Dark decay of holograms in photorefractive polymers
Reinhard Bittner
a)
and Klaus Meerholz
a),b)
Chemistry Department, Physical Chemistry, University of Munich, Butenandtstr. 11,
D-81377 Munich, Germany
Gregory Steckman and Demetri Psaltis
California Institute of Technology, 1200 E. California Boulevard, MS 136-93, Pasadena, California 91125
共Received 20 December 2001; accepted for publication 14 May 2002兲
The decay of holograms stored in photorefractive polymer composites based on
poly共N-vinyl-carbazole兲 with and without extrinsic deep traps is investigated. The photorefractive
phase shift is identified as one of the key parameters determining the dark decay dynamics. This has
important implications for all kinds of photorefractive imaging applications including holographic
data storage. A trade off will be required between accepting a certain degree of hologram distortion
due to two-beam coupling on the one hand and achieving high hologram stability during idle periods
in the dark with the external field applied on the other. © 2002 American Institute of Physics.
关DOI: 10.1063/1.1492848兴
The photorefractive 共PR兲 effect is one of the most prom-
ising reversible holographic storage mechanisms.
1
Under
nonuniform illumination, the refractive index of the photo-
sensitive material is modulated due to the generation of mo-
bile charge carriers in the bright regions, their subsequent
redistribution, and eventual trapping in the dark areas. This
gives rise to a space-charge field E
SC
, which modulates the
refractive index of the material through the linear electro-
optic effect and orientational effects.
2,3
Photorefractivity in
amorphous polymers has been intensively investigated,
4,5
and these systems have been widely recognized as potential
active media in rewritable holographic optical memories for
security applications,
6
in associative memories,
7
or in adap-
tive ultrasound sensors.
8
Due to the rather low dielectric con-
stants of polymers (⬍ 10), oppositely charged carriers
show a rather strong tendency to recombine. As a result, only
rather short storage times are anticipated. However, so far,
the dark decay 共referred to as ‘‘dd’’ hereafter兲 of the holo-
grams in periods when the system is idle, i.e., held in the
dark with the external field still applied, has been mostly
neglected in literature on organic PR materials, even though
it is important for the aforementioned applications. In this
letter, we present systematic investigations of the dd of PR
gratings in PR polymers. Our results will give evidence that
the phase shift between the interference pattern and the re-
corded index grating, the commonly accepted fingerprint of
photorefractivity, is one of the key parameters, yielding
slower dd for a larger phase shift.
The investigated materials contained the photoconductor
poly共N兲vinylcarbazole 共PVK, 39 wt %兲, the plasticizer
N-ethylcarbazole 共10 wt %兲, the eutectic mixture of two EO
chromophores 2,5-dimethyl-4共p-nitrophenylazo兲-anisole 共25
wt %兲, and 3-methoxy-4共p-nitrophenylazo兲-anisole 共25
wt %兲, and finally the sensitizer 2,4,7-trinitro-fluorenone
共TNF, 1 wt %兲. We also prepared a similar material doped
with 0.82 wt% 共replacing PVK兲 of the commonly used
hole conductor N,N
⬘
-bis共3-tolyl兲-N,N
⬘
-diphenyl-benzidine
共TPD兲, whose highest occupied molecular orbital levels are
situated about 0.5 eV below those of PVK. Thus, TPD moi-
eties constitute deep traps within the carbazole transport
manifold, and therefore a longer storage time was expected.
We refer to the materials as ‘‘C’’ without and ‘‘CT’’ with
extrinsic traps. The glass-transition temperature was T
g
⫽ 14 °C 共differential scanning calorimetry, heating rate 20
K/min兲 for both composites. The devices were sandwich
structures of the PR composites between two transparent
indium-tin-oxide-coated glass slides.
4–8
The active layer
thickness was d⫽ 125
m.
To determine the performance of the investigated mate-
rials degenerate four-wave-mixing and two-beam-coupling
experiments were carried out using a HeNe laser (
0
⫽ 633 nm). Holograms were recorded in tilted configuration
with s-polarized writing beams 共external tilt angles
␣
1
⫽ 50° and
␣
2
⫽ 70°, respectively, with respect to the sample
normal兲. The internal intensities of the writing beams as de-
termined from the half height width of their Gaussian pro-
files were similar (I
1
⬇I
2
), yielding a grating contrast close
to unity. Prior to the writing process an electric field E
0
was
applied to the device, which was also preilluminated for 30
min by beam 2. Hereafter, beam 1 was switched on, and after
writing the grating for a certain time t
rec
both beams were
switched off simultaneously.
