Mach–Zehnder interferometer measurement of the Pockels effect
in a poled polymer film with a coplanar electrode structure
H. R. Cho, M. J. Shin, S. H. Han, and J. W. Wu
a)
Department of Physics, Ewha Womans University, Seoul 120-750, Korea
͑Received 28 May 1996; accepted for publication 14 October 1996͒
Mach–Zehnder interferometry was used to measure the Pockels effect in a poled electro-optic
polymer thin film with a coplanar electrode structure. The beam at the sample arm of the Mach–
Zehnder interferometer passed through a polymer thin film which had been spin-coated on top of a
clear gap between two electrodes patterned on an optical substrate. This unique optical geometry
enabled the Pockels coefficients of the poled electro-optic polymer film in the directions of the
ordinary and the extraordinary optic axes to be determined independently. As an example, the tensor
ratio r
33
/r
13
for a stilbene-dye-doped polyimide guest/host polymer film was determined
experimentally; the ratio turned out to be 4.6, which was higher than the value of 3 predicted by the
thermodynamic model. © 1996 American Institute of Physics. ͓S0003-6951͑96͒03251-2͔
Optical characterization of an electro-optic ͑EO͒ poly-
mer film can be performed in various ways: for example,
analysis of the optical waveguide structure,
1
single-beam po-
larization interferometry,
2
Fabry–Perot interferometry,
3
etc.
Mach–Zehnder interferometry ͑MZI͒, however, is the most
frequently adopted approach for EO polymers in integrated-
optics waveguide switching devices.
4
MZI has already been employed to measure the Pockels
effect in EO polymer films with reflection geometries.
5
Elec-
trode poling of an EO polymer, however, can be achieved in
two different electrode structures, namely, the parallel-plate
͑PP͒ and the coplanar ͑CP͒ electrode geometries.
6,7
The CP
electrode geometry is known to have an advantage over the
PP electrode geometry in reducing the number of processes
involved in preparing and characterizing an EO film.
8,9
Fur-
thermore, the CP structure has more direct relevance to
integrated-optics waveguide devices for which the birefrin-
gence between the TE and the TM modes should be carefully
controlled. In this letter, MZI was applied to an EO polymer
thin film with a CP electrode to determine the Pockels coef-
ficients along the ordinary and the extraordinary axes. To our
knowledge, this was the first application of MZI to a CP
electrode structure, enabling the independent determination
of the Pockels coefficients in the directions of the ordinary
and the extraordinary optic axes.
The group symmetry of a poled EO polymer belongs to
the point group C
ϱ
v
with the optic axis (3-axis͒ along the
ϱ-fold rotational symmetry axis. When an identical electrode
as the one used for electric field poling is employed for the
ac modulation, the components of refractive indices, which
are modulated due to the Pockels effect, are n
3
and n
1
and
have the following index changes:
⌬
ͩ
1
n
1
2
ͪ
ϭ⌬
ͩ
1
n
o
2
ͪ
ϭr
13
E
3
, ⌬
ͩ
1
n
3
2
ͪ
ϭ⌬
ͩ
1
n
e
2
ͪ
ϭr
33
E
3
.
For incident light with a polarization angle
relative to the
3-axis, the refractive index n
and the index change ⌬n
related to r
are easily obtained from the Fresnel relation and
are given by
1
n
2
ϭ
cos
2
n
e
2
ϩ
sin
2
n
o
2
, ͑1͒
r
ϭr
33
cos
2
ϩr
13
sin
2
. ͑2͒
It is easy to see that the Pockels coefficients r
13
and r
33
can
be determined independently by varying the polarization
angle
.
When a poled EO polymer film is spin coated on an
optical substrate with a CP electrode and is positioned in the
sample arm of a Mach–Zehnder interferometer, the interfer-
ence pattern of the light from MZI is given as
Iϭ
1
2
͓
E
01
2
ϩE
02
2
ϩ2
͉
E
01
͉͉
E
02
͉
cos
͑
ϩA cos ⍀t
͒
͔
Ϸ
1
2
͓
E
01
2
ϩE
02
2
ϩ2
͉
E
01
͉͉
E
02
͉
cos
͔
ϩA
͉
E
01
͉͉
E
02
͉
sin
cos ⍀t.
The phase modulation amplitude A in the above equation is
related to the Pockels coefficient r
for light with a polariza-
tion angle
through the formula
Aϭ
2
l⌬n
ϭ
n
3
r
V
m
l
d
, ͑3͒
where l is the thickness of the film, d the separation between
the two CP electrodes, and V
m
the ac modulation voltage.
Introducing the modulation amplitude I
⍀
ϭA
͉
E
01
͉
ϫ
͉
E
02
͉
sin
, we find that the modulation amplitude I
⍀
has a
sin
dependence on the optical bias
and that two peaks
are observed as the optical bias is varied. In the actual ex-
periment, the two peak heights, I
1
and I
2
appearing at
ϭ
/2 and
ϭ3
/2, were measured. Usually, I
1
and I
2
were not equal in intensity because of the Fabry–Perot mul-
tiple reflection effect inside the thin film. Now, the experi-
mental values of I
1
and I
2
can be related to the phase modu-
lation amplitude A by
A
͉
E
01
͉͉
E
02
͉
ϭ
I
1
ϩI
2
2
. ͑4͒
a͒
To whom correspondence should be addressed. Electronic mail:
jwwu@mm.ewha.ac.kr
3788 Appl. Phys. Lett. 69 (25), 16 December 1996 0003-6951/96/69(25)/3788/3/$10.00 © 1996 American Institute of Physics