Shrinkage during holographic recording in photopolymer films determined by holographic interferometry Mohesh Moothanchery,1 Viswanath Bavigadda,2 Vincent Toal,1 and Izabela Naydenova1,* 1

2

Centre for Industrial and Engineering Optics, School of Physics, Dublin Institute of Technology, Kevin Street, Dublin 8, Ireland

Department of Engineering Product Development, Singapore University of Technology and Design, 20 Dover Drive, Singapore 138682 *Corresponding author: [email protected] Received 28 August 2013; revised 10 November 2013; accepted 11 November 2013; posted 13 November 2013 (Doc. ID 196480); published 5 December 2013

Shrinkage of photopolymer materials is an important factor for their use in holographic data storage and for fabrication of holographic optical elements. Dimensional change in the holographic element leads to a requirement for compensation in the reading angle and/or wavelength. Normally, shrinkage is studied at the end of the polymerization process and no information about the dynamics is obtained. The aim of this study was to use holographic interferometry to measure the shrinkage that occurs during holographic recording of transmission diffraction gratings in acrylamide photopolymer layers. Shrinkage in photopolymer layers can be measured over the whole recorded area by real-time capture of holographic interferograms at regular intervals during holographic recording using a complimentary metal-oxidesemiconductor camera. The optical path length change, and hence the shrinkage, are determined from the captured fringe patterns. Through analysis of the real-time shrinkage curves, it is possible to distinguish two processes that determine the value of shrinkage in the photopolymer layer. These processes are ascribed to monomer polymerization and crosslinking of polymer chains. The dependence of shrinkage of the layers on the conditions of recording such as recording intensity, single or double beam exposure, and the physical properties of the layers, such as thickness, were studied. Higher shrinkage was observed with recordings at lower intensities and in thinner layers. Increased shrinkage was also observed in the case of single beam polymerization in comparison to the case of double beam holographic exposure. © 2013 Optical Society of America OCIS codes: (090.0090) Holography; (090.2880) Holographic interferometry; (160.5470) Polymers; (090.7330) Volume gratings; (160.5335) Photosensitive materials; (160.4670) Optical materials. http://dx.doi.org/10.1364/AO.52.008519

1. Introduction

Photopolymers have been under investigation for many years because of their importance in applications, such as liquid-crystal displays [1], holographic data storage [2–4], holographic optical elements [5], holographic displays [6,7], and holographic sensors 1559-128X/13/358519-09$15.00/0 © 2013 Optical Society of America

[8–12]. The properties that make photopolymer materials of great interest are their easy processing, high photosensitivity, relatively high refractive index contrast, and reasonable cost. Polymerization induced shrinkage is one of the main reasons why photopolymer materials are not more widely used in certain holographic applications such as holographic data storage and holographic optical elements. Shrinkage occurring in photopolymer layers was successfully measured using Bragg detuning 10 December 2013 / Vol. 52, No. 35 / APPLIED OPTICS

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of slanted holographic gratings [13–19]. The disadvantage of using Bragg measurements is that shrinkage measurements can be made only after holographic recording. The aim of this study was to use holographic interferometry to measure shrinkage in real time during holographic recording in an acrylamide photopolymer developed at the Centre for Industrial and Engineering Optics [20,21]. Holographic interferometry is a nondestructive technique that measures small static or dynamic changes occurring in an object [22–29]. The technique was introduced by Powell and Stetson [27] among others. The interferograms in our experiment were produced by interference between a light wave, which was reflected from the photopolymer layer surface and recorded in a separate hologram before photopolymerization began, and a wave reflected from the photopolymer surface during the photopolymerization process. The first hologram of the photopolymer layer surface was recorded at one wavelength in a layer, which was insensitive to the holographic grating recording process that takes place at different wavelengths. To the best of our knowledge, this is the first time that shrinkage measurements using holographic interferometry have been reported in photopolymer layers. 2. Theoretical Background