The recorded hologram was probed by a p-polarized
beam counterpropagating to beam 1. Due to the erasure of
the PR grating upon uniform illumination, we took the fol-
lowing precautions to reasonably approximate ‘‘real’’ dd:
First, the reading beam had more than 3 共at lowest recording
intensity兲 up to more than 5 共at highest recording intensity兲
orders of magnitude lower time-averaged intensity 共⬃250
nW/cm
2
兲 than the recording beams. Second, the read beam
was only applied from time to time using a fast magnetical
shutter. Between the readouts, the sample was held in the
dark. Overall, the read beam was on for less than 8% of the
total time the grating decay was monitored. The read beam
a兲
New address: Physical Chemistry Department, University Cologne, Lux-
emburgerstr. 116, 50939 Cologne, Germany.
b兲
Electronic mail: klaus.meerholz@uni-koeln.de
APPLIED PHYSICS LETTERS VOLUME 81, NUMBER 2 8 JULY 2002
2110003-6951/2002/81(2)/211/3/$19.00 © 2002 American Institute of Physics
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was chopped, and the internal diffraction efficiency
int
was
determined utilizing lock-in amplifiers.
int
was calculated
according to:
int
⫽ I
D
/
共
I
D
⫹ I
T
兲
. 共1兲
with I
D
as the power of the diffracted and I
T
as the power of
the transmitted reading beam. From the
int
, we calculated
the refractive index modulation ⌬n
p
according to
9
⌬n
p
⫽
共
asin
冑
int
•
共
cos
␣
1
⫹ cos
␣
2
兲
•
0
⬘
兲
/
共
2•
• d
兲
. 共2兲
The PR gain coefficient ⌫
s
was calculated according to
10
⌫
s
⫽ d
⫺ 1
关
ln
共
I
1
/I
10
兲
cos
␣
1
⫺ ln
共
I
2
/I
20
兲
cos
␣
2
兴
. 共3兲
Here I
1,2
are the intensities of the recording beams 1 and 2
after passing the device, and I
i0
are the corresponding values
without grating. Estimates of the phase shift
were obtained
by substituting ⌬n
s
and ⌫ in
1
⫽ asin
共
⌫
s
0
/
共
2
⌬n
s
兲兲
, 共4兲
accounting for the polarization anisotropy of the chro-
mophores (⌬n
p
/⌬n
s
⫽⫺2,2).
11,3
The experimental data
were normalized to the index modulation achieved at the end
of recording and fitted by bi- or triexponential decay func-
tions. In order to obtain a unified measure for the general
decay dynamics, we calculated the combined logarithmic av-
erages of the relaxation times 具
典 according to
12
具
典
⫽ exp
冉
兺
i
A
i
• ln
i
冊
;
兺
i
A
i
⫽ 1. 共5兲
The dd kinetics was found to be at least two orders of
magnitude slower than the relaxation of the orientational or-
der of the dipoles in the material. The latter was similar in
both materials as determined by independent transmission
ellipsometric experiments.
12
This proves that the grating de-
cay is governed exclusively by the decay of the PR space-
charge field, i.e., essentially by the recombination of oppo-
sitely charged carriers. The decay curves exhibit
multiexponential behavior in contrast to earlier results on a
low-molecular-weight glass, where a simple monoexponen-
tial behavior was observed.
13
However, these latter results
are somewhat questionable, since the read beam was rather
strong and applied at all times. Therefore, low intensity era-
sure was performed rather than a reasonable approximation
of dark decay.
According to a theoretical framework proposed by Cui
et al.
14
covering the erasure process in PVK-based PR poly-
mers, the 共thermal兲 detrapping coefficient
␣
T
determines the
PR grating decay kinetics for the case of vanishing zero-
order hole density, which also applies to the dd. Presuming
charged sensitizers as the dominant PR trap species,
15
Poole–Frenkel behavior is implied for the field dependence
of
␣
T
leading to accelerated dd as a function of increasing
external field E
0
. Our findings agree with these consider-
ations, however, the dependence is much more pronounced
in material CT as compared to C 关Fig. 1共a兲兴.
Surprisingly, the dd is faster in material CT than in C,
whereas the recording process is much slower 共about a factor
of 5–6兲 in CT. The latter is in general agreement with earlier
results reported by Malliaras et al.
16
This finding may indi-
cate, that even though the TPD content is small 共about
10
21
cm
⫺ 1
, one extrinsic trap per 100 transporting sites兲 it
may contribute to charge transport in the dark. By contrast,
the photoconductivity proceeds through the cabazole mani-
fold and is hindered by the trapping in TPD, and therefore
the recording in CT is slower than in C.
It was even more striking that in both materials, the dd
depended strongly on the intensity of the recording 共!兲 beams
I
rec
⫽ I
1
⫹ I
2
关Fig. 1共b兲兴. Since at a given E
0
, the thermal
detrapping coefficient is a characteristic material constant,
we propose that the recombination of charge carriers might
depend on the displacement ⌬ between the positive and
negative carrier distributions. Assuming that the negative
carriers were immobile and would remain on the TNF sites
where they were initially generated, in zero-order approxi-
mation 共i.e., neglecting recombination effects兲, the PR phase
shift
would correspond to half of the displacement ⌬ and
could, therefore, serve as a qualitative measure for ⌬. Ac-
cordingly, a larger
would reflect a larger ⌬ with reduced
mutual overlap between of the positive and negative carrier
clouds and, thus, a reduced number of potential recombina-
tion sites available near a mobile charge carrier. As a result,
the average number of recombination events should be re-
duced, and the dd would take longer. We estimated
from
concomittant gain measurements during recording using Eq.
