonlinear optical susceptibility χ (3) (−ω; 0, 0, ω) at each concentration was determined. In addition, the static polarizabilitychange 1α and the static dipole-moment change 1µ were evaluated. Furthermore, the picosecond emission-decay profiles
and the time-resolved emission spectra for 0.1–40 wt% DEANST-doped PMMA films were measured. From the experimental
results, it was concluded that DEANST molecules in PMMA films aggregate at concentrations over 5 wt%. This aggregation gives rise to two new absorption bands. The intermolecular interaction affected by aggregation causes a decrease in
1µ, in the average effective third-order molecular hyperpolarizability hγ (−ω; 0, 0, ω)ieff , and in the nonproportional behavior in |χ (3) (−ω; 0, 0, ω)| with increasing dopant concentration. Furthermore, this aggregation explains the absorption spectralchange, the EA spectral shift and the existence of two emission-decay constants with concentration. Finally, the average aggregation number of DEANST molecules was evaluated to be two, which suggests that DEANST molecules in the PMMA film
form a dimer at concentrations over 5 wt%.
KEYWORDS: charge-transfer molecule, nonlinear organic material, polymer, electroabsorption, third-order optical nonlinearity,
time-resolved emission spectrum, aggregation, dimer

1. Introduction
Organic materials with π -conjugated electron systems havereceived considerable attention because of their high opticalnonlinearities. It is known that, among those materials, theorganic molecules possessing the structure of donors and acceptors substituted into the π -conjugated system have higher
optical nonlinearities, owing to the intramolecular chargetransfer. The present work concerns one of those materials, 4-(N,N-diethylamino)-β-nitrostyrene (DEANST).1) In a
DEANST molecule, a diethylamino group as a donor, anda nitroehtylene group, as an acceptor, are attached to eachside of the aromatic ring, thus a DEANST molecule hasa large third-order hyperpolarizability, high solubility andgood crystallinity. Therefore, the extremely high solubilityof DEANST in polar solvents and in poly(methyl methacrylate) (PMMA) films2) makes us expect a material with a large
third-order nonlinear optical susceptibility χ (3) proportional
to the concentration. However, this linear relationship between χ (3) and concentration is not always self-evident athigh concentrations. In particular, at extremely high concentrations, the mechanism of the third-order optical nonlinearity
can be different from that at typical concentrations, even for
a concentrated system which does not show a clear or significant change of the absorption spectrum. In general, it is difficult to clarify the difference between the third-order nonlinear
mechanism of monomers and that of a lower degree of aggregates, such as dimers, in the same solvent, where absorption spectra almost overlap each other, unlike in the case of
J-aggregates.3) This may be one of the reasons why the nonlinear optical investigation of the molecular system, in which
absorption-spectrum-overlapping monomers and dimers coexist, has rarely been carried out so far.
Modulation absorption spectroscopy using an external
electric field is a powerful technique for the investigation of∗ mhide@eng.hokudai.ac.jp

the subtle differences between the electronic structures of acomplex compound. The permanent dipole moment and linear polarizability are key parameters that govern nonlinear
optical constants as well as linear optical constants. Fromthe measurement of electroabsorption, we can evaluate thechange in those parameters for the electronic transition froma ground to an excited state.4) Moreover, we can determine
the dispersion of the third-order nonlinear optical susceptibilities χ (3) (−ω; 0, 0, ω) through the Kramers-Kronig relation.5, 6) Thus we can clarify the origin of the nonlinearities.
The purpose of the present work is to clarify the mechanism of the third-order optical nonlinearity in DEANSTdoped PMMA films at low and high dopant concentrations.
The optical nonlinearity is investigated as a function of thedopant concentration over a wide range from 0.1 to 40 wt%,
using modulation absorption spectroscopy. The picosecond
time-resolved emission spectroscopy is also applied to reveal
the difference between the excited-state relaxation processes
at low concentrations and at high concentrations. As a result, it is shown that at high concentrations over 5 wt%, aggregates which reduce the effective third-order hyperpolarizability are formed, and hence third-order susceptibility is notproportional to the concentration of DEANST molecules.
2. Experimental and Analysis
2.1 Sample preparation
DEANST was synthesized based on ref. 1 and purified byrecrystallization by a slow-cooling method. PMMA (Aldrich)
was used as a host material. Conductive indium-tin-oxide(ITO)-coated quartz glass was employed as a substrate. The
polymer solution with DEANST was spin-coated on the substrate and then dried at room temperature for 5–6 h. The
concentration of DEANST relative to the weight of PMMA
was varied in the range of 0.1–40 wt%. Semitransparent aluminum was deposited on the film surface as a counterelectrode. A typical sample thickness was about 0.1–0.2 µm,
which was measured by multiple-beam interferometry (Mi-4056

H. M URAKAMI et al.

Jpn. J. Appl. Phys. Vol. 38 (1999) Pt. 1, No. 7A

zojiri BM-4).

