Concentration variation of quadratic NLO susceptibility in PMMA-DR1 side chain polymer

Article abstract of DOI:10.1080/15421401003720017

Chemical synthesis and concentration dependence of two second order NLO tensor components: Χ⁽²⁾_pp(-2ω ω, ω) and Χ⁽²⁾_sp(-2ω ω, ω) was studied for a side chain polymer PMMA-DR1 in thin films by optical second harm

Full text of DOI:10.1080/15421401003720017

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Concentration Variation of Quadratic
NLO Susceptibility in PMMA-DR1 Side
Chain Polymer
a b
c
d
d
b
F. Kajzar
, O. Krupka , G. Pawlik , A. Mitus & I. Rau
a
Angers University , POMA Laboratory , Angers, France
b
Faculty of Applied Chemistry and Materials Science, University
Politehnica Bucharest , Bucharest, Romania
c
Department of Chemistry , Taras Schevchenko Kiev National
University , Kiev, Ukraine
d
Institute of Physics, Wroclaw Technical University , Nabrzeze
Wyspianskiego, Wroclaw, Poland
Published online: 28 May 2010.
To cite this article: F. Kajzar , O. Krupka , G. Pawlik , A. Mitus & I. Rau (2010) Concentration
Variation of Quadratic NLO Susceptibility in PMMA-DR1 Side Chain Polymer, Molecular Crystals and
Liquid Crystals, 522:1, 180/[480]-190/[490], DOI: 10.1080/15421401003720017
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Mol. Cryst. Liq. Cryst., Vol. 522: pp. 180=[480]–190=[490], 2010
Copyright # Taylor & Francis Group, LLC
ISSN: 1542-1406 print=1563-5287 online
DOI: 10.1080/15421401003720017
Concentration Variation of Quadratic
NLO Susceptibility in PMMA-DR1
Side Chain Polymer
1
F. KAJZAR, O. KRUPKA, G. PAWLIK,
,2
3
4
4
A. MITUS, AND I. RAU
2
1
Angers University, POMA Laboratory, Angers, France
Faculty of Applied Chemistry and Materials Science, University
2
Politehnica Bucharest, Bucharest, Romania
3
Department of Chemistry, Taras Schevchenko Kiev National
University, Kiev, Ukraine
4
Institute of Physics, Wroclaw Technical University, Nabrzeze
Wyspianskiego, Wroclaw, Poland
Chemical synthesis and concentration dependence of two second order NLO tensor
components: vpp ðꢀ2x; x; xÞ and vsp ðꢀ2x; x; xÞ was studied for a side chain poly-
ð2Þ
ð2Þ
mer PMMA-DR1 in thin films by optical second harmonic generation techniques.
The noncentrosymmetry was created by the corona poling technique. The results
ð2Þ
show that for small chromophore concentrations the vpp ðꢀ2x; x; xÞ susceptibility
follows linearly the density number of active chromophores, reaches a maximum,
than decreases and stabilizes.
Keywords Concentration dependence of SHG susceptibility; electric field
poling; NLO susceptibility; nonlinear optics; poled polymers; second harmonic
generation
Introduction
Electro-optic polymers [1–3] have emerged as a new class of photonic materials for
different kinds of application in second order nonlinear optical devices and parti-
cularly in optically active waveguides. They marry excellent optical quality of usually
optically inactive, amorphous, polymer matrix with highly nonlinear optical active
chromophores, embedded in. The necessary for this kind of applications noncentro-
symmetry is obtained either by DC field [4] or by all optical poling [5]. Because of the
amorphous structure and solubility these materials usually can be easily processed
into good optical thin films. Such property is particular importance as most of
applications are targeted waveguiding configuration.
Address correspondence to F. Kajzar, Angers University, POMA Laboratory, 2 bd
yL aa hv oo oi s. ice or m, Angers 49045, France. Tel.: þ40213154193; Fax: þ40213154193; E-mail: frkajzar@
180=[480]

(
2)
Concentration Variation of v Susceptibility in PMMA-DR1 181=[481]
The research in this field is driven by numerous practical applications, such as:
.