共4兲. Indeed,
increases strongly with decreasing I
rec
关Fig.
FIG. 1. Dependence of the averaged dd time constants dd
具
dd
典
共solid sym-
bols, left-hand side axis兲 and the PR phase shift
共open symbols, right-hand
side axis兲 for material C 共squares兲 and CT 共circles兲: 共a兲 on the electric field
for t
rec
⫽ 500 s 共C兲 and t
rec
⫽ 1500 s 共CT兲 at I
rec
⫽ 42 mW/cm
2
; 共b兲 on the
recording intensity for t
rec
⫽ 500 s 共C兲 and at E
0
⫽ 32 V/
m; and 共c兲 on the
recording time at E
0
⫽ 32 V/
mandI
rec
⫽ 42 mW/cm
2
. The lines are to
guide the eye.
212 Appl. Phys. Lett., Vol. 81, No. 2, 8 July 2002 Bittner
et al.
Downloaded 27 Aug 2009 to 128.178.48.60. Redistribution subject to AIP license or copyright; see http://apl.aip.org/apl/copyright.jsp
1共b兲, open symbols兴 and yields the slower dd in agreement
with our explanation.
We now check this interpretation for the field depen-
dence. With increasing field,
decreases in CT 关Fig. 1共a兲兴,
and, since simultaneously the decay becomes faster, which is
in agreement with the given interpretation. By contrast, in C,
increases slightly when the field increases, which should
lead to a slowing of dd, but instead the dd is even slightly
accelerated by the field. Obviously, in this case, the phase-
shift effect is compensated by the field-induced decrease of
␣
T
as discussed herein. For comparison, in the doped mate-
rial CT, both of these effects cooperate accelerating the dd at
higher fields.
Recently, we discovered a strong dependence of the era-
sure kinetics on the recording time in undoped PVK-based
materials.
7,17
Therefore, we expected a similar influence on
the dd kinetics, which, surprisingly, was not the case for C
关Fig. 1共c兲兴. This finding also shows that the dd kinetics is
independent of the actual strength of the hologram 共i.e., the
number of charges involved in the space-charge field兲, which
varies by a factor of almost 5 from the shortest to the longest
recording time applied. In contrast, in the doped material CT,
the dd does depend on the recording time. Both of these
findings can also be explained by the phase-shift effect, since
increases strongly with time in CT, while it varies little in
C 关Fig. 1共c兲兴.
Figure 2 compiles the data for all experiments discussed
in a master plot. The dark decay times
具
dd
典
show a clear
dependence on the estimated phase shifts
. The fact that the
observed trend is consistent even for both investigated mate-
rials indicates that the PR phase shift represents a dominant
factor for the dd behavior. We may estimate that the longest
具
dd
典
is in the order of 2000 s in our material for the maxi-
mum phase shift of 90°.
In conclusion, we have performed a systematic investi-
gation of the dark decay in PR polymers. The dd was found
to be governed by the decay of the space-charge field and—
mostly remarkably—depended on the phase shift of the PR
grating. This is particularly important for the application of
PR polymers. In order to store distortion-free images, the
energy transfer between the write beams 共two-beam-coupling
‘‘gain’’兲 is undesired, because it leads to fringe bending and
contrast loss of the hologram.
1
To avoid this, small gain co-
efficients ⌫ are required, which are 共simultaneously assum-
ing large index modulation amplitudes兲 correlated with small
PR phase shifts. The latter, however, yield a fast dd of the
recorded information as the results in this letter clearly dem-
onstrate. Thus, a trade off between these counteracting trends
is necessary. The phase-shift effects may even vary in differ-
ent areas of an image 共e.g., due to different intensities, fringe
visibility m, etc.兲, leading to time-dependent contrast and dis-
tortion of images subjected to idle periods during processing,
where dd can take place.
This work was supported by the Volkswagen Foundation
共Germany兲, the European Space Agency 共ESA兲, the Fonds
der Chemischen Industrie 共Germany兲, the Bavarian–
California Technology Center 共BaCaTec, Germany兲, and the
Deutscher Akademischer Austauschdienst 共DAAD, Ger-
many兲. The authors acknowledge fruitful discussions with E.
Mecher and F. GallegoGomez 共both of the University of Mu-
nich兲.
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FIG. 2. Averaged dd time constants
具
dd
典
of material C 共open symbols兲 and
material CT 共solid symbols兲 as a function of the corresponding PR phase
shifts
. Details of the particular experimental parameters are explained in
the captions of Fig. 1. The lines are to guide the eye.
213Appl. Phys. Lett., Vol. 81, No. 2, 8 July 2002 Bittner
et al.
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