128
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 41, NO. I , FEBRUARY 1992
Electrooptic Characterization of Organic Media
Ajay Nahata, Member, IEEE, Chengjiu Wu, and James T. Yardley
Abstract-We have developed an electrooptic characterization apparatus based on an ac-modulated Senarmont compensator, which is particularly suited for studying the electrooptic
response of thin polymer films. The system is capable of measuring the Pockel's effect at a variety of wavelengths with a
minimum phase shift sensitivity of 1 microradian. Sample-tosample variations in the coefficient measurements are less than
15%. We have made a systematic evaluation of thin, poled electrooptic polymer films on coplanar electrodes to demonstrate
the usefulness of the apparatus. We describe corrections for the
fringing effects of the applied electric field. We have verified
the reproducibility of the electrooptic data through an examination of the polymer thickness dependence. We have also measured the poling field dependence of the electrooptic coefficient and obtained a best-fit molecular dipole value in excellent agreement with the reported value obtained from EFISH
and solvatochromism measurements.
I. INTRODUCTION
N recent years, there has been increased interest in the
nonlinear optical and electrooptic properties of organic
materials. Many different measurement techniques have
been reported for the characterization of x'~'materials [ 11,
[ 2 ] . In particular, second harmonic generation has been
used to evaluate the macroscopic nonlinear optical properties [ 3 ] , [4], while EFISH has been used to measure the
microscopic properties [5], [ 6 ] .It is, therefore, desirable
to use a technique with which both types of properties can
be measured.
We present a description of an electrooptic measurement apparatus capable of directly obtaining both fundamental microscopic and macroscopic nonlinear optical
properties quickly and easily. The basic theory of the apparatus is described along with corrections for the fringing effects of the applied electric field. We demonstrate
the utility of this instrument by measuring the electrooptic
response of a model polymer system as a function of
polymer thickness and poling field strength.
I
A. Apparatus Description
The basic experimental arrangement used to measure
the electrooptic coefficients, shown in Fig. 1, is an acmodulated Senarmont compensator with lock-in detection
[7]. The initial clean-up polarizer ensures that the polarization of the light is at 45" with respect to the principal
axes of the electrooptic material. The analyzing polarizer
is set at -45 , in the crossed polarizer configuration. The
Soleil-Babinet compensator is used to convert the linearly
polarized light to circularly polarized by inducing a n / 2
optical phase shift. This maximizes the sensitivity for linear intensity modulation. It also allows for linear signal
response, as will be shown below.
If we let 4 represent the optical phase difference between the ordinary and extraordinary rays travelling
through the sample and compensator,
O
where the first term represents the phase shift due to the
birefringence in the sample,
represents the optical
bias induced by the compensator, and
represents the
phase shift from the applied electric field. The light intensity after the analyzing polarizer is given by
I = Io(l - cos 4)/2
where I, is the light intensity after the clean-up polarizer.
We have assumed that there is no optical loss in the system.
For linear intensity modulation, the compensator must
be adjusted for 50% light transmission immediately after
the analyzer. It should be noted that the modulation must
be kept relatively small, less than approximately lo%, in
order for the intensity to be a linear function of the input
signal. As stated earlier, this compensator setting also allows for maximum sensitivity. The static optical phase
shift is therefore given by
11. THEORY
The basic theory of the measurement apparatus is presented below, as well the theory of electrooptics in poled
polymers and the corrections for the fringing electric fields
from thin coplanar electrodes.
Manuscript received May 14, 1991; revised September 26, 1991.
The authors are with Allied-Signal, Inc., Morristown, NJ 07962.
IEEE Log Number 9105577.
(2)
1
(2m
2
=-
+ 1)n
m = 0 , 1, 2, 3 ,
*
(3)
For the linear electrooptic effect, if a modulating voltage
of the form V = V, sin ( u t ) is applied across the electrodes, the induced phase shift will also be of the form
= A44 sin (ut). The corresponding change in the
transmitted light intensity can be found by substituting (1)
0018-9456/92$03.00
0 1992 IEEE
NAHATA et al. : ELECTROOPTIC CHARACTERIZATION
I29
Ground
I
1
V
L
Fig. 2. Semi-infinite coplanar electrodes separated by a gap of 2 a. The
electrodes are assumed to be infinitely thin.
J
Fig. 1. Experimental arrangement for electrooptic measurements using C:
chopper, P: polarizer, SBC: Soleil-Babinet compensator, and A: analyzing
polarizer. A schematic of the sample geometry with coplanar electrodes is
shown in the lower right comer.
(7)
and (3) into (2). Using a well-known modulation identity
relating the sine of a sine function to a Bessel's function
series expansion [SI, we can write
where ni and ni are the refractive indexes.