Laser frequency tuning through frequency doubling by SHG, sum, difference
frequency generation, optical parametric oscillation (OPO)
Optical parametric amplification (OPA) of weak signals
Electrooptic modulation for optical signal transmission
Linear rectification for generation of THz electric pulses
.
.
.
Several thin films preparation techniques were developed and=or applied for
noncentrosymmetric thin film fabrication such as:
.
.
.
.
.
Langmuir-Blodgett technique [6,7]
Solution casting of isotropic [8] and liquid crystalline polymers [9,10]
Epitaxial or quasi-epitaxial growth [11,12]
Self assembly [13]
Intramolecular charge transfer systems [14]
All these techniques present some advantages and disadvantages. Concerning
the electro-optic modulation (EOM) application the best results were obtained with
isotropic polymers, functionalised with highly responsive NLO chromophores [15].
High modulation rate (113 GHz), low half wavelength V (voltage below 1 V) [16]
p
were demonstrated. Electro-optic modulation was also demonstrated with corru-
gated waveguides [17]. Also second harmonic generation (SHG) [18] and optical
parametric amplification (OPA) [19] in waveguiding configuration were demon-
strated. Electro-optic polymers exhibit also large third order NLO properties. A
low control fluence all optical commutator was demonstrated [20].
One of the important problem encountered with electro-optic polymers is the
chromiophore aggregation. In order to get second-order NLO effect the constituent
chromophores have to lack center of inversion. The most efficient, known actually,
are the quasi 1D charge transfer chromophores. These chromophores exhibit not only
a large first hyperpolarizability bzzz component, important for practical applications,
but also a large ground state dipolar moment l. A large dipole moment is important
for orientation as it increases the ordering energy lE, where E is the applied poling field.
But at the same time it leads to a large dipole-dipole interaction leading to their aggre-
gation. Such aggregates are centrosymmetric with no second order NLO response.
Moreover they scatter light increasing in this way the unwanted propagation losses.
On the other hand the second order NLO susceptibility of a poled polymer is given by:
ð2Þ
v
ðꢀx3; x1; x2Þ ¼ NF < b ðꢀx3; x1; x2Þ >IJK
ð1Þ
IJK
ijk
where N is the active molecules number density and F is the factor taking account of
local field (crystal field) acting on molecules.
2
F ¼ ðfxÞ f2x
ð2Þ
For a spherical symmetry molecule
x
e þ 2
f x
¼
ð3Þ
3
x
where e is the medium dielectric constant at x frequency.

1
82=[482]
F. Kajzar et al.
<> is the configurational average taken over all chromophore orientations.
For poled polymers and CT chromophores, taking account of the Kleinman’s
(
2)
relations [21], there are two nonzero v tensor components given by (for details
see e.g., Ref. [22]) the diagonal
ð2Þ
3
v
¼ NFbzzz < cos H >
ð4Þ
ð5Þ
ZZZ
and the off diagonal one
1
ð2Þ
2
v
¼
NFbzzz < sin H cos H >
XXZ
2
where Z is direction of the poling field and H is angle which makes the molecular axis
with Z direction.
For diagonal tensor component the configurational average <> in Eq. (4)
spans between zero for an isotropic system and 1 for a perfectly ordered system.
In the last case of a perfectly ordered polymer with all molecular axes pointing
ð2Þ
in the same direction the off diagonal component v
ꢁ 0.
XXZ
increases linearly with increasing chromophore
ð2Þ
According to Eq. (2) v
ZZZ
concentration. In practice it is not the case because of the already mentioned chromo-
phore aggregation. Therefore it is important to know how the bulk susceptibility
depends on the NLO chromophore concentration to optimise its value. Systematic
studies were done on the Disperse Red 1 (DR1) chromophore grafted on PMMA
(polymethyl methacrylate) polymer. For this purpose side chain polymers with
different DR1 substitution levels were synthesized.
DR1 chromophore (full name: N-Ethyl-N-(2-hydroxyethyl)-4-(4-nitrophenylazo)
aniline) is one of the most studied quasi 1D charge transfer (CT) molecules with
enhanced first hyperpolarizability. Typing just Disperse Red 1 (DR1) on Google
website one obtains 1,450,000 references. Indeed, it can be considered as a model
molecule for second order nonlinear optics, but not only. This molecule, due to the
easiness to excite the double ‘‘ꢀN=Nꢀ’’ bond shows an unusual ability to change
its conformation from trans to cis form and vice versa. This transformation is connec-
ted with its volume change, just change of its rotational mobility. For example there is
a ca. 10% decrease of the volume occupied by molecule passing from trans to cis form.