Real-time holographic interferometry helps to determine minute changes in an object in real time by superimposing the image reconstructed from the hologram of the object on the object itself while it is undergoing change. The vector displacement (L) at a point on the surface of the object can be determined using holographic interferometry, since the vector displacement is proportional to the phase difference between two interfering beams [25]. The phase difference Δ is given by Δ  2π∕λkˆ 2 − kˆ 1   L  K  L;

(1)

where kˆ 1 and kˆ 2 shown in Fig. 1 represent unit vectors in the directions of illumination and observation, respectively. K is known as the sensitivity vector [28,29]. The change in optical path length δ of the beam due to change in the position d of the surface with respect to angles of illumination and observation is δ  dcos θ1  cos θ2 ;

(2)

where θ1 and θ2 are the angles of illumination and observation, respectively. The change in optical path length can also be expressed in terms of the wavelength λ as δ  nλ;

(3)

where n is a real number. From Eqs. (2) and (3), the object displacement d is 8520

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d  nλ∕cos θ1  cos θ2 :

(4)

Shrinkage in photopolymer layers can be determined by real-time capture of holographic interferograms during holographic recording. The interferograms are produced by interference between the holographical reconstruction of a light wave, which traversed the photopolymer layer or was reflected from its surface before photopolymerization began, and a wave traversing or reflected from the photopolymer surface during the photopolymerization process. The photopolymer layer in which the hologram was recorded is insensitive to the light used for the holographic grating recording in the photopolymer layer under study. A virtual instrument (VI) developed in LabVIEW (Version 8.2) was used to capture interferograms using a complimentary metal-oxide-semiconductor (CMOS) camera at regular intervals. By counting the number of dark fringes (n) and knowing the angles of illumination and observation, the change in optical path difference can be calculated, and hence the shrinkage. The important feature of holographic interferometry is that the fringes corresponding to the displacement of the object are produced in real time. Because of the small difference between the angle of illumination and the angle of observation of the photopolymer surfaces, the shrinkage measured by this arrangement of beams is mainly in the direction of normal to the surface. The absolute shrinkage of the layers was determined from Eq. (4), where the relative shrinkage was determined by dividing the absolute shrinkage by the layer thickness. The limitations of the proposed experimental setup are determined by the accuracy with which we can count the number of interference fringes. If we assume that we can count fringes with a precision of one half of an interference fringe, this sets the accuracy of the shrinkage measurement to be λ∕4 or 0.16 μm. 3. Experimental Procedure A. Sample Preparation

Two types of samples were prepared in this experiment. A green-light sensitive layer was used for recording at 532 nm and a separate red-light sensitive layer was used for recording at 633 nm. The greenlight sensitive photopolymer layer was prepared as described in [19]. Briefly, 8.4 mmol of acrylamide monomer was added to a 9 ml stock solution of polyvinyl alcohol (20% wt∕wt water stock solution). Then, 15.1 mmol of triethanolamine was added. To this solution, we added 1.3 mmol of N,N-methylene bisacrylamide and 0.5 mmol of Erythrosine B dye dissolved in 4 ml water. Using this photopolymer solution, volumes of 0.35, 0.55, and 0.8 ml were spread on 25 mm × 75 mm glass plates coated with black matte paint on the back (in order to avoid back reflection from glass). The samples were allowed to dry for

Fig. 1. Optical path difference diagram.

24 h. The sample thicknesses after drying were 70, 110, and 160  3 μm, respectively. The layer thickness was determined using a white light interferometer (WLI). The photopolymer layer was cut and the area of this cut was imaged with the WLI surface profiler. Information about the layer thickness was extracted from this image. A second solution, for preparation of red-light sensitive layers was made up using the same amounts of acrylamide, N,Nmethylene bisacrylamide, and triethanolamine, while 17.5 ml of polyvinyl alcohol (10% wt∕wt water stock solution) and 1.37 mmol of Methylene blue (MB) dye dissolved in 4 ml water were used. Using this solution, 0.6 ml was spread on a 25 mm × 75 mm glass plate and allowed to dry for 24 h. The corresponding layer thickness after drying was 60  3 μm. These red-light sensitized layers were used to record holograms of the surface of the green-light sensitive layers that were analyzed. B.