Poled polymers belong to the point symmetry group
mm and have five nonzero electrooptic coefficients, rij
[12]: r33, rI3 = r23 ; r42 = rS1,where r33can be thermo2(1/10) = 1 (-1)""2[J, (A@) sin (ut)
dynamically related to the other four coefficients. In our
J3(A&) sin (3wt) + . -1
(4) geometry, the electric field is applied along the poling z
axis of the polymer causing a phase shift given by
where the J's are Bessel's functions of the first kind. For
fundamental frequency detection, to first approximation,
this can be rewritten as
+
+
-
2(Z/Z0) = 1
+ (- l),+
A4; sin (ut)
(5)
B. Electrooptics in Poled Polymers
Nonlinear optical effects arise from the polarization response of a material to external electromagnetic fields. In
the expansion of the macroscopic electric polarizability of
a material in terms of the electric field, the first nonlinear
susceptibility is a third-rank tensor whose value is zero in
materials having a center of inversion. Therefore, a macroscopic noncentrosymmetric structure is necessary for a
second-order nonlinear optical response. Electric field
poling is a convenient method for creating the requisite
polar order [9].
In the limit of the oriented gas model with a one-dimensional dipolar molecule and a two-state model for the
molecular polarizability [lo], the second-order susceptibility, x333,of a poled polymer film can be related to the
poling field E by
=
w 2
V (f 1 f
AC
C. Electric Field Correction
The electric field is applied across the polymer film via
thin coplanar electrodes, shown in Fig. 2. Since the polymer film is, in general, considerably thicker than the electrodes, the plane parallel electrode approximation does not
hold. The electric field in the gap region not only has
components parallel and perpendicular to the substrate,
but is also strongly position dependent [ 131. For our geometry, the perpendicular component has negligible contribution.
In order to compensate for the field variation of the horizontal component across the gap, an average field factor,
F,, must be defined.
(9)
P,(-w;
w , 0) L3
where N / V is the number density of the dye molecules,
thef's are the appropriate local field factors, p is the dipole moment, p is the molecular hyperpolarizability, and
L3 is the third-order Langevin function [ 1 11 describing the
electric field induced polar order at poling temperature
Tp Tg.
In general, the electrooptic coefficients in a poled polymer can be related to the second-order susceptibility as
shown in (7):
-
where 1 is the light pathlength, X is the wavelength of the
probe beam, and E, (voltage/electrode gap) is the applied
electric field along the z axis.
J J
where z is in the direction of the horizontal field component, and y is perpendicular to the substrate. V, is the applied voltage, and 2 a is the gap width. The limits of integration run from one electrode edge to the other and
from the substrate surface to the top of the electrooptic
material. The electric field is assumed to be uniform along
the electrode edge.
This type of average is only accurate when the probe
beam is uniform across the gap. The laser employed in
130
IEEE TRANSACTIONS ON INSTRUMENTATION A N D MEASUREMENT, VOL. 41, NO. I , FEBRUARY 1992
TABLE I
AVERAGEFIELDFACTORS
VERSUSELECTROOPTIC
MATERIAL
THICKNESS
Material
Thickness
Fz
GFz
0.01a
0.05a
0. la
0.5a
1 .Oa
2.0a
5.0a
0.98
0.90
0.86
0.71
0.60
0.47
0.29
0.84
0.81
0.80
0.68
0.59
0.47
0.29
Physical Pathlength [in u n i t s of a]
Fig. 3. Effective pathlength versus physical pathlength (in terms of half
gap-widths). The solid line incorporates the average field factor (IeR= F z l ) ,
whereas the dashed line assumes a uniform field (Len = I ) .
these experiments, however, has a Gaussian beam profile.
The normalized equation for the intensity profile of a circular Gaussian beam is given by
Z(z, x)
=
[
-exp -~; z 2 ]
7rd
(10)
where w is the 1/ e 2 beam radius. Unlike the electric field
distribution, the light intensity has a maximum at the center of the gap. To account properly for this intensity distribution, a more precise average field factor, GF,, is given
by
2a
GF, = -
"
jj
s
4a, Y )
sss
*
I ( z , x) d z dY dx
*
(11)
Z(z, x) dz dy dx
The value of 2w is set to the gap width. The limits of
integration for the y and z coordinates are identical to those
given for (8). The limits for the x axis run from +CO to
-W.
Table I gives the value of the average field factor for
several material thicknesses (in terms of half-gap widths).
Regardless of which average field factor is used, the electric field in (7), E,, must be replaced with F , ( V , / 2 a) or
GF,(V,/2 a). These corrections are only valid when the
polymer thickness is considerably greater than the electrode thickness. It should be noted that for the typical geometries employed in this work, the poled polymer thicknesses range from 0.01 a to 0 . 2 a (2 a = 25 pm).