4057

was 50 mW. The signal was detected by a synchroscan streak
camera (Hamamatsu Photonics, M1955) attached to a polychromator. The measured wavelength range for all samples
was 1.98–2.62 eV (627–473 nm) and the time resolution was∼3 ps.

2.2 Experimental setup
We performed two types of measurement: electroabsorption spectroscopy measurement and picosecond timeresolved emission measurement. All the measurements werecarried out at room temperature. As shown in Fig. 1, themeasuring system for electroabsorption spectroscopy consistsof a 150 W Xe-arc lamp (Hamamatsu Photonics), a grating
monochromator (Oriel 77250, the wavelength resolution is
1 nm), appropriate color filters to cut off the second-orderdiffraction light, and a photomultiplier tube (Hamamatsu Photonics, H5783-06) to detect a signal. In the electroabsorption
measurement, a sinusoidal ac electric field with a modulation frequency of ∼1 kHz and a field strength on the orderof 105 V/cm was applied to the sample. The field-inducedchange in absorption intensity was detected by a lock-in amplifier (Stanford Research Systems, SR-830) at the second
harmonic of the modulation frequency. The measurement
was performed in the range of 2.07 eV (600 nm) to 3.59 eV(345 nm).
The experimental setup for the time-resolved emission
measurement was similar to the previously employed one.7)
The light source was a mode-locked Ti:sapphire laser (Clark)
pumped by an Ar-ion laser (Coherent, Innova 310). The pulse
duration was about 100 fs centered at around 790 nm. The average power at a 100 MHz repetition rate was about 1 W. The
second-harmonic wave (395 nm, ∼ 200 fs), generated by frequency conversion from the fundamental wave using a lithium
triborate (LBO) crystal, was used as an excitation light of thesample. The typical average power of the excitation pulses

2.3 Determination of χ (3) (−ω; 0, 0, ω) and γ (−ω; 0, 0, ω)
dispersions
The third-order nonlinear optical susceptibility
χ (3) (−ω; 0, 0, ω) can be calculated from absorption spectraA(ω), Kerr-effect electroabsorption spectra 1A(ω), refractive index n(ω) and refractive index change 1n(ω).5, 6) The
refractive index n(ω) is related to the absorption coefficientthrough the Kramers-Kronig (K-K) relation, and the refractive index change 1n(ω) due to electromodulation can be obtained using the following derivative form of the K-K relation,
Z ∞1A(ω0 )
c
dω0 ,
(2.1)
1n(ω) = Pπ
ω0 2 − ω20where P denotes the Cauchy principal value of the integral
and c is the velocity of light. This relation is valid for thecase where the frequency of the applied electric field is low
and the system can be regarded to be in a steady state. The
third-order nonlinear optical susceptibility χ (3) (−ω; 0, 0, ω)
can be expressed by1[(n(ω)1n(ω) − k(ω)1k(ω))χ (3) (−ω; 0, 0, ω) =6π F 2+i(n(ω)1k(ω) + k(ω)1n(ω))] ,(2.2)

Xe Lamp
L

Computer
M

F

M3
M2

M1
PrinterPort

SampleStepping
Motor

Stepping Motor
Driver

RS232C

M5

Trans

Power Amp.

M4
M : Monochromator
F : Filter
L : UV Lens
M1,M2,M4,M5 : Concave Mirror
M3 : Al Mirror
PMT : Photomultiplier Tube
Osc : Oscillator
DMM : Digital Multimeter
Fig. 1.

PMT
Osc

Lock-in Amp.
I-V Amp.

DMM

Low-pass
FilterExperimental setup for electroabsorption measurement.

