Characterization of a PVA/acrylamide photopolymer. Influence of a cross-linking monomer in the final characteristics of the hologram

Optics Communications 224 (2003) 27–34

www.elsevier.com/locate/optcom

Characterization of a PVA/acrylamide photopolymer.Influence of a cross-linking monomer in the

final characteristics of the hologram

Cristian Neippa, Sergi Gallegob, Manuel Ortu~nnob, Andr�ees M�aarqueza,Augusto Bel�eendeza,*, Inmaculada Pascualb

a Departamento de F�ıısica, Ingenier�ııa de Sistemas y Teor�ııa de la Se~nnal, Universidad de Alicante, Apartado 99, E-03080 Alicante, Spainb Departamento Interuniversitario de �OOptica, Universidad de Alicante, Apartado 99, E-03080 Alicante, Spain

Received 22 January 2003; received in revised form 6 April 2003; accepted 1 July 2003

Abstract

The use of high thickness photopolymers for holographic recording is particularly promising for storage of data

information. Therefore it is interesting to characterize such materials in order to improve the quality of the holograms

recorded on them. In this work we make use of a first harmonic diffusion model to characterize a polyvinyl alcohol/

acrylamide photopolymer. In particular we analyze the effect of adding a cross-linking monomer to this material in the

temporal evolution of the transmission efficiency.

� 2003 Elsevier B.V. All rights reserved.

PACS: 42.40 Pa; 42.40 Ht; 42.40 Lx; 42.70 Ln; 42.70 Jk

Keywords: Holography; Holographic recording materials; Photopolymers; Volume holograms

1. Introduction

Photopolymers are systems of organic mole-cules that rely on photoinitiated polymerization to

record volume phase holograms. Characteristics

such as good light sensitivity, large dynamic range,

good optical properties and relatively low cost

make photopolymers one of the most promising

* Corresponding author. Tel.: +3465903651; fax:

+3465909750.

E-mail address: [email protected] (A. Bel�eendez).

0030-4018/$ - see front matter � 2003 Elsevier B.V. All rights reserv

doi:10.1016/S0030-4018(03)01719-X

materials for write-one, read-many (WORM) ho-

lographic data storage applications [1,2].

Photopolymer systems for recording hologramstypically comprise one or more monomers, a

photoinitiation system and an inactive component

often referred to as a binder [3]. Other components

are sometimes added to control a variety of

properties such as sensitivity and viscosity of the

recording medium [4]. Although complex, the

mechanism of hologram formation is supposed to

be a consequence of various processes, being themost important of them the monomers poly-

merization. The basic mechanism for the radical

ed.

mail to: [email protected]

28 C. Neipp et al. / Optics Communications 224 (2003) 27–34

polymerization can be considered as succession of

different processes. The first step is the initiation

process. This process involves the production of

free radicals, which bind to monomers creating the

chain-initiation species. After initiation, these

species propagate by combining with othermonomer molecules forming a large polymer

chain. Finally, when the radical of the growing

polymer bonds with a free radical a dead polymer

is formed. These are the basic steps describing the

polymerization process. Complete models [5–8] by

taking into account these processes are described

in some works. For instance, the ‘‘Nonlocal-re-

sponse diffusion model’’ proposed by Sheridanet al. [6–8] describes the material behaviour during

photoplymerization in terms of a nonlocal re-

sponse, which is due to the growth of the chains of

photopolymer away from their initiation point,

what implies a ‘‘spreading’’ of photopolymer. In

these models, not only polymerization plays an

important role in the mechanism of hologram

formation, but also monomer diffusion, whichtakes place from the nonexposed to the exposed

zones. Some other models also provide accurate

description of the mechanism of hologram for-

mation such as the model proposed by Zhao and

Mourolis [9], later refined by Colvin et al. [10]. The

model proposed by Zhao comprises the basic ideas

of all diffusion based models: the mechanism of

hologram formation is assumed to be a conse-quence of the interplay between the processes of

monomer polymerization and monomer diffusion,

which take place when the material is illuminated.

On the other hand the model proposed by Piazolla

and Jenkins [11] is a first harmonic diffusion model

of a relatively simple mathematical treatment,

which permitted obtaining an analytical expression

for the refractive index modulation created insidethe hologram by photoplymerization and diffusion

mechanisms.

