Multiplexed holographic transmission gratings recorded
in holographic polymer-dispersed liquid crystals: static and
Sébastien Massenot, Jean-Luc Kaiser, Maria Camacho Perez, Raymond Chevallier,
and Jean-Louis de Bougrenet de la Tocnaye
The optimization of the experimental parameters of two multiplexed holographic transmission gratings
recorded in holographic polymer-dispersed liquid crystals is investigated. Two methods are used to record
the holograms: simultaneous and sequential multiplexing. These two processes are optimized to produce
two multiplexed Bragg gratings that have the same and the highest possible diffraction efficiencies in the
first order. The two methods show similar results when suitable recording parameters are used. The
parameters of the recorded gratings (mainly the refractive-index modulation) are retrieved by use of an
extension of the rigorous coupled-wave theory to multiplexed gratings. Finally, the response of the
gratings, and we expect a possibility of switching from one grating to the other.
Holographic polymer-dispersed liquid crystals (H-
PDLCs) have already shown a promising future, es-
pecially in optical information processing, color
reflective displays,1and telecommunications.2This
holographic material has the combined advantages of
photopolymers (self-processing material, easy devel-
opment robustness) and the properties of liquid crys-
tals, which provide a switchable behavior with larger
electro-optic effects under low voltage. Such holo-
grams are composed of a succession of polymer-rich
planes and liquid-crystal-rich planes. They are ob-
tained through a holographic process: An interfer-
ence pattern induces photopolymerization in the
constructive interference zones, and the monomers
diffuse from low exposed zones to strongly exposed
zones. At the same time, the liquid crystal migrates
in Fig. 1.
By choosing the materials judiciously such that the
refractive index of the polymer is equal to the ordi-
nary index of the liquid crystal, it is possible to erase
the hologram totally by applying an electric field.
Electrically switchable components have already
been fabricated with this technique (Bragg gratings3
and switchable lenses,4for example).
To obtain more-complex functions, one generally
stacks several different holograms. To avoid the need
for stacking of components, it would be useful to in-
vestigate whether several holograms can be recorded
in the same H-PDLC cell, enabling several functions
to be performed simultaneously and cost effectively.
In contrast to recording several holograms in con-
ventional holographic materials such as dichromated
gelatin, doing so in self-processing materials (H-
PDLCs, photopolymers) requires some precautions.
mers consumed during the recording process are not
reusable and will disturb subsequent diffusion of the
remaining monomers. The material undergoes a kind
If we want to multiplex holograms in H-PDLCs it is
necessary to know which parameters are critical and
should be controlled to obtain good-quality holo-
grams. In this paper we propose to study the forma-
tion of two different period holographic transmission
Bragg gratings (which are the simplest possible ho-
lograms) in a H-PDLC (see Fig. 2). The holograms are
characterized from static and dynamic points of view.
With such structures containing two collinear pe-
riodicities we have to face several problems during
recording. Recording parameters have to be adjusted
such that the two gratings have the same and the
highest possible diffraction efficiency in the first or-
der. To do this, we studied two recording techniques:
grow together, and sequential multiplexing, in which
the gratings are recorded successively. The advan-
tages and disadvantages of these two methods are
concentrations and sizes of liquid-crystal droplets.
Some of them are smaller than others and undergo
greater constraints when an electric field is applied.
The electro-optic behavior of the component changes
as a result.
After an introduction to the multiplexing of holo-
grams in photopolymerizable materials, we describe
the theoretical tool used to calculate multiplexed
gratings. This tool helps us to retrieve the refractive-
index modulations of the two gratings, which is an
interesting result of characterizing such materials.
These values are the critical parameters in a static
study of the hologram. Then the optimization of the
recording parameters for the two experimental set-
ups (simultaneous and sequential multiplexing) are
presented. We conclude with a presentation of the
dynamic characterization of such holograms under
an applied electric field.
One component of the formation of H-PDLCs is pho-
topolymerization and monomer transport. From this
point of view, H-PDLCs behave as photopolymers.
Hologram Multiplexing in H-PDLCs
Recording techniques used for these materials can be
directly applied to H-PDLCs.