4058

Jpn. J. Appl. Phys. Vol. 38 (1999) Pt. 1, No. 7A

H. M URAKAMI et al.

where F is the amplitude of the applied electric field and k
and 1k are the extinction coefficient and its change due toelectromodulation, respectively, represented by
λ
A(ω),
4π
λ
1A(ω),
1k(ω) =
4πk(ω) =

(2.3)
(2.4)

where λ is the wavelength.
Theaveragethird-order
hyperpolarizabilityhγ (−ω; 0, 0, ω)i is expressed byχ (3) (−ω; 0, 0, ω),(2.5)
hγ (−ω; 0, 0, ω)i =N L(0)2 L(ω)2
where N is the molecular number density. Here L(ω) is theLorentz local-field factor given by²(ω) + 2,(2.6)
L(ω) =
3
where ² is the dielectric constant.
2.4 Derivation of static dipole-moment change and static
polarizability change
When an electric field is applied to isotropic samples, thechange in absorption spectrum can be described by a linear
combination of an absorption spectrum and its first and second derivatives, as follows:4, 8, 9)
µ ¶
· µ ¶
A
A
d
+ a1
1A(E, F)/E = a0
E
dE E
¸
µ ¶
A
d2
+
·
·
·
R(θ )[L(0)F]2 ,+a2
d E2 E(2.7)
where E is the photon energy. a0 , a1 and a2 are, respectively,
given by
a0 =

X2
2Y
+
,
µ2ng
µng

(2.8)

a1 =

2X
1
1µ + 1α,
µng
2

(2.9)

1
(1µ)2 ,
(2.10)
2
where 1µ and 1α are the permanent-dipole-moment difference and the linear-polarizability difference between an
excited state and a ground state. Here, µng , X and Y are
the transition-dipole moment, the transition-dipole-moment
polarizability and its hyperpolarizability, respectively. They
have a relationship expressed in the dyadic notation

where ξ is the angle between the directions of µng and 1µ,
and θ is the angle between the directions of the applied electric field and the polarization vector of the incident light. In
the present study, R(θ ) is reduced to 1/5 because ξ = 0◦ andθ = 90◦ from the above-mentioned assumption and the configuration of the experimental setup.
The first, second and third terms in eq. (2.7) correspond tothe change in oscillator strength, spectral shift and broadening
induced by the applied electric field, respectively. When thechange in linear polarizability is significant, the first derivative of the absorption spectrum is dominant in the electroabsorption spectrum. In contrast, when the change in the permanent dipole moment is significant, the second derivative isdominant. This formula is valid for an isolated absorption
band due to a single electronic transition.
3. Experimental Results
3.1 Absorption and electroabsorption spectra
The absorption spectra for DEANST/PMMA films dependon the concentration of DEANST molecules. Figure 2 shows
the absorption spectra (A) from 0.1 to 40 wt% dopant concentrations, which are scaled so that the peaks are of thesame height. The first dipole-allowed electronic transition
band of the DEANST molecule is at ∼ 2.8 eV, corresponding to the π -π ∗ transition.10, 11) It is noted that small shoulders, which are slightly larger on the low-energy side, appear
on both sides of the absorption spectrum at dopant concentrations over 15 wt%.
Figure 3 shows the electric-field-modulated absorption(EA) spectrum for DEANST-doped PMMA thin film
(DEANST/PMMA film) together with the absorption spectrum for the dopant concentration of 0.1 to 40 wt% in theregion of 2.07 to 3.59 eV (600 to 345 nm). The position of
the first peak of the EA spectrum is the absorption edge of thesample. The magnitude of the signal change (1A) induced by
the electric field ( ∼ 105 V/cm) is on the order of 10−5 –10−4 .
When the dopant concentration of the sample varies from 0.1
to 40 wt%, the EA signal shifts to the low-energy side follow-

a2 =where F int is the internal electric field (F int = L(0)F). In
eqs. (2.8)–(2.10), we assume that all the electric properties of
DEANST are dominated by only one component along the
Z -axis (Z -axis is defined as the long axis of the DEANST
molecules). Namely, the vectors µng and 1µ, the tensors X
and Y and 1α can be expressed by µng,z , 1µz , X zz , Yzzz and
1αzz , respectively. Thus, we use the scalar notation µng , 1µ,
X, Y and 1α. R(θ ) is a general sensitivity function given by1[5 + (3 cos2 ξ − 1)(3 cos2 θ − 1)],
(2.12)R(θ ) =
15

[Normalized]

0.8

0.6

40 wt%

0.1 wt%0.4

Aµng (F int ) = µng + X · F int + F int · Y · F int + · · · , (2.11)

1.0

0.2

0.0
2.0

2.2

2.4

2.6

E

2.8

3.0

3.2

3.4

3.6

[eV]

Fig. 2. Normalized absorption spectra of DEANST/PMMA films in the
dopant concentration range of 0.1–40 wt%.