An alternative way of looking at the average field factor
is that it defines the effective pathlength of the electrooptic material. In this case, the applied electric field, E,, is
equal to V z / 2 a, and the pathlength is effectively equal to
F, * I or GF, * I. The relationship between the physical
pathlength and the effective pathlength, F, * I, (in terms
of half-gap widths) is shown in Fig. 3. From the figure,
it is apparent that the maximum effective thickness, in this
situation, is approximately 3.5 a.
111. EXPERIMENTAL
As was stated above, application of the applied electric
field was accomplished using coplanar electrodes. Thin
film, slit type aluminum electrodes (distance between
electrodes, 25 pm; electrode dimensions, 5 mm X 9 mm;
thickness, 0.1 pm) were photolithographically defined on
quartz substrates. Solutions of 20 mol% polymer bound
Disperse Red #1 of varying concentrations were spin cast
onto the substrates at speeds between 2000 and 4000 rpm,
yielding film thicknesses between 0.1 pm and 3 pm. All
samples were heated to the glass transition temperature of
the polymer, Tg = 132"C, and poled using field strengths
ranging from 0 to 2.5 MV/cm. The current was monitored to insure that no dielectric breakdown occurred.
After a suitable equilibrium period, the samples were
cooled to room temperature in the presence of the electric
field, freezing in the new noncentrosymmetric dipole
alignment.
The probe beam from a laser diode, operating at 810
nm, was focused so that the beam width through the electrode gap was 25 pm. For all measurements, the probe
beam propagated perpendicular to the poling axis and was
linearly polarized at 45 with respect to the poling z axis.
Measurement of the field-induced phase shift was accomplished using l-kHz sinusoidal electric fields of up to 60
kV/cm peak and a dual phase lock-in amplifier for fundamental frequency detection.
IV. RESULTS
The reproducibility of data was examined by measuring
the thickness dependence of the electrooptic effect in a
poled polymer. Since it is generally assumed that there is
no orientation anisotropy of the nonlinear chromophore at
the film surfaces, the electrooptic coefficients are expected to be independent of thickness. A series of samples
with thicknesses ranging from 0.1 pm to 3 pm were poled
at 0.5 MV/cm. The resulting electrooptic coefficients are
shown in Fig. 4. As expected, r33appears to be independent of thickness. As can be seen from the graph, variations in sample-to-sample measurements are less than
approximately 15 % .
The linear electrooptic coefficient, r33, is expected to
be linear with respect to the poling field for low field
strengths. However, at sufficiently large field strengths,
NAHATA et al.: ELECTROOPTIC CHARACTERIZATION
0
2
1
131
4
3
Film Thckness [ ~ m ]
Fig. 4. Electrooptic coefficient, r33, versus polymer thickness for a 20
mol% polymer bound Disperse Red #1 copolymer. The samples were poled
at 0.5 MV/cm.
than 15% . We have also measured the poling field dependence of the linear electrooptic effect. The poling dependence can be well described by the theory presented. The
best-fit value for the molecular dipole moment obtained
from a nonlinear least-squares fit is in excellent agreement
with values obtained from EFISH, solvatochromism, and
differential capacitance measurements, thereby demonstrating the utility of the apparatus for measuring fundamental microscopic and macroscopic nonlinear optical
properties.
REFERENCES
[ l ] D. S . Chemla and J. Zyss, Eds., Nonlinear Properties of Organic
Molecules and Crystals, Vols. I and 2. Orlando FL: Academic,
0.0
0.0
:
I
0.5
,
;
1.0
.
/
1.5
’
;
20
.
;
2.5
:
3.0
Poling Field [MV/cm]
Fig. 5. Electrooptic coefficient, r3), versus poling field for a 20 mol%
polymer bound Disperse Red #1 copolymer. --- Linear extrapolation;
---- Nonlinear least squares fit of (5) and (6).
the higher order terms of the Langevin function cause a
deviation. Fig. 5 shows the measured r33 versus poling
field for a 20 mol% polymer bound Disperse Red #l. A
nonlinear least-squares fit of the measured electrooptic
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Debye. This is in excellent agreement with the reported
value of 8.7 Debye obtained for Disperse Red 1 in PMMA
by the concentration dependent differential capacitance
measurements [ 5 ] .
V. CONCLUSIONS
An electrooptic characterization apparatus has been implemented based on an ac-modulated Senarmont compensator. The apparatus has minimum phase shift sensitivity
of 1 microradian. We have shown that the electrooptic
coefficient, r,,, is independent of thickness. Sample-tosample variation in the coefficient measurements is less
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