Experimental Setup

The experimental setup is shown in Fig. 2. It comprises two independent pairs of interfering beams. The He–Ne beam scattered from the surface (S) of the Erythrosine B (EB) green-light sensitive layer interferes with a reference beam that records a

Glass R R

G

Fig. 2. Combined holographic grating recording and holographic interferometry system.

hologram (H) of the surface, S, in the red-light-sensitive layer. A glass plate was used instead of a mirror in order to equalize the intensities of the two He–Ne beams. The light reconstructed from the hologram, H, is allowed to interfere with light scattered from S during subsequent recordings of a holographic grating in the green-light sensitive layer. In this way, we implemented live fringe or real-time holographic interferometry to study small changes in the surface S of the green-light sensitive layer. The angle of illumination of the EB layer and the angle of observation were 26.2° and 33.7°, respectively. From the combined intensity of the 633 nm beams, the light reflected from the EB sample surface and from the glass plate was 0.5 mW∕cm2 . The EB layer does not absorb at 633 nm, thus, this recording does not introduce dimensional changes in the layer under study. The hologram in the red-light sensitive layer was recorded for 140 s. Because of the self-processing nature of the photopolymer, this hologram was fully developed at the end of the recording process and ready to be used in the real-time holographic interferometry experiment. After a delay of 20 s, the beam from a Torus 532 nm laser was switched on. This beam was spatially filtered and split into two beams (Fig. 2). The combined intensity from the 532 nm beams was 5 mW∕cm2. The beams were overlapped with one another to record a holographic grating in the EB layer. This caused shrinkage of the EB layer. The camera recorded interference fringes (Fig. 2) due to the superposition of two beams. The first was a reconstruction from the hologram H of an image of the surface S of the unexposed green-light sensitive photopolymer layer (EB layer). The second beam was the He–Ne beam reflected from the surface of the green-light sensitive layer as it shrank during exposure to green light This shrinkage introduced a time dependent phase difference between the two beams, thus a changing interference pattern was observed. The setup was sensitive almost exclusively to the out-of-plane shrinkage of the EB layer. The sensitivity to in-plane shrinkage depended on the very small difference between the sines of the angles of illumination and observation. It worth noting that the MB layer also shrank during holographic recording with red light, but once the hologram was recorded, there were no further dimensional changes and all further changes were due only to shrinkage of the EB layer. Due to shrinkage, a change occurs in the optical path of the red beam reflected from the surface of the green-light sensitive layer, and this change can be calculated from the number of fringes that appear. The fringes can be observed visually during the recording of the holographic grating in the green-light sensitive layer, but due to their limited visibility, we implemented a subtraction procedure for the images captured by the CMOS camera. A LabVIEW (Version 8.2) coded VI was used with a National Instruments IMAQ-1409 frame grabber card to capture the images. The camera (AVT Guppy F-036B) was set in externally triggered mode and 10 December 2013 / Vol. 52, No. 35 / APPLIED OPTICS

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supplied by a digital to analog converter (D/A) board with a digital pulse to initiate each image capture. The digital pulse frequency can be varied from 1 to 25 Hz. A reference frame was subtracted from each incoming frame and the results represent the change in the interferogram displayed on the computer monitor in real time. The reference frame and other acquired frames were also stored in the computer. The movement of the interference fringes was captured as a live video, which was processed using NI Vision Assistant software. The advantage of using the subtraction method for the production of secondary fringes is that it can produce high contrast [26]. The reference frame was captured at the end of the recording of the hologram in the red-light sensitive layer, just before switching on the green laser. In order to ensure that the fringes are the result only of the holographic or single beam recording in the green-light sensitive layer, the reference frame was subtracted from the current frames before switching on the green laser for at least 20 s. No fringes were observed during this period. 4. Experimental Results