As such conformational changes are connected with the change of p electron conju-
gation length, as result the material index of refraction is changing too. The trans-cis
izomerization is believed also to be, at least in part, responsible for the mass transpor-
tation when e.g., the side chain polymers with grafted DR1 are subjected to inhomo-
geneous illumination of light [23–25]. Molecules from bright areas move to the dark
ones. Trans-cis izomerization process is exploited also in all optical poling [26] of
polymers and play also an important role in optical depoling [27,28].
The concentration dependence of another quadratic susceptibility tensor which
describes the linear electro-optic effect was performed for another, similar chromo-
phore which is Disperse Red 19 (DR19) dissolved in PMMA matrix (guest-host
system) [29]. The authors observe almost a linear increase of the linear electro-optic
coefficient r in function of DR19 weight concentration up to 30 w%, in agreement
with Eq. (4). However, as it is discussed below, 30% w concentration corresponds
to a relatively small chromophore mole concentration (<10%), because of its large
molecular mass in comparison with that of the host monomer. In the present study

(
2)
Concentration Variation of v Susceptibility in PMMA-DR1 183=[483]
we go far beyond this concentration and we measure the electronic part of quadratic
susceptibility by using the SHG technique, which gives the fast electronic part of
quadratic susceptibility. The experiments are done for side chain polymers, for which
it is believed that the chromophore aggregation takes place at higher dye loading
as in guest-host systems. Also both tensor components: the diagonal and the off
diagonal are determined for each chromophore concentration studied.
Chemical Synthesis
Characterization Techniques
1
H NMR (500 MHz) spectra were recorded by the ‘‘Bruker Advance DRX-500’’
spectrometer using DMSO-d as solvent. Chemical shifts are in ppm from the
6
internal standard tetramethylsilane. UV-VIS measurements were performed at room
temperature with a Perkin-Elmer UV=VIS=NIR Lambda 19 spectrometer. For
solution using a pure silica liquid cell was used while thin films were deposited on
the BK7 glass substrate. The Differential Scanning Calorimetry: Q20 DSC model
was used to determine the glass transition temperatures (Tg) of all polymers. The
sample was initially stabilized and after the first scan was made at the heating rate
ꢂ
ꢂ
ꢂ
of 10 C=min up to 200 C then cooled to 20 C. Finally, a second scan was performed
ꢂ
ꢂ
heating the sample at the rate of 10 C=min up to 200 C. The measured glass
transition temperatures were in good agreement with the reported values [30,31]. Size
exclusion Chromatography: The molecular weights and the molecular weight distri-
bution of the polymers were taken with a system equipped with a guard column,
followed by 2 columns, using the Spectra SYSTEM RI-150 and a Spectra SYSTEM
ꢂ
UV2000 detectors. The solvent used was THF at a flow rate of 1 ml=min at 35 C.
Polystyrene standards were used for calibration.
Materials Synthesis
0
0
-[(2-Methacryloyloxyethyl)ethylamino]-4-nitroazobenzene (M). 4 -[(2-Methacryl-
oyloxyethyl)ethylamino]-4-nitroazobenzene was prepared by the procedure described
4
0
below 4 -[(2-hydroxyethyl)ethylamino]-4-nitroazobenzene (2 g, 0.006 mol) and
triethylamine (0.65 mL. 0.0065 mol) was dissolved in THF (35 mL). The solution
was kept in an ice bath for 10 min. Then methacryloyl chloride (0.67 mL.
0
.0065 mol) was added dropwise during 30 min to reaction mixture. The resulting
ꢂ
mixture was stirred during 5 hours at 0 C. The solvent was removed by rotary
evaporation, and the residue was washed with a solution of sodium carbonate
(0.7 g) in water (40 mL). The solid was filtered, washed with water, and air dried.
The solid was recrystallized from methanol. Crystals, yield 80%.