Jpn. J. Appl. Phys. Vol. 38 (1999) Pt. 1, No. 7A

H. M URAKAMI et al.

1.0x1040 wt%-11

40 wt%

0.0
(3)

-1.0

Reχ
(3)
Imχ
(3)
|χ |

-11

35 wt%
1.0x10
0.5
0.0
-0.5
-1.0
-11
1.0x1025 wt%
0.5

35 wt%[esu]

25 wt%

20 wt%

χ(3)(−ω;0,0,ω)∆Ascaled

4059

15 wt%

0.0
-0.5
5x10

-12

20 wt%

0
-5
8x10

-12

4

15 wt%

0
-4

5 wt%

-8
2x10

-12

5 wt%

0
-2

0.1 wt%
4x10

-14

2

0.1 wt%0-2

2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6

E

[eV]

Fig. 3. The scaled EA spectra of DEANST/PMMA films (solid lines) in the
dopant concentration range of 0.1–40 wt%, and corresponding absorption
spectra (broken lines). All EA spectra were corrected for differences inapplied field and optical density (see text).

ing the absorption-spectrum change. In order to compare themagnitudes of the EA signals, the spectra are normalized by
the following equation:12)
1Ascaled =1A,
2
Amax Fint(3.1)

where Amax is the maximum value of the absorption spectrum
and Fint is the internal electric field. 1Ascaled is proportional
to the interaction strength between the sample and the electricfield. As the concentration of DEANST molecules increases,
the magnitude of the first peak of the scaled EA signal decreases up to 15 wt%, above which, change is negligible. Thechanges in absorption and EA spectra with concentration re--4
2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6

E

[eV]

Fig. 4. Dispersion of the third-order nonlinear optical susceptibility
χ (3) (−ω; 0, 0, ω) for DEANST/PMMA films in the dopant concentration
range of 0.1–40 wt%. Solid, broken and dotted lines represent the real part,
imaginary part and absolute value of χ (3) (−ω; 0, 0, ω), respectively.

veal that the properties of DEANST in PMMA change dramatically at around the concentration of ∼15 wt%.
3.2 Third-order optical nonlinearity
Figure 4 shows dispersions of the real part, the imaginary part and the absolute value of χ (3) (−ω; 0, 0, ω) for
0.1 to 40 wt% DEANST/PMMA films, which were calculated in the manner described in §2.3. The absolute valueof χ (3) (−ω; 0, 0, ω) for the 35 wt% DEANST/PMMA film is
1.6 × 10−12 esu in the nonresonant region (2.1 eV). This value
agrees with the value of χ (3) (−3ω; ω, ω, ω) = 2 × 10−12 esu
at 1.17 eV (1.06 µm) for a 33.5 wt% DEANST/PMMA film

Jpn. J. Appl. Phys. Vol. 38 (1999) Pt. 1, No. 7A

H. M URAKAMI et al.

measured by an optical third-harmonic generation technique.2)
Using the experimental result of the lowest-concentration
sample (0.1 wt%), the averaged third-order hyperpolarizability hγ (−ω; 0, 0, ω)i is evaluated to be 5.8 × 10−35 esu at
2.1 eV. This value is 3.6 times larger than the value ofhγ (−ω; 0, 0, ω)i = 1.602 × 10−35 esu at 2.06 eV calculatedby an ab intio self-consistent-field method.10) This deviation
is explained as follows. In the far-off-resonant region, where
the contribution to the EA signal by the electrostrictive effectbecomes significant, the value of hγ (−ω; 0, 0, ω)i from the
EA spectroscopy can be overestimated.
Figure 5 shows concentration dependences of the maximum values of hγ (−ω; 0, 0, ω)i and |χ (3) (−ω; 0, 0, ω)|.
Here we emphasize that hγ (−ω; 0, 0, ω)imax calculated fromthe |χ (3) (−ω; 0, 0, ω)|max decreases with dopant concentration over 10 wt%. Unless the intermolecular interaction isconsidered, the nonlinearity hγ (−ω; 0, 0, ω)i in a moleculeis, in general, independent of the concentration, and hence themacro-nonlinearity |χ (3) (−ω; 0, 0, ω)| is proportional to theconcentration.13) However, |χ (3) (−ω; 0, 0, ω)| obtained fromour experiment is not proportional to the dopant concentration, particularly at high concentrations. Thus, the molecular
nonlinearity hγ (−ω; 0, 0, ω)i decreases with concentration.
The reason for this behavior will be discussed in §4.
3.3 Evaluation of static dipole-moment difference and static
polarizability difference
The absorption spectrum of the charge-transfer molecule isgenerally so broad that the direct numerical derivative of theabsorption spectrum with the measured wavelength resolutionof 2 nm becomes very noisy. This makes the analysis using
the direct numerical derivatives difficult. In order to avoid
this difficulty, we first fit the absorption spectrum to a skewed
Gaussian band,8)A(E) = b0 exp[−(E − E 0 )2 /b12 − b2 (E − E 0 )3
− b3 (E − E 0 )4 ].