A hologram of the front surface of the 70 μm thick EB layer was recorded in a 60 μm MB layer using the interference of a 633 nm beam reflected from the front surface of the EB layer and a reference beam reflected from a glass plate. The reconstructed image from this hologram, shown in Fig. 3(a), was used as the reference image for the static subtraction method. It was captured after the recording process at 633 nm was completed and the MB sensitive photopolymer layer was fully polymerized. When the EB sample was not undergoing polymerization, no fringes were produced by the subtraction of the reference image, as shown in Fig. 3(b). The result of the subtraction was observed for several seconds, thereby confirming that the fringes appearing at the next stage were produced only while recording a holographic grating. The interferogram is shown in Fig. 3(c), where the EB layer was undergoing polymerization using the 532 nm beam. Figure 3(c) clearly shows a dark fringe and the number of fringes appearing varied with exposure. In order to determine the effect of layer thickness and recording intensity on shrinkage, transmission diffraction gratings with a spatial frequency of 1000 lines∕mm were recorded.

A. Influence of Recording Intensity on Shrinkage

Figures 4(a)–4(c) show the relative shrinkage in 70, 110, and 160 μm thick layers, respectively, for three different recording intensities: 1, 5, and 10 mW∕cm2 . From Fig. 4, one can observe that relative shrinkage was lower in the layers recorded at higher intensity and increased absolute shrinkage was observed in layers of higher thickness. The shrinkage data were collected until no new fringes were appearing in the interference pattern. Initially, a single exponential asymptotic function was used to fit the shrinkage curves but the error of the fit was too large. The next choice of fitting function was a stretched exponential function. The use of such function could be justified because during polymerization that leads to shrinkage, the properties of the photopolymer layer, mainly its permeability, change gradually. The permeability determines the mobility of the monomer molecules and thus the polymerization rate. However, the stretched exponential fit did not fit the experimental data any better, which is a clear indication that there is not a single process that determines the dynamics of the photopolymer shrinkage, especially at higher recording intensities. The shrinkage in photopolymer materials was mainly attributed to the photopolymerization process, which leads to the creation of long polymer chains that have different morphologies than the monomer molecules. This normally leads to the creation of a denser material and causes a dimensional change of the photopolymerized layers, which can be observed as shrinkage. The photopolymer system studied in this paper had two monomer molecules, one of which played the role of a cross linker. It is reasonable to assume that the photopolymerization reactions in which these two molecular species are involved are happening on slightly different timescales. The polymerization rate of monomer molecules and the rate of crosslinking of polymer chains are processes that both depend on the number of available free radicals; thus, the processes depend on intensity. On the other hand, it is reasonable to expect that these two processes have a different dependence on intensity. For a crosslinking event to take place, it is necessary that two polymer chains be in close proximity to each other. This could be achieved either by high free radical concentrations or by more mobile (shorter) polymer chains. Both

Fig. 3. (a) Reference frame produced by capturing the beam reconstructed by the hologram recorded in the red-light sensitive layer, (b) result of subtraction of the reference frame from the current frame (before switching on the green laser), and (c) result of subtraction of the reference frame from the current frame (after switching on the green laser). 8522

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Fig. 4. Row shrinkage versus exposure energy for a spatial frequency of 1000 lines∕mm with (a) 70 μm, (b) 110 μm, and (c) 160 μm thick gratings recorded at A-1 mW∕cm2 , B-5 mW∕cm2 , and C-10 mW∕cm2 .

