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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 11, Iss. 2 — Jan. 27, 2003
  • pp: 181–190
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Temporal evolution of the angular response of a holographic diffraction grating in PVA/acrylamide photopolymer

S. Gallego, M. Ortuño, C. Neipp, C. García, A. Beléndez, and I. Pascual  »View Author Affiliations


Optics Express, Vol. 11, Issue 2, pp. 181-190 (2003)
http://dx.doi.org/10.1364/OE.11.000181


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Abstract

In this paper we evaluate the temporal evolution, after exposure, of a diffraction grating stored in a PVA/acrylamide photopolymer. We also study the overmodulation of the refractive index inside the hologram, which gives rise to a particular behaviour of the angular response of diffraction efficiency. This evolution takes place in our photopolymer due to the incorporation of dimethylacrylamide (DMAA), which is a liquid at room temperature and so favours diffusion of the species in solution from the zones of greater concentration to those of lower concentration.

© 2002 Optical Society of America

1. Introduction

Photopolymers are systems of organic molecules 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 materials for write-once, read-many (WORM) holographic data storage applications [1

1. R. A. Lessard and G. Manivannan, eds., Selected Papers on Photopolymers, MS 114, (SPIE Optical Engineering Press, Belligham1996).

, 2

2. D. J. Lougnot, “Self-processing photopolymer materials for holographic recording,” in Polymers in Optics: Physics, Chemistry, and Applications, R. A. Lessard and W. F. Frank, eds., Crit. Rev. Opt. Sci. Technol., Proc. SPIECR63, 190–213 (1996).

].

Photopolymer systems can spontaneously develop their holographic image during recording without requiring post-exposure processing steps. This real-time recording characteristic elimates the need for complicated development procedures, and is particularly useful for applications such as holographic memories. However, this characteristic prevents us from measuring the angular response of a hologram stored in a photopolymer at different points on the same diffraction efficiency curve. In order to determine the angular response at different points of the same diffraction efficiency curve, it is necessary to obtain various holograms with diffraction efficiencies corresponding to different points on the same graph and determine the angular response of each of these holograms.

Photopolymer systems for recording holograms typically comprise one or more monomers, a photoinitiation system and an inactive component often referred to as a binder. Other components are sometimes added to control a variety of properties such as sensibility and viscosity of the recording medium [3

3. H. J. Coufal, D. Psaltis, and G. T. Sincerbox, eds., Holographic data storage (Springer-Verlag, Berlin2000), p 171.

]. In this paper we work with PVA/acrylamide photopolymer. The behaviour of this photopolymer is well know [4

4. S. Martin, P. E. Leclere, Y. L. Renotte, V. Toal, and Y. F. Lion, “Characterization of an acrylamide-based dry photopolymer holographic recording material,” Opt. Eng. 33, 3942–3946 (1994). [CrossRef]

8

8. C. García, A. Fimia, and I. Pascual, “Holographic behavior of a photopolymer at high thicknesses and high monomer concentrations: Mechanism of polymerization,” Appl. Phys. B 72, 311–316 (2001). [CrossRef]

]. Now we evaluate the temporal evolution in darkness, after exposure, of an overmodulation of refractive index and the resulting angular response of diffraction efficiency, obtained using Kogelnik’s theory for the volume phase transmission holograms recorded. This temporal evolution (reconstructed in the opposite sense to that which takes place during exposure) is possible due to the incorporation of dimethylacrylamide (DMAA), which is a liquid at room temperature and so favours diffusion of the species in solution from the zones of greater concentration to those of lower concentration. This enables the evolution of the hologram at different points on the diffraction efficiency curve to be determined. By mean of the temporal evolution considered, the values of the refractive index modulation and the angular response at severl points could be obtained. The angular response of the same grating in the recorded direction is not possible due to the behavior in real time exhibited by photopolymerizable materials based on PVA/acrylamide. In such materials when exposure is discontinued in order to measure the angular response and the material is then exposed again to the laser, it does not react as it did before [9

9. C. García, I. Pascual, A. Costela, I. García-Moreno, C. Gómez, A. Fimia, and R. Sastre, “Hologram recording in polyvinyl alcohol/acrylamide photopolymers by means of pulsed laser exposure,” Appl. Opt. 41, 2613–2620 (2002). [CrossRef] [PubMed]

]. In other words, the behaviour of the photopolymer in the case of two non-consecutive exposures is different to its behaviour in the case of one continuous exposure which is the sum of the former two. In consequence, we would like to point out that the presence of DMAA also enables us to study the diffusion mechanisms within our photopolymer that allows us to observe phenomena like the “temporal evolution” that we have studied in this paper.