1
HNMR (DMSO-d ), d(ppm): 8.16 (d, 2H, Ar), 7.87 (d, 2H, Ar), 7.85 (d, 2H,
6
Ar), 6.81 (d, 2H, Ar), 6.1 (s, 1H, CH ), 5.59 (s, 1H, CH ), 4.39 (m, 2H, OCH ),
2
2
2
3
.72 (m, 2H, NCH ), 3.57 (m, 2H, NCH ), 1.93 (s, 3H, CH ), 1.24 (m, 3H, CH ).
2 2 3 3
Polymers Synthesis
Polymers with desired chromophore concentrations were obtained by free-
radical polymerization in toluene. The polymerizations were carried out in 10 wt%
0
toluene solution of 4 -[(2-methacryloyloxyethyl)ethylamino]-4-nitroazobenzene and

1
84=[484]
F. Kajzar et al.
Figure 1. The synthesis route of studied PMMA-DR1 side chain polymers (nþm ¼ 1).
methylmethacrylate with monomers initial mole ratios corresponding to the desired
concentration. The polymerization processes were conducted using AIBN as a free
ꢂ
radical initiator (1 wt% of monomers) and at 80 C for more than 24 h in argon
atmosphere. The initial mixtures were degassed with repeated freeze cycles. The
synthesized copolymers were isolated from the reaction solution by precipitation into
methanol followed by reprecipitation from toluene into methanol and then dried at
ꢂ
7
0 C overnight. The copolymerization ratios were calculated on the basis of the inte-
1
gration ratio of H NMR measurements; kmax ¼ 276, 476 in THF; in thin film on the
glass slide kmax ¼ 474. The synthesis route of the studied PMMA-DR1 side chain
polymers is shown in Figure 1. Polymers with mole fraction C ¼ n ¼ 0.08, 0.15,
m
0
.35, 0.50, and 0.65 were obtained (m ¼ 1-n).
Thin Film Deposition and Poling
Thin films of studied polymers were obtained by spin coating of filtered solutions on
carefully cleaned BK7 glass slides. The principle of deposition (of the mixture with
certain viscosity) is based on a homogeneous spreading out of the solution on the
rotating substrate with an angular speed of 1000 rpm. The studied polymers are sol-
uble in a large range of organic solvents. We used as solvent 1,1,2-trichlororethane
for the quality of thin film formation. The same polymer concentrations of 100 g=l
were used. Immediately after the deposition, the films were cured in an oven at
ꢂ
80 C and for 60 minutes in order to eliminate any remaining solvent. The thicknesses
of thin films were of about 150 nm, as measured with a profilometer.
The required noncentrosymmetry in thin films was obtained by corona poling
technique [4] (cf. also Kajzar et al. [3], Rau and Kajzar [32]). The poled films were
placed at the distance of 20 mm from the discharge needle to which a high voltage
of 6 kV was applied and during 3 mins. Then films were cooled down to room
temperature under the applied poling field. This poling time is sufficient to obtain
maximum of poling efficiency. All studied films were poled at the same conditions.
No extra electrode on the substrate was used, as the conductivity of BK7 glass is
sufficient to ensure the poling process. Figure 2 shows the optical absorption
spectrum of a thin film of PMMA-DR1 C ¼ 0.5 (50 mol%) before (solid line) and
m

(
2)
Concentration Variation of v Susceptibility in PMMA-DR1 185=[485]
Figure 2. Optical absorption spectrum of a thin film of PMMA-DR1 50 mol% before (solid
line) and after (dashed line) poling.
after (dashed line) poling. The ordering is observed by the decrease of the thin film
optical absorption at normal incidence and the noncentrosymmetry by its red shift
(cf. Page et al. [33]).
Second Harmonic Generation Experiments
The optical SHG measurements were done immediately after the poling in order to
avoid decrease of NLO response by relaxation. The measurements were performed
using a Q switched Nd:YAG laser, operating at 1.0642 mm fundamental wavelength
with 13 ns pulse duration and 10 Hz repetition rate. The experimental set-up is shown
schematically in Figure 3. The films were mounted on a goniometer, mounted on a
rotation stage. The SHG intensities were collected in function of the incidence angle
by rotating thin film around an axis perpendicular to the beam propagation direction
and coinciding with. They were corrected for fundamental beam intensity variations by
Figure 3. Schematic presentation of the experimental setup: F’s – absorptive filters, P –
polarizer, A – analyzer, S sample, Si – silicon photodiode, PMT – photomultiplier.