Previous research has demonstrated the recording of
two diffraction gratings in photopolymers, but in
those cases the gratings were slanted and had the
same periods5,6(the fringes of the two gratings were
symmetrically slanted with regard to the normal of
the surface). In this configuration the formation ki-
Several slanted fringe transmission gratings with an
optimization of the recording procedure have been
obtained in photopolymers with similar diffraction
efficiencies for each grating.7In our case, the two
gratings have different periods, which means that
each has its own formation kinetic. During recording,
strong competition will occur between the formation
of the two gratings. Studies of crossed gratings re-
corded in photopolymers have been obtained8that
show the spatial dependence of the photopolymeriza-
tion and the monomer transport. The diffusion asso-
ciated with the second grating is weakly perturbed by
the first (monomers diffuse in orthogonal directions).
With respect to H-PDLCs, several multiplexing
studies have been made9,10that were oriented more
toward reflective displays. The combination of trans-
mission and reflection gratings with photonic crystal
structures has also been studied.11,12
Here we study in detail the formation kinetics of
two transmission gratings (with symmetrical fringes)
to see which critical parameters are involved and the
way in which they could be useful for improving the
recording of more-complex structures with a larger
multiplex. We also wish to optimize the recording
process to get two gratings with the same and max-
imum diffraction efficiencies.
State of the Art
The diffusion equation for the monomer concentra-
of parallel interference fringes of periods ?1and ?2is
of the form (according to Ref. 13) of
Physical Aspects of Recording Multiplexed Holograms
?x?D(x, t)??(x, t)
1?2??(x, t), (1)
where ??x, t? is the monomer concentration, D?x, t? is
the diffusion coefficient, and F0
(F0? ??I0, where ? is the polymerization rate coeffi-
cient and I0is the irradiance associated with the re-
Such an equation is quite difficult to solve. The
form of the solution for monomers is a two-
indium tin oxide; LC, liquid crystal.
(Color online) H-PDLC structure after recording. ITO,
Fig. 2.Multiplexing of two transmission Bragg gratings.
dimensional Fourier expansion that takes into ac-
count the contributions of the two periodicities.
In addition, several specific phenomena that occur
in H-PDLCs (anisotropic phase separation, incoher-
ent scattering, incomplete phase separation), as well
as the difficulty in learning precisely the value of
some material constitutive parameters, mean that
the study of such recordings has to be made experi-
ing in real time the formation of the hologram.14As
was mentioned above, two periodic systems are
formed in the material. In our case the objective is to
obtain gratings that have the highest and balanced
diffraction efficiencies under Bragg incidence.
Multiplexed holographic gratings can be modeled
with the rigorous coupled-wave theory for isotropic
media.15The original method has been extended to
gratings with two periodicities that can be oriented
independently of each other. This technique allows us
to calculate multiplexed gratings (the grating vectors
are parallel) as crossed gratings (grating vectors are
perpendicular). Implementations of the extension of
rigorous coupled-wave theory to two-dimensional
gratings can be found in Refs. 16 and 17.
Modeling of Multiplexed Diffraction Gratings
Recent improvements in the rigorous coupled-wave
theory were used; they include notably the scattering
matrix algorithm,18which lends an unconditional
stability to the method, as well as factorization rules
for Fourier series of the product of two periodic func-
tions, and they allow us to work with only continuous
components of electric field E.19,20
Below, we show some examples of multiplexed holo-
graphic gratings and study their differences from two
single gratings. In the first case (Fig. 3), we consider
two gratings whose periods are similar (?1? 1.3 ?m
and ?2? 2.1 ?m) so there is an overlap between the
responses of the two gratings. The thickness of the
gratings is fixed at 18 ?m (this value corresponds to
the size of the spacers that we used to obtain the
H-PDLC cells), and the gratings have the same
refractive-index modulation, ?n ? 0.015.
In this configuration, coupling effects occur be-
tween the two gratings, and their respective diffrac-
tion efficiencies decrease.
When the Bragg angles are quite different (Fig. 4),
the perturbation of one grating by the other becomes
less significant. Simulation parameters are the same
as described above, except that the period of the first
grating is 0.7 ?m.