(3.2)

Secondly, using the derivative from the fitted absorption spectrum, we analyze the EA spectrum. Here, we assume thatthe component proportional to the absorption spectrum in themeasured EA spectrum is negligible, that is, a0 = 0 in eq.
(2.7).
For example, Figs. 6(a) and 6(b) show the absorption andEA spectra at the dopant concentration of 0.1 wt%, together
with fitting results based on eqs. (2.7) and (3.2). The EA spectrum can be decomposed into the first- and second-derivative
components. From these results, the values of 1µ and 1α
can be evaluated to be 7.7 debye and 2.4 × 10−21 cm3 , respectively. The value of 1µ is somewhat smaller than that for
4-(N,N-dimethylamino)-β-nitrostyrene (DMANST) (1µ =10.3 debye4) ) which has almost the similar molecular structure.
Over the dopant concentration of 15 wt%, the measured
EA spectra are dissimilar in shape to the first and second

3.0x10-2

0.1 wt%
(a)

2.5
2.0

A

4060

1.5
1.0
0.5

-11

0.0

(a)
1.0x10

1.5

-4

(b)

Experimental data
First derivative
Second derivative
Sum of derivatives

1.0

0.5
0.5

∆A

(3)

|χ (−ω;0,0,ω)|max [esu]2.0x100.0-33
3.0x10<γ(−ω;0,0,ω)>max [esu]Experimental data
Theoretical fit

0.0

(b)

2.5

-0.5

2.0
1.5
1.0

-1.0

0.5
0.0

2.0
0

10

20

30

40

Concentration [wt%]Fig. 5. Concentration dependences of (a) |χ (3) (−ω; 0, 0, ω)|max and (b)hγ (−ω; 0, 0, ω)imax for DEANST/PMMA films. Broken lines represent|χ (3) (−ω; 0, 0, ω)|max and hγ (−ω; 0, 0, ω)imax value without the intermolecular interaction.

2.2

2.4

2.6

E

2.8

3.0

3.2

3.4

3.6

[eV]

Fig. 6. (a) Absorption spectrum of 0.1 wt% DEANST/PMMA film (solidline) and its theoretical fit (broken line). (b) Electroabsorption spectrum(solid line) and its theoretical fit (dotted line) together with the contribution of the first and second derivatives of the absorption spectrum (brokenlines).

Jpn. J. Appl. Phys. Vol. 38 (1999) Pt. 1, No. 7A

H. M URAKAMI et al.

0.8

35 wt%
(a)

A1
A2
A3

A

0.6

(A2 /A1 and A3 /A1 ). Both increase with dopant concentration.
Concentration dependences of 1µ and 1α values of thethree absorption bands are shown in Fig. 9. It is seen that, withincreasing dopant concentration, the values of 1µ decrease
while those of 1α negligibly change. Moreover, it should be
noted that the ratio of the 1α value of the A1 absorption band
(1α A1 ) to that of the A2 band (1α A2 ) is about one to two,since this ratio represents the ratio of effective volume sizeof the species yielding 1α A1 to that of the species yielding
1α A2 .14)
3.4 Picosecond temporal behaviors of emission
The left-hand side of Fig. 10 shows the emission-decay