1
86=[486]
F. Kajzar et al.
measuring it with a fast Si photodiode, located just behind the laser cavity. The
intensity of fundamental beam was controlled by using calibrated neutral filters and
the spurious light, coming particularly from flash lamps, was eliminated by using
absorptive cut-off filters. Its polarization was controlled by the polarizer and half
wavelength plate. By rotating the last the incident light polarization direction was
moved smoothly without changing its intensity. Because the corona poling orient chro-
mophores in the direction of the applied film, i.e., perpendicular to the thin film surface
and existence of only two nonzero tensor components the range of incidence angle
variation has to be very large, as at the normal incidence no SHG signal is observed.
The poled films exhibit 1mm point symmetry. For this symmetry, if one takes
(
2)
account of the already mentioned Kleinman’s relations [21], there are 2 nonzero v
ð2Þ
ð2Þ
tensor components: v
, v
, where is the direction of the poling field (perpen-
XXZ
ZZZ
dicular to the thin film surface). Both can be measured by using two configurations
of polarizations of input fundamental (f) and output harmonic (h) fields.
The output SHG intensity for a thin film is given by
"
#2
ð2Þ
3
v
ðhÞ
ꢀ
ꢀ
ꢀ
ꢀ
1
28p
c2
eff
2
Du
2
x
2
I2x ¼
AðhÞTðhÞ I sin
ð6Þ
De
2
ð2Þ
where v is an effective second order NLO susceptibility for a given propagation
eff
direction defined by the propagation angle h, I is the fundamental beam intensity
x
and A(h), T(h) are, the factors arising from boundary and transmission conditions,
respectively. De ¼ e ꢀ e is the dielectric constant dispersion between harmonic
2
x
x
(2 x) and fundamental (x) frequencies, c is the light velocity in vacuum and Du is
the phase mismatch between fundamental (f) and harmonic (h) beams:
4
p l
Du ¼ u ꢀ u
¼
ðnx cos hx ꢀ n2x cos h2xÞ
ð7Þ
x
2x
kx
where Hx (2x) is the propagation angle at x(2 x) frequency, respectively and nx(2x)
are the corresponding refractive indices.
In order to determine both nonzero tensor components two SHG measurements
are to be performed in s-p and p-p fundamental – harmonic beam configurations.
(2)
In the s-p polarization configurations the effective v (ꢀ2xx,x) susceptibility is
given by:
ð2Þ
ðs ꢀ pÞ ¼ vð2Þ sin 2h
p
2x
v
ð8Þ
eff
XXZ
In the p-p fundamental – harmonic beam configuration it is given by
ð2Þ
ðp ꢀ pÞ ¼ vð2Þ sin h sin h þ v
2
p
x
p
2x
ð2Þ
p
x
p
x
p
x
p
2x
v
cos h ðcos h þ 2 sin h cos h Þ ð9Þ
eff
ZZZ
XXZ
ð2Þ
Thus in the s-p polarization configuration one obtains unambiguously the v tensor
component. This value, injected into Eq. (9) for SHG intensity formula (Eq. (6)) for
XXZ
ð2Þ
p-p polarization configuration gives the value of the v
tensor component.
ZZZ
Equation (6), through Eqs. (7)–(9) shows that the SHG intensity depends on
the propagation length, while it is important to measure it as the function of the

(
2)
Concentration Variation of v Susceptibility in PMMA-DR1 187=[487]
ð2Þ
ð2Þ
1
2
1
2
Table 1. Quadratic susceptibilities dsp (¼ v
ðꢀ2x; x; xÞ) and d (¼ v
XXZ
pp
ZZZ
ðꢀ2x; x; xÞ) in pm=V as measured for different molar concentrations of the side
chain polymer PMMA-DR1. Z is the poling direction. The numbers in brackets
are standard deviations. For calibration the value of d ¼ 0.5 pm=V [34] was used
1
1
Molar concentration (%)
dsp (pm=V)
dpp (pm=V)
8
29 (3)
35 (4)
12 (1)
19 (2)
18 (2)
72 (7)
111 (11)
52 (5)
57 (6)
59 (6)
1
3
5
6
5
5
0
5
incidence angle. We have done it by rotating the film around an axis perpendicular to
the propagation direction and coinciding it. The incident angle SHG intensity depen-
dence can be then fitted using Eq. (6), and respectively (8) or (9), depending on the
fundamental – harmonic beam polarization.