To begin with, we choose gratings with widely dif-
ferent periods to prevent coupling effects between
them and so obtain the maximum diffraction effi-
Simulations of Multiplexed Gratings
The recording setup used is illustrated in Fig. 5. Two
pairs of mutually incoherent beams coming from an Ar?
laser at 514.5 nm aregenerated(labeledA1andA2and
B1 and B2 in Fig. 5) to prevent the formation of parasite
gratings. Shutters and neutral-density filters are placed
in the different optical paths to adjust the recording pa-
rameters (exposure time and irradiance).
The optical path difference between the two paths
corresponding to the two gratings is not high enough
with regard to the coherence length of the Ar?laser.
A half-wave plate has been added to the path corre-
transmission of similar period diffraction gratings: (a) separate, (b)
Comparison of the angular selectivities of holographic
transmission diffraction gratings with widely differing periods: (a)
separate, (b) multiplexed.
Comparison of the angular selectivities of holographic
crossed polarizations. This half-wave plate is added
to the path corresponding to the grating that has the
longest period, a loss of contrast will occur because
the polarization of the beams will undergo a reorien-
tation after the reflection on the mirrors (the two
polarizations will not be parallel).
In this way, the presence of unwanted gratings is
prevented. The half-wave plate is removed when the
gratings are recorded sequentially.
In addition, two beams from a He–Ne laser at
632.8 nm are used to illuminate the H-PDLC cell at
Bragg incidence to visualize in real time the forma-
tion of each of the two gratings. In this way we are
able to quantify the different rates of formation for
the different gratings.
cipal monomer, Ebecryl 1290 (30%); two comonomers,
solution (10%) composed of the colorant Rose Bengal
(3%), the coinitiator N-phenylglycine (7%), and two reac-
tive diluents, 1-vinyl-2-pyrrolidinone (45%) and trimeth-
ylolpropane tris(3-mercaptoproprionate) (45%).
We then obtain H-PDLC cells by sandwiching a
polymer mixture between two glass substrates cov-
ered with conductive indium tin oxide layers. First
spacers of 18 ?m were sprayed on the substrates to
guarantee the thickness of the cell (Fig. 1).
After exposure to interference patterns, the cells
underwent an UV postexposure to consume the re-
maining monomers and the Rose Bengal colorant.
Parameters of the H-PDLC Mixture
In this configuration, the monomer diffusion associ-
ated with a grating will be strongly disturbed by the
formation of the second grating. In addition, locally
the contrast of the fringes of the interference pattern
is not optimal because there are zones where the
exposure energy has an intermediate level. For ex-
ample, if we record two gratings of periods ?1
? 0.73 ?m and ?2? 2.1 ?m and assume that all the
beams used for the recording have the same power
and that the contrast of the fringes generated by each
beam pair is maximum, the interference pattern
looks like the curve shown in Fig. 6.
We can see that the way in which the hologram is
formed differs according to the location and that the
formation of the liquid-crystal droplets is affected
such that the droplets have different sizes.
For the two gratings the competition between the
two phenomena that participate in the recording pro-
cess (monomer diffusion and polymerization) is not
the same, which produces an imbalance in the for-
mation of the two gratings (one grating will grow
faster than the other). To have similar diffraction
efficiencies it becomes necessary to adjust the power
of the recording beams to limit the dominance of the
We made some preliminary recordings of separate
gratings to see how the two gratings form indepen-
dently of each other and whether one grows faster
time evolution of the first-order diffraction efficien-
cies of gratings of periods 0.73 and 2.1 ?m, respec-
Note that for similar exposure energies the 2.1 ?m
grating grows faster than the 0.73 ?m grating. We
must therefore slow down the formation kinetic of
this grating by exposing the grating to a lower energy
to make both gratings grow at the same speed.
Recording of Separate Gratings
An example of optimization of the recording param-
eters in simultaneous multiplexing is shown in Fig. 8.
The irradiance relative to the 0.73 ?m grating was
kept constant at a value of 51.5 mW?cm2, and we
varied the irradiance associated with the 2.1 ?m
As we can see, the irradiance of the two gratings
needs to be strongly imbalanced (nearly a ratio 1:2) if
Optimization of the Recording Parameters
Fig. 5.(Color online) Experimental setup for recording.
(which corresponds to beating between two sinusoidal patterns).