In this work we will use a first harmonic diffu-

sion based model to characterize a high thickness

polymeric material [12]. The use of high thickness

photopolymers is interesting for data storage ap-

plications and hologram multiplexing [13]. There-

fore, it is important to analyze the influence of thedifferent experimental conditions in the quality of

the final holograms recorded on high thickness

photopolymer materials. Some works have been

published in this direction [14–17]. In this work we

will analyze in particular the influence of adding a

second crosslinking monomer (N,N 0-methylene-

bis-acrylamide) to a polyvinyl alcohol (PVA)/ac-

rylamide photopolymer. The addition of thismonomer was found to stabilize the final holo-

gram recorded on the polymer material. We will

also demonstrate that the diffusion based model is

highly predictive and good agreement between the

theoretical model and the experimental data is

found.

2. Theoretical model

2.1. First harmonic diffusion-based model

In order to give a theoretical support to the

experimental data a first harmonic diffusion based

model is commented in this section. This model is

presented in [12] so only a short review is com-mented here. This is a similar model to that pro-

posed by Piazolla and Jenkins [11] also some

modifications are added to explain the differences

in the refractive indexes of the monomer and the

polymer [18].

First, we will assume that the material is ex-

posed to a sinusoidal interference pattern of the

form

IðxÞ ¼ I0b1þ m cosðKgxÞc; ð1Þwhere m is the beam intensity modulation, Kg is the

grating wave number and I0 the average recordingintensity.

Because the consumption of monomer due to

polymerization is more rapid in the bright regions

than in the dark ones, we will assume that the freemonomer presents a sinusoidal spatial concentra-

tion which is phase shifted 180� with respect to the

intensity pattern. Therefore the concentration of

monomer, /ðmÞ, can be expressed as

/ðmÞðx; tÞ ¼ /ðmÞ0 ðtÞ � /ðmÞ

1 ðtÞ cosðKgxÞ; ð2Þwhere t is the time, /ðmÞ

0 is the average monomer

concentration and /ðmÞ1 the first order of the

monomer concentration and polymer concentra-

tion, /ðpÞ as

Table 1

Composition of polymeric material of type 1

Acrylamide 0.40 M

Triethanolamine 0.20 M

Yellowish eosin 2.5� 10�4 M

Polyvinylalcohol (Fluka 18–88) 7% w/v

Table 2

Composition of polymeric material of type 2

Acrylamide 0.40 M

Triethanolamine 0.20 M

Yellowish eosin 2.5� 10�4 M

Polyvinylalcohol (Fluka 18–88) 7% w/v

N,N 0-Methylene-bis-acrylamide 0.05 M

C. Neipp et al. / Optics Communications 224 (2003) 27–34 29

/ðpÞðx; tÞ ¼ /ðpÞ0 ðtÞ þ /ðpÞ

1 ðtÞ cosðKgxÞ; ð3Þwhere/ðpÞ

0 is the average polymer concentration and

/ðpÞ1 , the first order of the polymer concentration.

Due to polymerization the concentration ofmonomer decreases with time. Simultaneously due

to the gradient of monomer concentration estab-

lished between the nonexposed and exposed zones

the free monomer diffuses away from the dark

to the bright regions. The equation which de-

scribes the variation of monomer concentration,

taking into account these two processes is [11]

o/ðmÞ

ot¼ �kRðtÞIðxÞ/ðmÞðx; tÞ þ o

oxD

o

ox/ðmÞðx; tÞ;

ð4Þwhere / stands for the volume fractions of the

different compounds, (m) and (p) stand for

monomer and polymer, respectively, D is the dif-fusion constant, which we assume to be constant,

IðxÞ the illumination intensity and kRðtÞ the poly-

merization rate. The polymerization rate controls

the rate of creation of polymer from monomer and

as will be demonstrated in Section 4, it is influ-

enced by the addition of a cross-linking monomer

to the initial solution.