0.4

Ratio of the absorption intensity

derivatives and even their sum. In other words, we cannot
fit the EA spectra over the dopant concentration of 15 wt%
when we consider only one absorption band. Thus, we decompose the absorption spectra into three bands. For example, Fig. 7 shows the results for the dopant concentration of
35 wt%. Figure 7(a) shows the measured absorption spectrum and the three decomposed absorption bands. The central
absorption band has the same shape as the absorption spectrum observed for the lower-concentration samples, namely
a skewed Gaussian shape (denoted by A1 ). The other absorption bands also have Gaussian shapes (denoted A2 andA3 on the lower- and higher-energy sides of the center absorption band, respectively). Figure 7(b) shows the measured
and fitted EA spectra with the contributions of first and second derivatives of the three absorption bands. The measured
spectrum is reproduced well by the fitting. 1µ and 1α values for each absorption band are evaluated using eqs. (2.9)
and (2.10).
Figure 8 shows the concentration dependence of the absorption intensities of A2 and A3 normalized by that of A1

4061

A2/A1

0.3

0.2

0.1

A3/A1

0.4
0.0
15

20

25

30

Concentration

0.2

35

40

[wt%]

Fig. 8. Dopant concentration dependences of the ratios of the absorption
intensities, A2 /A1 and A3 /A1 .

0.0
4x10

-4

Experimental data
Sum of derivatives
2
2
dA1/dE + d A1/dE

(b)

2

2

2

2

6x10

dA3/dE + d A3/dE

∆α

2

∆A

[cm3]

dA2/dE + d A2/dE

0

-21

A2

(a)
4
2

A1

0
-2
-4

A3

-6
10

∆µ [D]

-2

-4
2.0

2.2

2.4

2.6

E

2.8

3.0

3.2

3.4

3.6

[eV]

Fig. 7. (a) Absorption spectrum of 35 wt% DEANST/PMMA film (solidline) and three decomposed absorption bands (broken lines). (b) Electroabsorption spectrum (solid line) and its theoretical fit (dotted line) together with the contribution of derivatives of three absorption bands (broken lines).

(b)

8
6

A1
A2
A3

4
2
0
0

10

20

Concentration

30

40

[wt%]

Fig. 9. Dopant concentration dependences of (a) 1α and (b) 1µ values of
DEANST/PMMA films for the three absorption bands.

4062

Jpn. J. Appl. Phys. Vol. 38 (1999) Pt. 1, No. 7A

Emission Intensity [arb. units]

40 wt%

2.26 ± 0.02 eV

25 wt%

2.29 ± 0.02 eV

20 wt%

2.32 ± 0.02 eV

15 wt%

2.34 ± 0.02 eV

5 wt%

2.42 ± 0.02 eV

0.1 wt%00 ps
100 ps200 ps2.26 ± 0.02 eV

35 wt%

H. M URAKAMI et al.

200

300

τ1

Decay constants (ps)
τ2

0.1
5
15
20
25
35
40

510
100
21
18
15
12
12

270
132
128
125
124
122

4. Discussion

400 2.0 2.1 2.2 2.3 2.4 2.5 2.6Time [ps]Concentration(wt%)

doped PMMA films are listed in Table I. It is found thatthe emission decay profile in the lowest-concentration sample (0.1 wt%) consists of one component, while the emission
in the higher concentration region (not less than 5 wt%) has afast- and a slow-decay component. The emission-peak photon energy of the fast-decay component is higher than that of
the slow-decay component. Both the time constants of the
fast- and slow-decay components (τ1 and τ2 ) decrease withdopant concentration. Moreover, the time-resolved emission
spectra of both fast- and slow-decay components shift to thelower-energy side with increasing dopant concentration.

2.46 ± 0.02 eV

100

Table I. Emission decay constants for 0.1 to 40 wt% DEANST/PMMA
films.

E[eV]

Fig. 10. The emission decay profiles at around the emission peak of E 0with the energy resolution width 21E of 20 meV in the dopant concentration range of 0.1–40 wt% for DEANST/PMMA films (left-hand side) andcorresponding time-resolved emission spectra at t0 = 0, 100 and 200 ps(right-hand side).

profiles I (t, E 0 ±1E) at around the emission peak of E 0 withthe energy resolution width 21E of 20 meV in the dopant
concentration range of 0.1–40 wt% for DEANST/PMMA
films. The corresponding time-resolved emission spectra
I (t0 + 1t, E) at t0 = 0, 100 and 200 ps are also shown on
the right-hand side in Fig. 10. The emission decay signals are
obtained as an integral with respect to the energy width 21E
around E 0 and the time-resolved spectral signals are obtained
as an integral during the interval of 1t = 30 ps from t0 where
the time origin t0 = 0 is set as the arrival time of the excitation
pulse peak to the sample.
Emission decay time constants for 0.1 to 40 wt% DEANST-