As measuring absolute intensities is usually difficult one uses generally a
standard with usually is a plate of an a-quartz single crystal. We used an y-cut single
crystal and the SHG measurements we performed at the same experimental
ð2Þ
ð2Þ
conditions. As value for v
we used that reported by Choy and Byer (v
¼
XXX
XXZ
1
pm=V at 1 064 nm [34]).
ð2Þ
XXZ
films with different chromophore molar content expressed in percents, are listed in
ð2Þ
The measured values of v
and v
tensor components for the studied thin
ZZZ
Table 1 for both tensor components, expressed in the commonly used notation: d ¼
sp
ð2Þ
ð2Þ
v
=2 and d ¼ v
pp
=2. We observe an almost linear increase of these tensor com-
XXZ
ZZZ
ponents up to C ¼ 0.15 (15 mol %) of DR1 and a decrease at higher concentration.
m
For concentrations starting from C ¼ 0.35 (35 mol %) the both tensor components
m
stabilizes and remains constant.
A similar behavior is observed in the case of solution of lyotropic liquid crystals
(LC) in water [35]. At low concentration only monomers are present. Their concen-
tration increases linearly with LC concentration. At higher concentration micelles (a
kind of aggregates) appear and their concentration is increasing rapidly, while the
monomer concentration stabilizes and remains constant when increasing LC concen-
tration. It means that all introduced LC molecules either attach to micelles or form
new ones.
This result is very important from the point of view of practical applications of
these materials in second order NLO devices. They show that there is an optimal
concentration of chromophores. Its increase leads to aggregation, decrease of
NLO response and as a harmful consequence, the light scattering.
6
. Conclusion
The present study confirms earlier funding of Robinson and Dalton [29] that there is
an optimal chromophore concentration Copt in electro-optic polymers for which the
bulk quadratic susceptibility reaches its maximum. For concentrations smaller than
Copt both susceptibilities follow linearly the chromophore concentration, as it should
(
2)
be. For higher concentrations (C>Copt) v susceptibility decreases. The maximum is

1
88=[488]
F. Kajzar et al.
reached at relatively low molar concentration of about C ¼ 0.15 or very close to this
m
value, as for the next concentration of 35 mol% it falls to less than one half of the
(
2)
maximum value. Both v components: the diagonal and the off diagonal follow
ð2Þ
ð2Þ
similar dependence on concentration and the ratio vpp =vsp remains constant within
experimental accuracy with a value of about 3. It corresponds to a moderate poling,
characteristic for isotropic polymers, as it is the case here (free gas model).
The difference with the earlier study of Robinson and Dalton concerning the
concentration dependence of quadratic susceptibility can be easily explained. Both
molecules exhibit very similar molecular structure (cf. Fig. 4) and we can expect very
similar behaviour. In fact it arises from the fact how the chromophore concentration
is labelled. Although C ¼ 0.3 (30 wt %) seems to be a high concentration, in fact it is
w
small if we look at the number of chromophores introduced to the system (mole frac-
tion). Thus to compare our findings with their we have to use the same concentration
description. Indeed, using weight concentration dependence may be misleading
because it doesn’t refer directly to the number of substituted monomer-chromophore
segments and the number of non substituted monomers in polymer chain. A simple
relation between the molar and the weight concentration can be easily derived for a
side chain polymer, which is given by
R
Cm ¼ Cw
ð10Þ
1
þ ð1 ꢀ RÞCw
where
Mmon
R ¼ M
ð11Þ
seg
is the ratio of molecular mass of the unsubstituted monomer (Mmon) to the segment
monomer þ chromophore (Mseg).