Volume phase holograms [10

10. L. Solymar and D. J. Cooke, Volume Holography and Volume Gratings (Academic, London1981), p. 79.

] are under intensive study as possible information storage media due to their potential for achieving high storage densities. From the physical point of view, the mathematical content of Kogelnik’s theory [11

11. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Sys. Tech. J. 48, 2909–2947 (1969).

] is simpler than that of other theories, and it also gives analytical solutions for diffraction efficiency properties. Therefore, for volume phase unslanted holograms in which a sinusoidal diffraction grating has been recorded, the transmitted wave is given by the following equation:

R(d)=exp(jξαd2cosθ)[cosϕ+j(ξϕ)sinϕ]
(1)

and the diffracted wave by:

S(d)=jexp(jξαd2cosθ)sinϕϕν
(2)

ϕ=ν2+ξ2
(3)

where ν and ξ are given by the equations:

ν=πΔndλcosθ
(4)
ξ=dϑ2cosθ
(5)

and

ϑ=β2σ22β
(6)

Δn is the refractive index modulation and λ is the wavelength of reconstruction in air, whereas β and σ are the propagation constants of the transmitted and diffracted waves, respectively [10

10. L. Solymar and D. J. Cooke, Volume Holography and Volume Gratings (Academic, London1981), p. 79.

, 11

11. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Sys. Tech. J. 48, 2909–2947 (1969).

].

The diffraction efficiency, η, can be expressed as:

η=exp(αdcosθ')sin2(ν2+ξ2)121+(ξ2ν2)
(7)

Parameter ν, given by Eq. (4), controls the diffraction efficiency when the incident wave impinges on the plate at the Bragg condition (ξ = 0).

Therefore, for volume phase holograms in which a sinusoidal and unslanted diffraction grating has been recorded, the diffraction efficiency at Bragg’s angle is given by the following equation:

η=exp(αdcosθ')sin2ν
(8)

This present study is centred on an analysis of the temporal evolution, following exposure, of overmodulation in PVA/acrylamide photopolymers. Of many factors involved in the refractive index modulation, the polymer formation is the most important, thereby the refractive index modulation is a result of the differences between the exposed and non-exposed zones. In the first, there is polymer, formed by radical polymerization of the monomer, and in the second only the monomer. The recording material used is composed of a matrix of polyvinyl alcohol (PVA) as binder, acrylamide (AA) as monomer, triethanolamine (TEA) as radical generator, yellowish eosine (YE), as sensitizer and dimethylacrylamide (DMAA) to favour diffusion of the species dissolved in the dry film obtained.

Incorporation of DMAA makes it possible to use high concentrations of AA with less risk of crystallization. Furthermore, it facilitates homogenization of the chemical species present in the film of recording material by favoring their diffusion. Diffusion of polymer from the exposed zones (higher concentration) to the non-exposed zones (where no polymer is present initially) makes the index modulation decrease over time [4

4. S. Martin, P. E. Leclere, Y. L. Renotte, V. Toal, and Y. F. Lion, “Characterization of an acrylamide-based dry photopolymer holographic recording material,” Opt. Eng. 33, 3942–3946 (1994). [CrossRef]

] (this phenomenon is not usually seen in a conventional photopolymer, whose composition is not designed to achieve such an effect). We can therefore study how, in a diffraction grating that initially exhibits clear signs of overmodulation, the index modulation decreases until such signs disappear. Since DMAA is volatile, for the index modulation to decrease until it reaches values close to zero, there must be sufficient residual concentration of DMAA in the dry film to favor the complete, rapid diffusion of the dissolved species. It is also possible to stop the decrease in index modulation at any time by partially evaporating the DMAA by heating the plate in darkness (80°C for 30 minutes).