factors will be facilitated by higher intensity recordings. Thus, one could expect that the crosslinking will be much more efficient at higher recording intensities. Monomer polymerization, in contrast, is more efficient at lower intensities that facilitate the formation of longer polymer chains. The picture described here is a significantly simplified model of what happens in reality, since the two processes take place simultaneously and chains are crosslinked as they grow. Nevertheless, one could make an attempt to separate the contributions of these two processes to photopolymer shrinkage. It is also possible that in real time we can observe simultaneous shrinkage due to polymerization and swelling due to diffusion of monomers either from the back side of the thick photopolymer layer or from areas outside the recorded grating. If the effect of diffusion is observable in the shrinkage dynamics, one would expect swelling of the layer; thus, the amplitude of one of the two exponents would be negative. It is possible that shrinkage dynamics will be also influenced by the diffusion of the monomer molecules from dark to bright fringe areas. Such diffusion would contribute to a stronger holographic structure and thus could influence the ability of the layer to shrink. On the basis that there is more than one process that is expected to contribute to shrinkage dynamics, we departed from attempts to use a single exponential fit and tried a double exponential asymptotic function of the form

y  a − b  exp−t∕τ1  − c  exp−t∕τ2 

(5)

to fit the curve of shrinkage versus time. The fitting parameters are the final value of shrinkage (a), the amplitudes of the two exponential components in the fitting function (b and c), and the time constants (τ1 and τ2 ). The information about amplitudes is important because it indicates which of the two processes contributes more to the final shrinkage and how their contributions are influenced by the recording intensity and the thickness of the layer. The results of the fitting procedure are presented in Table 1. It can be seen from the results in Table 1 that for all three thicknesses at low recording intensities, the double exponential fit converged to a single exponential fit. That is why the symbol NA (not applicable) was used in the first column of Table 1. Thus, at this recording intensity, it was not possible to distinguish between the contributions of crosslinking and monomer polymerization to the shrinkage of the layers. The amplitudes of the two terms of the exponential fitting function had positive values for all recording conditions. This excludes the possibility that any of the two processes contributing to the shrinkage dynamics was the result of diffusion of monomers from either the unpolymerized area surrounding the grating or from the back side of the thicker photopolymer layers. These results are further analyzed in Section 5. 10 December 2013 / Vol. 52, No. 35 / APPLIED OPTICS

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Table 1.

Thickness (μm) 70

110

160

B.

2

Data from the Fitting of Relative Shrinkage versus Exposure Time

Intensity (mW∕cm )

Relative Shrinkage (%)

Amplitude b

τ1 (s)

Amplitude c

τ2 (s)

1 5 10 1 5 10 1 5 10

3.5  0.16 4.3  0.51 30 3.3  0.03 3.3  0.05 2.8  0.096 3.4  0.59 3.5  0.09 2.83  0.05

NA 0.86  0.17 1.34 NA 0.86  0.08 1.28  0.25 NA 0.48  0.0017 0.96  0.15

NA 4.17  0.13 9.09  0 NA 9.6  0.014 3.02  0.15 NA 7.4  0.07 4.78  0.075

3.09  0.15 3.4  0.28 1.21 3.4  0.025 2.44  0.05 1.83  0.15 3.53  0.046 3.06  0.1 2.28  0.2

58  0.0002 47.6  0.007 30  0 62.5  0.0004 71.4  0.001 34.4  0.006 71  0 62.5  0.0017 29.4  0.004

Influence of the Thickness of Layers on Shrinkage

Figure 5 shows the shrinkage versus exposure time for a recording intensity of 1 mW∕cm2 for three different layer thicknesses: 70, 110, and 160 μm. From Fig. 5, we can see that the rate of shrinkage with exposure decreased with increasing exposure. From Fig. 5(a), one can see that the absolute shrinkage was higher in case of thick layers and lower in case of thin layers, whereas the relative shrinkage was higher for thin layers as shown in Fig. 5(b). Table 1 shows the data from the fitted curve of relative shrinkage versus exposure time for the three different thicknesses and intensities that were displayed in Fig. 4. From the data, we can see that in all three sets of layers of different thickness, lower shrinkage occurred at the higher intensity of recording. 5. Discussion