Interference pattern for simultaneous multiplexing
we want the two gratings to grow at the same speed
and give maximum diffraction efficiencies. The holo-
graphic material is quite sensitive to variations in
exposure energy; one grating can dominate the other
quickly, disturb it, and even prevent its formation. In
addition, we can remark that for each recording a
change in the formation rate occurs near 50 s. We
assume that this is so because there are several
monomers in the material that are not consumed at
the same rate.
We show in Fig. 9 a recording result in which the
two gratings are quite well balanced: The exposure
energies are 16.66 mW?cm2for the 2.1 ?m grating
and 36.38 mW?cm2for the 0.73 ?m grating.
The reason that we cannot reach diffraction effi-
ciencies close to 100% is that the maximum
refractive-index modulation obtainable with our ma-
terial is too small. If we denote by ?nmaxthe highest
refractive-index modulation that can be obtained
distributed between these N gratings such that
Such a hologram was angularly characterized with
a TE-polarized He–Ne laser at 632.8 nm. Two-
dimensional rigorous coupled-wave theory allows us
to retrieve the refractive-index modulation associ-
ated with each grating by adjusting simulation pa-
rameters to fit experimental results. The results are
shown in Fig. 10.
We obtained the following refractive-index modu-
lations: ?n??2.1 ?m? 0.0088 and ?n??0.73 ?m? 0.0091,
so we have ?nmaxat least equal to 0.0179 (similar
values are reported in Ref. 14). These values, which
are provided by the theory, are for gratings made
from isotropic media; as this is not true in the case
that we are studying, we obtain an effective index
modulation for the TE polarization.
From the monomer diffusion point of view, the se-
quential multiplexing provides the highest energy
gradient, as the fringe contrast is maximum for each
recording. The recording of the first grating, however,
can strongly disturb the formation of the second grat-
energies I0for gratings of periods (a) 2.1 ?m and (b) 0.73 ?m.
Evolution of the first diffracted orders for three exposure
neous multiplexing. The variable parameter is the irradiance used
forthe 2.1 ?mgrating:(a)
? 24.5 mW?cm2, (c) I0? 25.7 mW?cm2, (d) I0? 26.8 mW?cm2.
Optimization of the recording parameters for simulta-
taneous recording setup.
Balanced multiplexed gratings obtained with the simul-
comparison of experimental results (dotted curves) and theoretical
prediction (continuous curves).
Angular characterization of two multiplexed gratings:
ing. In fact, if the first one is recorded and fixed in the
material, it will be difficult for the remaining mono-
mers to diffuse correctly during the second exposure.
As previously, the choice of the exposure energies
associated with each grating will be essential, but,
consequently, the exposure time of the first grating
must be determined. It seems straightforward to
record the longer-period grating first to allow the
formation of the second one (the diffusion of the
monomers will be easier).
We maintain the exposure energies associated with
the two gratings constant [16.13 mW?cm2?2.1 ?m?
and 32 mW?cm2?0.73 ?m?] and vary only the expo-
sure time of the first grating. Recording results are
shown in Fig. 11. Figures 11(a), 11(b), 11(c), and
11(d), correspond to first grating exposure times of 3,
4.3, 4.5, and 5 s, respectively, for the 2.1 ?m grating.
We remark that the optimum exposure time for the
first grating (in our experimental conditions) is quite
short ??4.3 s? and that the gratings continue to form
during the second exposure.
The exposure time of the first grating seems to be
a critical parameter. In our case, 3 s is not enough to
start the formation of the grating and 5 s is too long
if we want to obtain balanced gratings.
Optimization of the Recording Parameters
We dynamically characterized the previously re-
corded holograms by studying their response to an
applied voltage (a square wave at 1 kHz) at Bragg
incidence for each grating. To simplify the compari-
son, in Fig. 12 we plot normalized diffraction efficien-
cies versus the applied electric field.
We can remark that the 2.1 ?m grating switches
faster than the other and that the electric fields are
less than 8 V??m. This is so because the droplets
involved in this grating are larger than the droplets
associated with the grating of 0.73 ?m, so they switch
When the Angular Responses Do Not Overlap
at lower voltages. It even seems possible to erase one
grating by keeping the other at a high diffraction
efficiency. A disadvantage is that to observe such
effects we need two incident beams.