2. Experimental set-up

The photopolymerizable solution was prepared, under red light, by adding 1.3 ml of 8g/l yellowish eosin together with 16 ml of acrylamide and triethanolamine solution to 41.2 ml of PVA solution and 2 ml of DMAA. The concentration of each of the components with water as solvent can be seen in Table 1. The resulting solution was deposited on a 20 × 40 cm2 glass plate using an automatic depositor and adjusting the thickness of the film throw out the leftover solution. The plate was dried for a period of 72 hours in the dark and under normal laboratory conditions (T = 21–23°C, RH = 40–60%). Once dried it was cut into plates measuring 6.5 × 6.5 cm2 to be used in our experimental setup and the thickness was measured using Kogelnik’s equations [11

11. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Sys. Tech. J. 48, 2909–2947 (1969).

].

Table 1. Components of the photopolymerizable solution.

table-icon
View This Table

To study the behavior of the photopolymer as a holographic recording material, we obtained diffraction gratings using a holographic setup. The experimental device is shown in Fig. 1.

Fig. 1. Experimental set-up.

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 beams with an intensity ratio of 1:1. The diameter of these beams was increased to 1 cm with an expander, while spatial filtering was ensured. 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 working intensity at 514 nm was 5 mW/cm2. The diffracted and transmitted intensity were monitored in real time with a He-Ne laser positioned at Bragg’s angle (20.8°) tuned to 633 nm, where the material does not polymerize. In order to obtain the transmittance and diffraction efficiency as a function of the angle at reconstruction we placed the plates on a rotating stage. Transmittance and diffraction were calculated as the ratio of the transmitted and diffracted beam respectively to the incident power, and in order to take into account Fresnel losses the expression was multiplied by an appropriate factor.

3. Results and discussion

In order to analyze the behaviour of the photopolymer as a holographic recording material, we represented the diffraction efficiency at the Bragg angle as a function of exposure, as shown in Fig. 2, which corresponds to the 75 ± 2 µm plate used in this experiment. It can be seen that the diffraction efficiency increases at low exposures and reaches a maximum at an exposure of 75 mJ/cm2, when 98% of the light is diffracted. At this point, overmodulation of the index occurs and this can be explained mainly by polymerization of the monomer in the bright zones. In other words, the refractive index modulation is so great that ν takes on a value greater than π/2. This means that the diffraction efficiency at the Bragg condition begins to decrease (since the diffraction efficiency at the Bragg angle is governed by the function sin2ν [12

12. C. Neipp, I. Pascual, and A. Beléndez, “Theoretical and experimental analysis of overmodulation effects in volume holograms recorded on BB-640 emulsions,” J. Opt. A 3, 504–5513 (2001). [CrossRef]

]), whereas it increases at the lateral lobes. In order to study better the evolution of overmodulation after the grating is recorded, we shall concentrate our analysis on the angular response curves obtained plotting diffraction efficiency and transmission efficiency, 3, 4, 5, 6, 7 and 8, against deviation from the Bragg angle. Fitting these data by means of Kogelnik’s coupled wave theory, we can obtain values of the refractive index modulation, Δn, together with those of the absorption coefficient, α, and thickness, d, at each instant. The index modulation was seen to vary after exposure until the residual DMAA evaporated completely. In the fitting the α coefficient takes on values of around 0.0010 ± 0.0002 µm-1. These values indicate that the fraction of light absorbed and scattered by the hologram is very small—less than 5% of the incident light. The thickness d obtained from the fitting is 75 ± 2 µm in all cases.

Figure 3 corresponds to the angular response obtained immediately after exposure (point 1 in Fig. 2). It can be seen that the index modulation is quite high. In the central lobe, which fulfils the Bragg condition, the diffraction efficiency reaches only 30%. Here also there is asymmetry in the angular response. This type of phenomenon has been widely studied in photographic emulsions [12

12. C. Neipp, I. Pascual, and A. Beléndez, “Theoretical and experimental analysis of overmodulation effects in volume holograms recorded on BB-640 emulsions,” J. Opt. A 3, 504–5513 (2001). [CrossRef]

] and is due to the fact that with high index modulations, not only is there a phase grating but also a small amplitude modulation (absorption coefficient modulation, α) [13

13. C. Neipp, C. Pascual, and A. Beléndez, “Mixed phase-amplitude holographic gratings recorden in bleached silver halide materials,” J. Phys. D 35, 957–67 (2002). [CrossRef]

, 14

14. C. Neipp, I. Pascual, and A. Beléndez, “Experimental evidence of mixed gratings with a phase difference between the phase and amplitude grating in volume holograms,” Opt. Express 10, 1374–1383 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-23-1374. [CrossRef] [PubMed]

]. Therefore, in order to carry out a more precise fitting, this should be done based on the mixed gratings theory. However, the amplitude modulation can not be very high because the experimental data are not very different from the fitting done for pure phase gratings.