On the other hand the following equation de-scribes the formation of polymer by photopoly-

merization:

o/ðpÞ

ot¼ kRðtÞIðxÞ/ðmÞðx; tÞ: ð5Þ

Following a similar treatment as that made by

Aubrecht et al. [18] the first harmonic component

of the refractive index can be expressed as

n1 ¼ðn2dark þ 2Þ2

3ndark

"� n2m � 1

n2m þ 2

�� n2b � 1

n2b þ 2

�/ðmÞ

1

þn2p � 1

n2p þ 2

� n2b � 1

n2b þ 2

!/ðpÞ

1

#; ð6Þ

where ndark is the refractive index of the mixture ofcompounds without illumination and np, nm, nb arethe refractive indexes of the polymer, monomer

and binder, respectively.

By using Eqs. (1)–(5) and after some calcula-

tions the following expressions for the harmonic

terms can be derived:

d/ðmÞ0

dt¼ �kRðtÞI0 /ðmÞ

0

�� 1

2/ðmÞ

1

�; ð7Þ

d/ðmÞ1

dt¼ kRðtÞI0 /ðmÞ

0

h� /ðmÞ

1

i� /ðmÞ

1

sD; ð8Þ

d/ðpÞ0


0

�� 1

2/ðmÞ

1

�; ð9Þ

d/ðpÞ1


0

h� /ðmÞ

1

i; ð10Þ

where m was supposed to be 1 and the diffusion

time constant, sD, is defined as sD ¼ ðDK2g Þ

�1.

On the other hand the polymerization rate was

supposed to decay exponentially with time in the

following way [12]:

kRðtÞ ¼ k0 expð�utÞ: ð11ÞEqs. (7)–(10) combined with Eqs. (6) and (11)

are the basic equations of this first harmonic dif-fusion model.

3. Experimental

The photopolymerizable solution was prepared,

under red light, by mixing in a magnetic stirrer all

components (yellowish eosin, triethanolamine,PVA solution and monomers). The concentration

of each of the components in prepared solution

can be seen in Tables 1 and 2. The only monomer

in material of type 1 (Table 1) is acrylamide

whereas in the material of type 2 (Table 2) we also


added a cross-linking monomer (N,N 0-methylene-

bis-acrylamide). The resulting solution was de-

posited on a 20� 40 cm2 glass plate. The plate was

dried for a period of 48 h in the dark and under

normal laboratory conditions (T ¼ 21–23 �C,HR¼ 40–60%). Once dried we cut it into platesmeasuring 6.5� 6.5 cm2 to be used in our experi-

mental setup.

The setup used in the experiments to record the

transmission diffraction gratings on the photo-

polymer is presented in Fig. 1. An argon laser at a

wavelength of 514 nm was used to store diffraction

gratings by means of continuous laser exposure.

The laser beam was split into two secondary beamswith an intensity ratio of 1:1, that is m ¼ 1. The

diameter of these beams was increased to 1 cm

with an expander, while spatial filtering was en-

sured. The object and reference beams were

recombined at the sample at an angle of 16.8� to

the normal with an appropriate set of mirrors,

and the spatial frequency obtained was 1125 lines/

mm. The diffracted and transmitted intensity weremonitored in real time with a He–Ne laser posi-

tioned at Bragg�s angle (20.8�) tuned to 633 nm,

where the material does not polymerize.

In order to obtain the transmission efficiency as

a function of the angle at reconstruction we placed

the plates on a rotating stage. Transmission was

calculated as the ratio of the transmitted beam to

the incident power, and in order to take into ac-count Fresnel losses the expression was multiplied

by an appropriate factor. This factor was calcu-

lated as 0.8721 for a reconstruction angle of 20.8�in air under red light. The refractive index of the

Fig. 1. Experimental set-up.

polymer matrix was considered as 1.54, and for the

glass substrate a value of 1.52 for the refractive

index and 1.95 for the thickness were considered.