In our case (PMMA-DR1 side chain polymer) M ¼ 382.42, M
seg
¼ 100.12,
mon
and R ¼ 0.26. Thus for the maximum concentration of DR19 in PMMA studied
by Robinson and Dalton C ¼ 0.3 we obtain a molar concentration of C ¼ 0.064,
w
m
what corresponds to a small substitution rate, thus to a small aggregation level.
For DR19, whose molar mass is a little larger, this value will be a little smaller. In
fact Lei et al. [36] (see also Kuzyk et al. [37]) consider occurrence of aggregation
Figure 4. Chemical structures of DR1 and of DR19.

(
2)
Concentration Variation of v Susceptibility in PMMA-DR1 189=[489]
at C ¼ 0.15 of DR1 in PMMA (guest-host). M. Kuzyk [38] sets the limit at
w
C ¼ 0.12 for this system. It is commonly believed that in side chain polymers,
w
because of limited mobility, aggregation takes place at higher chromophore concen-
tration. Thus the observed here C ¼ 0.15 (15 mol %) limit looks as a very reasonable
m
and realistic one.
Acknowledgments
One of the authors (FK) would like to thank Prof. M. G. Kuzyk from Washington
State University ate Pullman, USA, for a fruitful discussion.
References
[1] (1997). Poled Polymers and Their Application to SHG and EO Devices, Myata, S. &
Sasabe, H. (Eds.), Gordon & Breach Sc. Publ: Amsterdam.
[
2] Kajzar, F., Jen, A., & Lee, K. S. (2003). Polymeric Materials and Their Orientation Tech-
niques for Second-Order Nonlinear Optics, in Polymers for Photonics Applications I, Lee,
K. S. & Wegner, G. Eds: Advances in Polymer Sc: Springer Verlag, Heidelberg, 161, 1.
3] Dalton, L. R. (2001). Advances in Polymer Science, in Polymers for Photonics
Applications I, in Lee, K. S. & Wegner, G. Eds: Advances in Polymer Sc: Springer
Verlag, Heidelberg, 161 1(2003), Springer-Verlag, Heidelberg, 158, 1.
[
[4] Comizzoli, B. (1987). J. Electrochem. Soc.: Solid Science and Technology, 134, 424.
[5] Charra, F., Kajzar, F., Nunzi, J. M., Raimond, P., & Idiart, E. (1993). Opt. Lett., 18, 941.
[6] Aktsipetrov, O. A., Akhmediev, N. N., Mishina, N. N., & Novak, V. R. (1983). Soviet
Phys. JETP Lett., 37, 207.
[
7] Bosshard, C. & Kupfer, M. (1996). Oriented Molecular Systems, in Organic Thin Films
for Waveguiding Nonlinear Optics: Advances in Nonlinear Optics Kajzar, F. & Swalen,
J. Eds., Gordon & Breach Sc. Publ., p. 163.
[
8] Kajzar, F. & Swalen, J. (1996). (Eds), Organic Thin Films for Waveguiding Nonlinear
Optics: Advances in Nonlinear Optics, Gordon & Breach Sc. Publ.: Amsterdam.
9] Gonin, D., No e¨ l, C., & Kajzar, F. (1996). Liquid Crystalline Polymers, in Kajzar, F. &
Swalen, J. Eds., Organic Thin Films for Waveguiding Nonlinear Optics: Advances in
Nonlinear Optics, Gordon & Breach Sc. Publ.: Amsterdam, p. 221.
[
[
[
10] Kajzar, F. & Noel, C. (1998). Adv. Mat. Opt. Electron., 8, 247.
11] Le Moigne, J. (1996). Epitaxy and Single Crystal Growth, in Organic Thin Films for
Waveguiding Nonlinear Optics: Advances in Nonlinear Optics, Kajzar, F. & Swalen, J.
Eds., Gordon & Breach Sc. Publ.: Amsterdam, p. 289.
[
[
12] Favaretto, L., Barbarella, G., R a˜ u, I., Kajzar, F., Caria, S., Murgia, M., & Zamboni, R.
(
2009). Opt. Express, 17, 2557–2564.
13] Facchetti, A., Annoni, E., Beverina, L., Beverina, L., Morone, M., Zhu, P., Marks, T. J.,
Pagani, G. A. (2004). Nature Materials, 3, 910.