The study of the effect of recording intensity on shrinkage revealed that lower shrinkage was observed at a higher intensity of recording. We can correlate the increased shrinkage at lower intensities of exposure, as was explained previously [19], with the fact that at a lower illumination intensity, the rate at which free radicals are generated is lower and thus the volume concentration of free radicals is lower. This leads to a lower rate of termination and the polymer chains have longer time to grow. The ultimate result is the creation of longer polymer chains

that are comprised of larger numbers of monomer molecules. One could expect that the morphology of long polymer chains is different than the morphology of short polymer chains. If long polymer chains are more entangled, the polymerized material is likely to be denser and to exhibit greater shrinkage. It has been previously demonstrated [30] that the shrinkage of photopolymer layers can be decreased by decreasing the length of the created polymer chains. We can explain the shrinkage in layers of different thicknesses, which were recorded with the same intensity and exposure time, by assuming that shrinkage is proportional to the amount of material that has been polymerized. From Fig. 5(a), we can see that the absolute shrinkage increased with layer thickness, whereas the percent shrinkage was greater for thinner layers, as shown in Fig. 5(b). It was clearly seen from Fig. 5(a) that while the absolute shrinkage in the thin layers reached saturation, the thick layers were still shrinking. It is possible that when saturation of shrinkage is achieved in the thick layers, the same relative shrinkage will be reached for all thicknesses. In analyzing the dynamics of the shrinkage, we observed that at a low intensity of recording, a single exponential function provided a sufficiently good fit for the data. In contrast, a two exponential function was required for the higher intensities (5 and 10 mW∕cm2 ). This implies that two processes are occurring on different timescales that lead to shrinkage

Fig. 5. (a) Absolute shrinkage and (b) relative shrinkage with respect to exposure times for a recording intensity of 1 mW∕cm2 and a spatial frequency of 1000 lines/mm at A-70 μm, B-110 μm, and C-160 μm. 8524

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Fig. 6. Relative shrinkage versus exposure time for a recording intensity of 4 mW∕cm2 using a single or a double beam in a (a) 90 μm and (b) 180 μm thick layer.

of the layer. The first is characterized by a time constant of a few seconds, while the second is characterized by a time constant in the order of tens of seconds. The process characterized by the shorter time constant is most probably also taking place during recording with a low intensity of 1 mW∕cm2, but the difference between the two processes was not evident. The process characterized by the longer time constant can be associated with the rate of polymerization. Both processes are intensity dependent. As one can see from Table 1, the time constants for the two processes become shorter with the increasing intensity of the recording, and thus, with increasing polymerization and crosslinking rates. The trend of a shorter time constant with increasing intensity was observed in layers of all three thicknesses. By comparing the amplitudes of the two exponential components in Table 1, one can see that the relative contribution of the faster process to the overall shrinkage was significantly and consistently smaller than that of the slower process. In order to reveal the physical origin of the first process characterized by the shorter time constant and its influence on shrinkage, photopolymer layers with 90 and 180 μm thicknesses were polymerized using two different exposure regimes. In the first experiment, a single beam of intensity 4 mW∕cm2 was used to polymerize the green-light sensitive photopolymer layer uniformly. In the second experiment, a holographic grating with a spatial frequency of 1000 lines/mm was recorded using two interfering beams with a combined beam intensity of 4 mW∕cm2. The results from the two experiments are compared in Fig. 6. These two experiments were carried out in order to determine if the diffusion of monomer Table 2.