4. Results and discussion

In order to characterize the high thickness

transmission diffraction gratings recorded on

photopolymers the angular response of the trans-

mittance was fitted by using the expression of the

transmission efficiency given by Kogelnik [19]

coupled wave theory. The relation between the

first harmonic component of the refractive index,n1, and the transmission efficiency, s, for volume

phase holograms in which a sinusoidal diffraction

grating has been recorded is given by the following

equation [20]:

s ¼ expð�ad= cos h0Þ 1

�� sin2 pn1d

k cos h0

� ��; ð12Þ

where k is the wavelength of reconstruction in air,

a takes into account the absorption and scattering

of the hologram (we have no means of differenti-ating them), d is the thickness of the hologram and

h0 is the angle of reconstruction in the recording

medium, related to the angle of reconstruction in

air by Snell�s law.By fitting the theoretical function given by

Eq. (12) to the experimental data of the angular

response of the transmittance, information about

the refractive index modulation, n1, the thickness,d, and the absorption coefficient, a, of the final

hologram can be obtained. Once the thickness, d,of the hologram was obtained by this method we

were able to fit the temporal evolution of the

transmission efficiency by using Eqs. (7)–(10) and

(12). So information about the parameters which

control the polymerization process can also be

obtained.At first we studied transmission diffraction

gratings which were recorded on a polymeric ma-

terial of type 1. Figs. 2 and 3 show the angular

dependence of the transmittance for two trans-

mission diffraction gratings recorded on a poly-

meric material of type 1, with different thickness.

The dots correspond to the experimental data

whereas the continuous line corresponds to the

Fig. 2. Transmittance as a function of the angle for a trans-

mission diffraction grating recorded on a polymeric material of

type 1, with a thickness of 86 lm.




Fig. 4. Temporal evolution of the transmittance for transmis-

sion diffraction grating recorded on a polymeric material of



theoretical fit using Eq. (12). The parameters of n1,a, d obtained after the theoretical fits are presented

in Table 3 for all the diffraction gratings studied.

In the case of the diffraction gratings presented in

Figs. 2 and 3 the final value of the thickness was

found to be different: d ¼ 86 lm, for diffractiongrating of Fig. 2 and d ¼ 101 lm, for the diffrac-

tion grating of Fig. 2. These differences in thick-

Table 3

Parameters obtained after the theoretical fit of the angular re-

sponse of the transmittance

n1 d (lm) a (lm�1)

Fig. 2 0.0033 86 0.00050

Fig. 3 0.0027 101 0.00060

Fig. 6 0.0038 71 0.00034

Fig. 7 0.0046 67 0.00050

Fig. 10 0.0050 98 0.00020

ness of the transmission gratings stored are due to

the deposition process explained in Section 3,

which is not completely controllable. So the pro-

duction of plates with exactly the same thickness is

not possible. Far from being a drawback, the

production of gratings with different thicknesspermits checking the diffusion based model pro-

posed. The curves of the temporal evolution of the

transmittance for the diffraction gratings stored

were fitted by fixing all the parameters of the

model proposed in Section 2, being the thickness,

d, the only variable parameter.

Figs. 4 and 5 show the transmittance as a

function of the time of exposure for the samediffraction gratings of Figs. 2 and 3, respectively.

Dots represent the experimental data, whereas the

continuous line correspond to the theoretical

function of the transmittance obtained by using







Table 4

Parameters obtained after the theoretical fit for the first harmonic diffusion based model

Polymer k0 (cm2 mW�1 s�1) u (s�1) sD (s) nm np

Type 1 0.020 0.015 30 1.56 1.60

Type 2 0.024 0.015 30 1.56 1.63


the commented first harmonic diffusion basedmodel. The parameters of the model used are

presented in Table 4 for all diffraction gratings

studied. As can be seen from Figs. 4 and 5, the

higher thickness of the hologram presented in

Fig. 4 implies that the zero of transmission effi-

ciency, which corresponds to the maximum dif-

fraction efficiency is reached earlier. In addition,

the energetic sensitivity is increased when the ho-logram is recorded with a higher thickness. On the

other hand, from Table 3 it can also be seen that

the refractive index modulation needed to obtain

maximum diffraction efficiency (minimum of

transmission efficiency) is lower when the thickness

is increased, a value of, n1 ¼ 0:0033 was needed for

the diffraction grating corresponding to Fig. 4 and

a value of n1 ¼ 0:0027, for the diffraction gratingof Fig. 5.

As commented in Section 3 we also added a

second monomer which has a cross-linking effect,

creating a photopolymeric material of type 2. Figs.