We saw in Section 3 [Fig. 3(b)] that, when the angular
responses of the gratings overlap, coupling effects
occur between the diffraction efficiencies of the two
gratings. If we work not at Bragg incidence but at an
intermediary angle where the curves of diffraction
efficiencies are crossing [Fig. 3(b)], we can expect a
modification of this coupling by applying an electric
field and even switch from one grating to the other. In
our configuration, we have a loss in diffraction effi-
ciency that is due to the fact that we are working with
one beam with an incidence between the Bragg an-
gles of the two gratings. The grating periods that we
chose were ?1? 1.3 ?m and ?2? 2.1 ?m.
From Fig. 13 we can see few coupling effects be-
tween the two gratings, as if the energy of one were
transferred to the other. This effect is not efficient; it
is possible to improve it by having higher refractive-
index modulations for the two gratings. For this pur-
pose, the phase separation during recording has to be
improved. An advantage is that the switching effects
occur for values of the electric field smaller than
When the Angular Responses Overlap
two sequentially multiplexed transmission gratings with different
exposure times for the first grating: (a) 3 s, (b) 4.3 s, (c) 4.5 s, (d) 5 s.
Time evolution of the first-order diffraction efficiency of
two gratings as a function of the applied electric field.
Normalized diffraction efficiency in the first order for the
ings as a function of the applied electric field when the angle of
incidence is between the two Bragg angles.
Diffraction efficiency in the first order for the two grat-
3 V??m. Variable beam deflectors and spectral band
selectors could be derived from this effect.
As in Subsection 6.A, beyond a certain voltage the
two gratings begin to be erased, and the grating that
has the shorter period switches more slowly than the
We have studied static and dynamic behavior of the
multiplexing of twotransmission
H-PDLCs. We have described how to optimize two
experimental setups to grow both gratings at the
same speed during the recording process. We ob-
tained similar results for the two multiplexing meth-
ods (simultaneous and sequential), but each of them
requires specific recording parameters.
In the case of simultaneous multiplexing the criti-
cal parameters are the irradiances associated with
the recording beam. Exposure energies have to be
adjusted to produce a balanced competition between
the diffusion of the monomers and the photopolymer-
ization for the two gratings. For the sequential re-
cording the exposure time of the first grating is
critical because, if this time is too long, the first grat-
ing will prevent correct diffusion of monomers for the
second grating. For the static characterization we
retrieved an estimation of the refractive-index mod-
ulations of the two gratings for TE polarization by
using rigorous coupled-wave theory. We checked that
the global refractive-index modulation that can be
obtainable is shared between the different recorded
gratings. This effect strongly limits the number of
holograms that can be recorded in the material. We
can estimate this number as ten; this material is not
appropriate for recording hundreds of holograms.
We have demonstrated the existence of some cou-
pling effects between two gratings when an electric
field is applied. It seems possible to amplify these
effects with more-elaborate work on the H-PDLC ma-
terial (by having a better phase separation to reach
higher refractive-index modulations). With conse-
quent coupling, we suspect that it will be possible to
switch electrically from one grating to the other. An
amplification of this switching effect could lead to
several interesting applications: selection of a spec-
tral band and optical switches, for example.
To improve the diffraction efficiencies and to reach
values close to 100% we can either increase the thick-
ness of the cells or work on the H-PDLC material to
reach a higher global refractive-index modulation
?nmax. However, the thickness cannot be increased
indefinitely because of the kinetics of the curing pro-
cess. The second application could be achieved with
better phase separation between polymer and liquid
crystals and control of the orientation of the director
of the liquid droplets (to have a higher index differ-
ence between liquid droplets and the polymer).
With reference to the recording process, a solution
to amplifying the switching effect could be to change
the configuration of one of the gratings. The first
grating would still be transmissive, with fringes or-
thogonal to the substrates, whereas the second grat-
ing would have slanted fringes to make both gratings
work at Bragg incidence instead of at an intermedi-
ary incident angle. Both will have higher diffraction
efficiencies, but it will be more complicated to achieve
the recording setup because of shrinkage effects that
occur with photopolymerizable materials. One has to
study this effect precisely to obtain a second grating
with the same Bragg angle as the first grating. An-
other suggestion could be the use of digital hologra-
phy to generate the multiplex structure and to
replicate this structure in H-PDLCs.
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