Polymerization Single beam Double beam

molecules from dark to bright fringes could be responsible for the fast exponential component in the shrinkage dynamics. If this was the case, one should observe a difference between the single and double beam exposures, since in the first case no such diffusion is expected. As seen in Fig. 6 and the fitting results presented in Table 2, even during the case of bulk polymerization using a single beam exposure, the process characterized by the shorter time constant was evident. This is an indication that the lateral diffusion from dark to bright fringes is not responsible for the short time constant process. We also observed that illumination with a single instead of double beam leads to significant increases of the rate of shrinkage in the 90 μm layers. The difference in the effect of the two regimes of illumination was less pronounced in the 180 μm layer. We observed faster and increased shrinkage in the case of single beam polymerization. This can be related to the fact that more monomer molecules will be converted to polymer in the case of single beam illumination, whereas in the case of double beam recordings, some of the monomers in the dark fringe regions will remain unpolymerized. The diffusion of monomer molecules during the double beam exposure will lead to mass transport into the shrinking regions, and thus, will counteract the dimensional change in these regions. As in the case of the double beam exposure, in the single beam exposure the relative contribution of the faster process to the overall shrinkage was smaller than the contribution of the slower process. Since two processes were observed in both regimes of illumination, it was concluded that the faster process was also related to polymerization. In the photopolymer system, two

Data from the Curve Fitting, Fig. 6

Thickness (μm)

Relative Shrinkage (%)

Amplitude b

τ1 (s)

Amplitude c

τ2 (s)

90 180 90 180

4.5  0.08 3.48  0.04 3.97  0.08 3.24  0.04

0.76  0.021 0.6  0.14 0.75  0.2 0.6  0.03

10  0.13 11.2  0.093 11.1  0.03 8.3  0.014

3.89  0.17 2.82  0.08 3.01  0.15 2.7  0.02

50  0.007 77  0.003 62.5  0.002 91  0.005

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monomer molecules were used: acrylamide and N,Nmethylene bisacrylamide. The second chemical plays the role of a crosslinker. It is possible that the crosslinking is the process that is characterized by the shorter time constant in the fit. At a low intensity of recording, both monomer polymerization and crosslinking occurred on the same timescale and the two processes were indistinguishable. When the intensity was increased, the free radical concentration was much higher, which facilitates crosslinking on a shorter timescale. This was observed as a separate process in the fit. Both processes occurred faster when the intensity was further increased, as one can see in Tables 1 and 2. It is worth noting that the crosslinking makes significantly smaller contributions than the polymerization of the monomer molecules. This is in agreement with the fact that the concentration of the acrylamide monomer was three times higher than the concentration of the crosslinker. 6. Conclusion

The effect of recording intensities and layer thicknesses on shrinkage was investigated by holographic interferometry. It was observed that the shrinkage was greater for gratings recorded with lower intensities of recording. This was ascribed to the fact that at a low intensity of recording, the termination rate was slower, more monomer molecules were polymerized, and mostly longer polymer chains were created. By ruling out the influence of lateral diffusion of monomer molecules on shrinkage, we can assume that both processes influencing the shrinkage were related to polymerization. We can ascribe the two time constants associated with shrinkage to (1) the rate of polymerization of monomer molecules (the process characterized by the longer time constant) and (2) the rate of crosslinking of polymer chains (the process characterized by the shorter time constant). In thick layers, the polymerization process, and hence the shrinkage, was not completed on the assumption that the shrinkage that occurred was proportional to the extent of polymerization. In thin layers, most of the monomer molecules will be converted to polymer, which results in increased relative, but not absolute, shrinkage. Faster and increased shrinkage in the case of single beam polymerization was observed. The increased shrinkage in the case of single beam illumination can be related to the fact that the amount of monomer molecules converting to polymer will be greater and more homogeneous across the illuminated area, which results in uniform polymerization. MM acknowledges support from the DIT Fiosraigh Scholarship Programme. The authors would like to acknowledge the School of Physics and FOCAS, DIT for technical support. References 1. J. Biles, “Holographic color filters for LCDs,” Society of Information Display 94 Digest, 403–406 (1994). 8526

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Shrinkage during holographic recording in photopolymer films determined by holographic interferometry.

Shrinkage of photopolymer materials is an important factor for their use in holographic data storage and for fabrication of holographic optical elemen...
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