Here, we can summarize the experimental results for
DEANST-doped PMMA films as follows: [1] the absorption spectra broaden with increasing dopant concentration, [2] the EA spectra shift to the low-energy sidewith increasing dopant concentration, [3] the magnitude of
the first peak of the EA signals decreases up to 15 wt%,
above which it does not change, [4] hγ (−ω; 0, 0, ω)imax decreases with increasing dopant concentration over 15 wt%, [5]|χ (3) (−ω; , 0, 0, ω)|max is not proportional to the dopant concentration over 15 wt%, [6] the absorption spectrum consistsof three bands over 15 wt% (lower- and higher-energy bands
appear), [7] the ratios of both A2 /A1 and A3 /A1 increase
with dopant concentration, [8] 1α negligibly changes withconcentration, [9] the ratio between 1α A1 and 1α A2 is about
1 : 2, [10] 1µ decreases with increasing dopant concentration over 15 wt%, [11] a slow-decay emission band appearson the low-energy side at dopant concentrations greater than
5 wt%, and [12] the emission-decay constant decreases withincreasing dopant concentration.
For the two-level model, the average third-order hyperpolarizability hγ (−ω; 0, 0, ω)i and the average linear polarizability hα(−ω; ω)i are represented by the following equations
based on the quantum-mechanical perturbation theory:15)

·
¸
1 X
1
1
2
2
|µ
|
(1µ)
+
,
ng
(ωng − ω − i0ng )3(ωng + ω + i0ng )3h̄ 3 nµ¶1
1
1X2|µng |+,
hα(−ω; ω)i ∝ωng − ω − i0ng
ωng + ω + i0ngh̄ nhγ (−ω; 0, 0, ω)i ∝where µng is the electronic transition dipole moment between
the excited state n and the ground state g and 1µ is thestatic-dipole-moment difference denoted in §2.4. 0ng is therelaxation rate between the excited state and the ground state.

(4.1)
(4.2)

h̄ωng is the energy difference between the excited state andthe ground state. In the case of the resonant condition, that is,in the case where the excitation photon energy of h̄ω is nearh̄ωng , hγ (−ω; 0, 0, ω)i of eq. (4.1) is reduced toJpn. J. Appl. Phys. Vol. 38 (1999) Pt. 1, No. 7Ahγ (−ω; 0, 0, ω)ireso ∝|µng |2 (1µ)2
1 X.
3h̄ n (ωng − ω − i0ng )3

H. M URAKAMI et al.

A3

(4.3)

In addition, hα(−ω; ω)i of eq. (4.2) in the low-frequency
limit, that is, the average static linear polarizability hα(0; 0)i,
is expressed by
1 X 2ωng |µng |2hα(0; 0)i ∝.
(4.4)
2 + 02h̄ n ωng
ng
The molecular hyperpolarizability hγ (−ω; 0, 0, ω)i, which
is defined as the nonlinearity in a molecule, is independentof the DEANST concentration, unless the intermolecular interaction is considered. However, the experimental result[4] indicates that DEANST molecules in PMMA film interact with each other and this interaction can influence µng
and/or 1µ. On the other hand, based on the expressionof hα(0; 0)i and the experimental result [8], it is reasonable to say that |µng | or 0ng negligibly changes with concentration. Thus, it is concluded that the decrease in 1µwith increasing dopant concentration causes the decrease inhγ (−ω; 0, 0, ω)imax . Furthermore, this explains the experimental result [5] well through eq. (2.5).
Based on the experimental results [3], [4], [6], [7], [10] and[12], we conclude that DEANST molecules aggregate in the
PMMA films at concentrations over 5 wt%,16) and the concentration of aggregates increases with the total DEANST
concentration. Thus, this aggregation affects the interaction among DEANST molecules. Consequently, both the absorption spectrum and the EA spectrum change and 1µ or
hγ (−ω; 0, 0, ω)i decreases with increasing dopant concentration. This is supported by the experimental results [1], [2] and[11]. Moreover, the experimental result [9] suggests that theaggregate is a dimer.
On the basis of these results and Kasha’s theory of aggregates,17) the origin of new absorption bands and the mechanism of the excited-state energy relaxation with two emission bands at high dopant concentrations are understood as
follows. Figure 11 shows the probable energy diagram of
DEANST/PMMA films in the high concentration region.
In this concentration region, both monomers and dimers of
DEANST molecules coexist. The monomer level is split into
two levels by the formation of aggregates. The lower energy
level (A2 ) is mainly dipole-transition-allowed, but the higher
energy level (A3 ) is partially dipole-transition-allowed. The
emission of DEANST/PMMA films with the lowest concentration is from the monomer level (A1 ) and the relaxation
rate (τ1−1 ) is slow. DEANST molecules begin to aggregate
at about 5 wt% concentration and the concentration of dimers
increases with the total DEANST concentration. Thus, therelaxation rate of monomers rapidly becomes faster with increasing dopant concentration because of the energy transferfrom monomers to dimers. Since the energy position of theemission from dimers is on the lower-energy side of that frommonomers, the relaxation from the lower level of dimer isslower than that from the monomer level. The relaxation rateof dimers (τ2−1 ) also becomes faster with increasing dopant
concentration due to the energy transfer between dimers.
It follows from the discussion above that thehγ (−ω; 0, 0, ω)i values in the higher concentration region evaluated in this study are the effective valThat is,ues of hγ (−ω; 0, 0, ω)i (hγ (−ω; 0, 0, ω)ieff ).