&
[14] Kajzar, F., Okada-Shudo, Y., Meritt, C., & Kafafi, Z. (2001). Synth. Metals, 117, 189.
[15] Chen, D., Fetterman, H. R., Chen, A., Steier, W. H., Dalton, L. R., Wang, W., & Shi, Y.
(
1997). Appl. Phys. Lett., 70, 3335.
[
[
16] Shi, Y., Zhang, Ch., Zhang, H., Bechtel, J. H., Dalton, L. R., Robinson, B. H., &
Steier, W. H. (2000). Science, 288(5463), 119–122.
17] Blau, G., Ruiz, L., Casablanca, P., Vitrant, G., Chollet, P. A., & Kajzar, F. (1996).
Electro-optic Modulation in Organic Waveguides Using GratingCouplers, in Photoactive
Organic Materials: Science and Application, Kajzar, F., Agranovich, V. M., & Lee, C.
Y.-C. Kluwer Academic Publishers: Dordrecht, pp. 275–280.
[18] Alshikh Khalil, M., Vitrant, G., Raimond, P., Chollet, P. A., & Kajzar, F. (1999). Opt.
Commun., 170, 281–284.

1
90=[490]
F. Kajzar et al.
[19] Khalil, M. A., Vitrant, G., Raimond, P., Chollet, P., & Kajzar, F. (2000). Appl. Phys
Lett., 77, 3713–3715.
[
20] Rodr ´ı guez, A., Vitrant, G., Chollet, P. A., & Kajzar, F. (2001). Appl. Phys. Lett., 79,
461–463.
[
[
[
[
[
[
21] Kleinman, D. A. (1962). Phys. Rev., 126, 1977–1979.
22] Rau, I. & Kajzar, F. (2008). Nonl. Opt. Quant. Opt., 38, 99–140.
23] Natansohn, A. & Rochon, P. (1999). Adv. Mater., 11, 1387–1391.
24] Kim, D. Y., Tripathy, S. K., Li, L., & Kumar, J. (1995). Appl. Phys. Lett., 66, 1166–1168.
25] Lefin, P., Fiorini, C., & Nunzi, J.-M. (1998). Pure Appl. Opt., 7, 71–82.
26] Charra, F., Kajzar, F., Nunzi, J. M., Raimond, P., & Idiart, E. (1993). Optics Lett., 18,
941–944.
[
[
27] Large, M., Kajzar, F., & Raimond, P. (1998). Applied Phys. Lett., 73, 3635–3637.
28] Combellas, C., Kajzar, F., Mathey, G., Petit, M. A., & Thiebault, A. (2000). Chem.
Phys., 252, 165–177.
[29] Robinson, B. H. & Dalton, L. R. (2000). Journal of Physical Chemistry A, 104(20),
4785–4795.
[30] Narita, M., Hoshino, F., Mouri, M., Tsuchimori, M. T., & Watanabe, O. (2007).
Macromolecules, 40, 623–629.
[31] Ho, M. S., Natansohn, A., & Rochon, P. (1995). Macromolecules, 28(18), 6124–6127.
[32] Rau, I. & Kajzar, F. (2008). Nonl. Opt. Quant. Opt., 38, 99–140.
[33] Page, R. H., Jurich, M. C., Reck, B., Sen, A., Twieg, R. J., Swalen, J. D., Bjorklund, G. C.,
&
34] Choy, M. & Byer, R. L. (1976). Phys. Rev. B., 14, 1693.
Wilson, C. G. (1990). J. Opt. Soc. Am. B, 7, 1239.
[
[
35] Oswald, P. & Pieranski, P. (2000). Les Cristaix Liquides: Concepts et Propri e´ t e´ s Physiques
Illustr e´ s par des Exp e´ riences, Gordon and Breach Science Publishers: Paris, Vol. 1., 51.
36] Lei, D., Runt, J., Sarari, A., & Newnham, R. E. (1987). Macromolecules, 20, 1797.
37] Kuzyk, M. G., Sohn, J. E., & Dirk, C. W. (1990). J. Opt. Soc. Am. B, 7(5), 843–858.
38] Kuzyk, M. G. private communication.
[
[
[