In this moment, the tendency of polyacrylamide chains to achieve homogenisation and the ease with which they can do so in this modified material means that, in a short time, the stored grating leaves the zone of overmodulation (point 1) and progressively evolves (points 2–6) as the polyacrylamide chains diffuse from the zones of greater concentration to those of lower concentration. It is even possible to obtain the angular response at a maximum diffraction efficiency (point 3) which is even greater than that obtained at the moment recording of the grating is completed (point 1).

An hour and a half later, Fig. 4 is obtained where we can see that the modulation has decreased to 0.005 and the diffraction efficiency at the Bragg angle is 80% (point 2 in Fig. 2), but there is still overmodulation (the diffraction efficiency reaches 15% at the lateral lobes); whereas 3 hours later (Fig. 5) the index modulation is Δn = 0.0044 and diffraction efficiency at the Bragg angle is 90% (point 3 in Fig. 2).

Fig. 2. Diffraction efficiency (DE) as a function of exposure in the Bragg angle.
Fig. 3. Diffraction efficiency (DE) and transmission efficiency (TE) as a function of the angle at reconstruction at point 1 in Fig. 2, immediately after exposure (Δn = 0.00678).

In Fig. 6, obtained 24 hours after the laser exposure, it can be seen that the index modulation is much lower, as occurs in Fig. 7 obtained 48 hours after exposure, and in Fig. 8, 96 hours after exposure (points 4, 5 and 6 in Fig. 2, respectively). However, it should be pointed out that the changes in index modulation in these latter figures are very small bearing in mind the time elapsed between measurements. This is due to the fact that the gradient of polymer concentration is now small and the DMAA concentration decreases as it evaporates with the result that the time taken to diffuse is greater. Since the high rate of diffusion of polymer is due to the presence of DMAA, it has been shown that this rate is considerably reduced if the polymer film is heated after laser exposure.

Fig. 4. Diffraction efficiency (DE) and transmission efficiency (TE) as a function of the angle at reconstruction at point 2 in Fig. 2, 11/2 hours after the grating isrecorded (Δn = 0.00503).
Fig. 5. Diffraction efficiency (DE) and transmission efficiency (TE) as a function of the angle at reconstruction at point 3 in Fig. 2, 3 hours after the grating is recorded (Δn = 0.00442).
Fig. 6. Diffraction efficiency (DE) and transmission efficiency (TE) as a function of the angle at reconstruction at point 4 in Fig. 2, 24 hours after the grating is recorded (Δn = 0.00227).
Fig. 7. Diffraction efficiency (DE) and transmission efficiency (TE) as a function of the angle at reconstruction at point 5 in Fig. 2, 48 hours after the grating is recorded (Δn = 0.001763).

Therefore the theoretical fittings of the experimental data obtained from the various angular response curves of the different points support our observations. In other words, the effect achieved is similar to that of going backwards along the diffraction efficiency versus exposure curve (Fig. 2). When the grating is recorded (from left to right along the curve), the increase in the difference in refractive index is principally a result of radical polymerization, whereas during what we call the “temporal evolution” of this material (from right to left), we obtain a progressive decrease in the difference in refractive index due to a diffusion phenomenon of the polyacrylamide chains that it make to vanish the diffraction grating progressively.

Fig. 8. Diffraction efficiency (DE) and transmission efficiency (TE) as a function of the angle at reconstruction at point 6 in Fig. 2, 96 hours after the grating is recorded (Δn = 0.00118).

In Figs. 9 and 10 the fraction of refractive index modulation remained of the initial refractive index modulation as a function of time has been presented. These figures give us an idea of the preservation of two gratings with similar thickness, one with DMAA (Fig. 9) and the other without DMAA (Fig. 10) stored in our phopolymer. In Fig. 9 we can see that in 96 hours, gratings containing DMAA have lost the 85% of the initial refractive index modulation, whereas gratings stored with polymer without DMAA (Fig. 10) have only lost a 13% after the same 96 hours.

Fig. 9. Fraction of refractive index modulation remained as function of time after the hologram was recorded. For films with DMAA.
Fig. 10. Fraction of refractive index modulation remained as function of time after the hologram was recorded. For films without DMAA.