4063

A1
knr

A2

τ1-1

Monomer

τ2-1

Dimer

Fig. 11. The energy diagram of DEANST/PMMA film in the higher concentration region. knr is the nonradiative relaxation rate from A1 to A2 .
τ1−1 and τ2−1 are the emittive relaxation rates from A1 to ground state andA2 to ground state, respectively.

hγ (−ω; 0, 0, ω)ieff is defined to be the third-order nonlinearity per monomer molecule whether DEANST molecules aggregate or not.
5. Conclusion
We measured the absorption and EA spectra for DEANSTdoped PMMA films in the dopant concentration range of
0.1–40 wt%. From these results, we calculated the dispersion of the third-order nonlinear optical susceptibility
χ (3) (−ω; 0, 0, ω) using the Kramers-Kronig relation. In addition, we evaluated the static polarizability difference 1αand the static dipole-moment difference 1µ. Furthermore,
we measured the picosecond emission-decay profiles and thetime-resolved emission spectra for DEANST-doped PMMA
films at 0.1–40 wt% concentrations. Consequently it was
found that the absorption spectrum, the EA spectrum, thetime-resolved emission spectrum, the maximum third-ordersusceptibility, the maximum hyperpolarizability and the permanent dipole-moment difference, except for the linear polarizability difference, significantly change at dopant concentrations over 5 wt%.
From these experimental results, we concluded that
DEANST molecules in PMMA films aggregate at concentrations over 5 wt%. This aggregation gives rise to two newabsorption bands. In addition, the intermolecular interaction affected by the aggregation causes a decrease in 1µ
and hγ (−ω; 0, 0, ω)ieff , and the nonproportional behavior
of |χ (3) (−ω; 0, 0, ω)| with increasing dopant concentration.
Furthermore, this aggregation explains the absorption spectral change, the EA spectral shift and the appearance of twoemission-decay constants with increasing dopant concentration. Finally, we evaluated the average aggregation number of
DEANST molecules to be two which suggests that DEANST
molecules in PMMA films form dimers at concentrations over
5 wt%.

4064

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H. M URAKAMI et al.
11) S. J. Lalama and A. F. Garito: Phys. Rev. A 20 (1979) 1179.
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13) In a strict sense, since refractive index n(ω) or Lorentz local field factor
L(ω) depends on the dopant concentration, |χ (3) (−ω; 0, 0, ω)|max is
not proportional to the dopant concentration. Thus, the broken line for|χ (3) (−ω; 0, 0, ω)|max values without the intermolecular interaction isslightly curved, not linear. However, even in the case of considering
the concentration dependence of L(ω) in the DEANST/PMMA films,|χ (3) (−ω; 0, 0, ω)|max can be regarded as almost proportional to thedopant concentration.
14) K. Misawa and T. Kobayashi: Nonlinear Opt. 14 (1995) 103.
15) R. W. Boyd: Nonlinear Optics (Academic Press, Boston, 1992) p. 101.
16) The evaluation of the concentration beginning with the aggregation(C a ) by means of the absorption and EA measurements differs fromthat of the emission measurements. This is due to the fact that the lattermeasurements are more sensitive than the former ones. Therefore, we
evaluated C a to be 5 wt% by the latter measurement.
17) M. Kasha: Radiat. Res. 20 (1963) 55.