6 and 7 show the transmittance as a function of the

angle for two diffraction efficiencies recorded on a

polymer material of type 2. Whereas Figs. 8 and 9

show the transmittance as a function of the time ofexposure for these diffraction gratings. It can be




seen that when a second monomer is added to the

polymeric material the rate of growth of the re-

fractive index modulation, n1, with time increases,

what implies that the transmittance decreases morerapidly with time. This can be easily checked if

Figs. 8 and 9 are compared with Figs. 4 and 5. This

behavior is corresponded with an increase in the

polymerization rate constant, k0, when a second

monomer is added to the material. In the case of

the material of type 1, the polymerization rate

constant, k0, was found to be of 0.020 cm2 mW�1










Fig. 11. Temporal evolution of the transmittance for trans-




s�1, whereas when a second monomer is added,

material of type 2, the polymerization rate con-

stant increases to a value of 0.024 cm2 mW�1 s�1.

This can be understood if one takes into accountthat the addition of a cross-linking monomer

supposes a quick rise of polymer molecular weight

obtained in the bright zones by cross-linking of

polyacrylamide chains, thus increasing the poly-

merization rate. On the other hand, a slight in-

crease of the refractive index of the polymer

created after polymerization was found in the

material of type 2 with respect to that of materialof type 1 (np ¼ 1:60 for material of type 1 and

np ¼ 1:63 for material of type 2). This is due to the

fact that the addition, in low concentration, of

bifunctional monomer to photopolymer formula-

tion has a crosslinking effect of polyacrylamide

chains, what implies a more compact polymeric

network.

Finally, Fig. 10 shows the angular response ofthe transmittance and Fig. 11 the transmission

efficiency as a function of time for a holographic

diffraction grating recorded in a polymeric mate-

rial of type 2 exhibiting over-modulation [17]. The

dotted points correspond to the experimental data

whereas the continuous line corresponds to the

theoretical fit. The increase in the transmission

efficiency after the peak in Fig. 11 is due to highvalues of the product, n1d, of the refractive index

modulation and the thickness of the hologram

[21]. This is possible because of the high thickness,

d � 98 lm, of the final hologram recorded in our

photopolymer material. Exact reproduction of the

experimental data was not possible because therewas a slight deviation from the Bragg condition as

a consequence of a small thickness change between

the recording and reconstruction. Therefore, the

zero of transmission efficiency was not reached by

the experimental curve. This slight deviation from

Bragg condition was only found in this overmod-

ulated grating. Nonetheless, good agreement be-

tween theory and experiment can be found.

5. Conclusions

A first harmonic based model is proposed to

characterize a high thickness photopolymer mate-

rial. Following the approach of the diffusion based

models, two processes play the main role in theformation of the diffraction grating: conversion of


monomer into polymer by photopolymerization

and diffusion of free monomer from the dark to

the bright regions. By considering these two pro-

cesses the mechanism of hologram formation can

be explained.

A PVA/acrylamide photopolymer was understudy. Transmission diffraction gratings were re-

corded on two kind of materials, material of type 1

and material of type 2. The angular response of

the transmittance was measured and by fitting the

theoretical function of the transmittance to the

experimental data, information about the refrac-

tive index modulation, the thickness and the ab-

sorption of the final hologram was obtained.The temporal evolution of the transmittance

was also evaluated for the diffraction gratings

studied, and information about the parameters

which control the polymerization and diffusion

processes were also obtained. It has been shown

that the addition of a cross-linking monomer to

material of type 1 meant an increase of the poly-

merization rate and also a slight increase of thepolymer refractive index.

Finally, it is remarkable that the recording of

holographic gratings on the same material with

different thickness permits checking the validity of

the diffusion model proposed. The parameters of

the model were fixed for each material studied with

exception of the thickness of the hologram, which

was obtained from the theoretical fit to the curvesof the angular response of the transmittance.

Good agreement has been found between the

theoretical model and the experimental data, what

confirms the validation of the diffusion based

model to explain the mechanism of hologram

formation in photopolymer materials.

Acknowledgements

This work was supported by Ministerio de

Ciencia y Tecnolog�ııa, CICYT, Spain, under pro-

ject MAT2000-1361-C04-04 and by the Oficina de

Ciencia y Tecnolog�ııa, Generalitat Valenciana,

Spain, under project GV01-130.

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Documents

Characterization of a PVA/acrylamide photopolymer. Influence of a cross-linking monomer in the final characteristics of the hologram