After 1100 hours, plates with DMAA doesn’t present a grating stored, but plates without DMAA have only lost a 17% of the initial refractive index modulation. As a consequence, it can be said that if DMAA is not used it is possible to preserve the stored gratings, but this is not the case if DMAA is used. Nonetheless, it is precisely this lack of preservation of the grating what allows us to analyze the temporal evolution presented in this work.

4. Conclusions

Transmission diffractive gratings of 1125 lines/mm have been stored in PVA/acrylamide photopolymer. Kogelnik’s coupled wave theory has been used to fit the angular response of transmission and diffraction efficiencies measured for the gratings studies. And we have obtained information, from eEq. (8), about the refractive index modulation (Δn), thickness (d) and absorption constant (α). In this manner we have determined the temporal evolution of diffraction efficiency of a hologram stored in a PVA/acrylamide photopolymer by measuring the angular response of the hologram immediately after exposure and in subsequent hours. By adding DMAA to the composition of the photopolymer used, it is possible to control certain properties of the polymer film, once it is dry. For example, crystallization, with high AA concentrations, may be prevented and thicker layers obtained. Moreover, fast temporal evolution of the diffraction grating stored takes place due to residual DMAA. This enables us to reconstruct the diffraction efficiency curve and the angular response at different points on this curve in the opposite direction, with good results fitting these data by means of Kogelnik’s theory. Finally, we can say the method described in this paper can be used to distinguish an overmodulation from a sinusoidal shape deviation.

Acknowledgments

This work was supported by the “Ministerio de Ciencia y Tecnología” (CICYT, Spain) under project MAT2000-1361-C04-04 and by the “Oficina de Ciencia y Tecnología” (Generalitat Valenciana, Spain) under project GV01-130.

References and links

1.

R. A. Lessard and G. Manivannan, eds., Selected Papers on Photopolymers, MS 114, (SPIE Optical Engineering Press, Belligham1996).

2.

D. J. Lougnot, “Self-processing photopolymer materials for holographic recording,” in Polymers in Optics: Physics, Chemistry, and Applications, R. A. Lessard and W. F. Frank, eds., Crit. Rev. Opt. Sci. Technol., Proc. SPIECR63, 190–213 (1996).

3.

H. J. Coufal, D. Psaltis, and G. T. Sincerbox, eds., Holographic data storage (Springer-Verlag, Berlin2000), p 171.

4.

S. Martin, P. E. Leclere, Y. L. Renotte, V. Toal, and Y. F. Lion, “Characterization of an acrylamide-based dry photopolymer holographic recording material,” Opt. Eng. 33, 3942–3946 (1994). [CrossRef]

5.

V. Weiss, E. Millul, and A. A. Friesem, “Photopolymeric holographic recording media: in-situ and real-time characterization,” in Holographic Materials II, T. H. Trout, ed., Proc. SPIE2688, 11–21 (1996). [CrossRef]

6.

S. Blaya, L. Carretero, R. Mallavia, A. Fimia, M. Ulibarrena, and D. Levy, “Optimization of an acrylamide-based dry film used for holographic recording,” Appl. Opt. 37, 7604–7610 (1998). [CrossRef]

7.

C. García, A. Fimia, and I. Pascual, “Diffraction efficiency and signal-to-noise ratio of diffuse-object holograms in real time in polyvinyl alcohol photopolymers,” Appl. Opt. 38, 5548–5551 (1999). [CrossRef]

8.

C. García, A. Fimia, and I. Pascual, “Holographic behavior of a photopolymer at high thicknesses and high monomer concentrations: Mechanism of polymerization,” Appl. Phys. B 72, 311–316 (2001). [CrossRef]

9.

C. García, I. Pascual, A. Costela, I. García-Moreno, C. Gómez, A. Fimia, and R. Sastre, “Hologram recording in polyvinyl alcohol/acrylamide photopolymers by means of pulsed laser exposure,” Appl. Opt. 41, 2613–2620 (2002). [CrossRef] [PubMed]

10.

L. Solymar and D. J. Cooke, Volume Holography and Volume Gratings (Academic, London1981), p. 79.

11.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Sys. Tech. J. 48, 2909–2947 (1969).

12.

C. Neipp, I. Pascual, and A. Beléndez, “Theoretical and experimental analysis of overmodulation effects in volume holograms recorded on BB-640 emulsions,” J. Opt. A 3, 504–5513 (2001). [CrossRef]

13.

C. Neipp, C. Pascual, and A. Beléndez, “Mixed phase-amplitude holographic gratings recorden in bleached silver halide materials,” J. Phys. D 35, 957–67 (2002). [CrossRef]

14.

C. Neipp, I. Pascual, and A. Beléndez, “Experimental evidence of mixed gratings with a phase difference between the phase and amplitude grating in volume holograms,” Opt. Express 10, 1374–1383 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-23-1374. [CrossRef] [PubMed]

OCIS Codes
(090.0090) Holography : Holography
(090.2900) Holography : Optical storage materials
(090.7330) Holography : Volume gratings

ToC Category:
Research Papers

History
Original Manuscript: December 10, 2002
Revised Manuscript: January 19, 2003
Published: January 27, 2003

Citation
S. Gallego, M. Ortuno, C. Neipp, C. Garcia, A. Belendez, and Inmaculada Pascual, "Temporal evolution of the angular response of a holographic diffraction grating in PVA/acrylamide photopolymer," Opt. Express 11, 181-190 (2003)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-2-181


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References

  1. R. A. Lessard and G. Manivannan, eds., Selected Papers on Photopolymers, MS 114, (SPIE Optical Engineering Press, Belligham 1996).
  2. D. J. Lougnot, �??Self-processing photopolymer materials for holographic recording,�?? in Polymers in Optics: Physics, Chemistry, and Applications, R. A. Lessard and W. F. Frank, eds., Crit. Rev. Opt. Sci. Technol., Proc. SPIE CR63, 190-213 (1996).
  3. H. J. Coufal, D. Psaltis and G. T. Sincerbox, eds., Holographic data storage (Springer-Verlag, Berlin 2000), p 171.
  4. S. Martin, P. E. Leclere, Y. L. Renotte, V. Toal and Y. F. Lion, �??Characterization of an acrylamide-based dry photopolymer holographic recording material,�?? Opt. Eng. 33, 3942-3946 (1994). [CrossRef]
  5. V. Weiss, E. Millul and A. A. Friesem, �??Photopolymeric holographic recording media: in-situ and real-time characterization,�?? in Holographic Materials II, T. H. Trout, ed., Proc. SPIE 2688, 11-21 (1996). [CrossRef]
  6. S. Blaya, L. Carretero, R. Mallavia, A. Fimia, M. Ulibarrena and D. Levy, �??Optimization of an acrylamidebased dry film used for holographic recording,�?? Appl. Opt. 37, 7604-7610 (1998). [CrossRef]
  7. C. García, A. Fimia and I. Pascual, �??Diffraction efficiency and signal-to-noise ratio of diffuse-object holograms in real time in polyvinyl alcohol photopolymers,�?? Appl. Opt. 38, 5548-5551 (1999). [CrossRef]
  8. C. García, A. Fimia and I. Pascual, �??Holographic behavior of a photopolymer at high thicknesses and high monomer concentrations: Mechanism of polymerization,�?? Appl. Phys. B 72, 311-316 (2001). [CrossRef]
  9. C. García, I. Pascual, A. Costela, I. García-Moreno, C. Gómez, A. Fimia and R. Sastre, �??Hologram recording in polyvinyl alcohol/acrylamide photopolymers by means of pulsed laser exposure,�?? Appl. Opt. 41, 2613-2620, (2002). [CrossRef] [PubMed]
  10. L. Solymar and D. J. Cooke, Volume Holography and Volume Gratings (Academic, London 1981), p. 79.
  11. H. Kogelnik, �??Coupled wave theory for thick hologram gratings,�?? Bell Sys. Tech. J. 48, 2909-2947 (1969).
  12. C. Neipp, I. Pascual and A. Beléndez, �??Theoretical and experimental analysis of overmodulation effects in volume holograms recorded on BB-640 emulsions,�?? J. Opt. A 3, 504-5513 (2001). [CrossRef]
  13. C. Neipp, C. Pascual and A. Beléndez, �??Mixed phase-amplitude holographic gratings recorden in bleached silver halide materials,�?? J. Phys. D 35, 957-67 (2002). [CrossRef]
  14. C. Neipp, I. Pascual and A. Beléndez, �??Experimental evidence of mixed gratings with a phase difference between the phase and amplitude grating in volume holograms,�?? Opt. Express 10, 1374-1383 (2002), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-23-1374">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-23-1374</a>. [CrossRef] [PubMed]

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