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Optics Express

  • Editor: Michael Duncan
  • Vol. 12, Iss. 8 — Apr. 19, 2004
  • pp: 1780–1787
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Acrylamide-N,N’-methylenebisacrylamide silica glass holographic recording material

L. Carretero, A. Murciano, S. Blaya, M. Ulibarrena, and A. Fimia  »View Author Affiliations


Optics Express, Vol. 12, Issue 8, pp. 1780-1787 (2004)
http://dx.doi.org/10.1364/OPEX.12.001780


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Abstract

In this paper, we describe a photopolymerizable silica glass based on acrylamide (AA) and N,N’-methylenebisacrylamide (BMA) as monomers, triethanolamine (TEA) as coinitiator and yellowish eosin (YE) as photoinitiator. We studied different compositions, analyzing the diffraction efficiency, energetic exposure and effective thickness obtained in the holographic gratings. A diffraction efficiency of 60 % with an energetic exposure of 139 mJ/cm2 and an effective thickness of 1.1 mm were obtained. Also, by varying the photopolymerizable composition of the material diffraction efficiencies higher than 80 % can be reached with an energetic exposure of 10 mJ/cm2 and an effective thickness of 113 µm. These values are similar to those obtained in conventional photopolymer systems in polyvinylalcohol and better than the values reached in other sol-gel compositions. Also, 9 holograms were angular multiplexed with diffraction efficiencies between 6 and 12 % and total exposure time shorter than 150 ms, with a dynamic range M/#=2.4.

© 2004 Optical Society of America

1. Introduction

Photopolymerizable holographic materials have the great advantage of recording and reading holograms in real time. In addition, photopolymers present characteristics such as good light sensitivity, real-time image development, large dynamic range, good optical properties, format flexibility, good image stability and low cost [1

1. L. Dhar, K. R. Curtis, M. L. Schilling, M. Schnoes, M. Tackitt, S. Campbell, W. L. Wilson, and A. Hill, “Digital holographic data storage in photopolymer systems,” in Advanced optical memories and interfaces to computer storage, vol. 3468, pp. 40–42 (SPIE, San Diego, 1998).

, 2

2. H. J. Coufal and G. T. Sincerbox, Holographic data storage (Springer, Berlin, 2000). [CrossRef]

, 3

3. G. J. Steckman, V. Shelkovnikov, V. Berezhnaya, T. G. nd I. Solomatine, and D. Psaltis, “Holographic recording in a photopolymer by optically induced detachment of chromophores,” Opt. Lett. 25, 607–609 (2000). [CrossRef]

]. Recently, due to these good properties, Aprilis HMD photopolymerizable holographic recording material has been optimized for holographic digital data recording, enabling a storage density greater than 100 bits/µm 2 and a dynamic range of at least M/#=22 to be reached [4

4. D. A. Waldman, C. J. Butler, and D. H. Raguin, “CROP holographic storage media for optical data storage at greater than 100 bits/µm2,” in Organic Holographic Materials and Applications, vol. 5216 (SPIE, San Diego, 2003).

]. Of these photopolymerizable compositions, acrylamide derivative monomers have been widely used in polyvinylalcohol-based films, showing high energetic sensitivity and diffraction efficiency [5

5. S. Blaya, L. Carretero, R. F. Madrigal, and A. Fimia, “Study of the optimization of a photopolymerizable holographic recording material based on polyvinylalcohol using angular responses,” Opt. Mater. 23, 529–538 (2003). [CrossRef]

, 6

6. S. Blaya, L. Carretero, R. Madrigal, and A. Fimia, “Study of effect of bifunctional crosslinking agent in polyvinylalcohol-based photopolymerizable holographic recording material using angular responses,” Jpn. J. Appl. Phys. Part 1 - Regul. Pap. Short Notes Rev. Pap. 41, 3730–3736 (2002).

, 7

7. S. Blaya, R. Mallavia, L. Carretero, A. Fimia, and R. F. Madrigal, “Highly sensitive photopolymerizable dry film for use in real time holography,” Appl. Phys. Lett. 73, 1628–1630 (1998). [CrossRef]

]. The requirement to achieve high storage density is to use a thick recording medium (greater than a millimeter), resulting large values for the average diffraction efficiency per data page and narrowed Bragg selectivity, wheraas in PVA films the values obtained were around 100 µm or in some cases close to 200 µm [8

8. C. García, A. Fimia, and I. Pascual, “Holographic behavior of a photopolymer at high thicknesses and high monomer concentrations: mechanism of photopolymerization,” Appl. Phys. B 72, 311–316 (2000). [CrossRef]

, 9

9. S. Blaya, L. Carretero, R. F. Madrigal, M. Ulibarrena, and A. Fimia, “New photopolymerizable holographic recording material based on polyvinylalcohol and 2-hydroxiethylmethacrylate (HEMA),” Appl. Phys. B-Lasers Opt. 74, 603–605 (2002). [CrossRef]

]. In this sense, an important alternative to a polymeric binder is silica glass, which can be made into thick films or monoliths with the desired thickness and properties such as high optical quality, rigidity and environmental stability [10

10. P. Cheben, T. Belenguer, A. Nuńez, F. del Monte, and D. Levy, “Holographic diffraction gratings recording in organically modified silica gels,” Opt. Lett. 21, 1857–1859 (1996). [CrossRef] [PubMed]

, 11

11. P. Cheben and M. L. Calvo, “A photopolymerizable glass with diffraction efficiency near 100 % for holographic storage,” Appl. Phys. Lett. 78, 1490–1492 (2001). [CrossRef]

]. However, the energetic sensitivity of these materials is still far from the best photosensitivity shown by a photopolymer [12

12. G. Ramos, A. Álvarez-Herrero, T. Belenguer, D. Levy, and F. del Monte, “Photopolymerizable hybrid sol-gel material for holographic recording,” in Organic holographic materials and applications, vol. 5216, pp. 116–125, SPIE (SPIE, San Diego, 2003).

, 7

7. S. Blaya, R. Mallavia, L. Carretero, A. Fimia, and R. F. Madrigal, “Highly sensitive photopolymerizable dry film for use in real time holography,” Appl. Phys. Lett. 73, 1628–1630 (1998). [CrossRef]

]. Therefore, in this paper we study holographic gratings recorded in a silica glass material into which the photosensitive composition normally used in PVA films (acrylamide, N,N’-methylenebisacrylamide, triethanolamine and yellowish eosin) was introduced.

2. Experimental section

Table 1. Composition of the different silica glass photosensitive materials studied

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Holographic gratings were recorded in symmetric geometry using a Nd:YAG laser (Coherent Verdi V5) operating in the second harmonic at 532 nm with a spatial frequency of 1100 lines/mm and a beam ratio of 1:1. The diffracted beam intensity of a He-Ne laser (Uniphysics), working at the wavelength of 633 nm, where the material does not absorb, was monitored in real-time with a photodetector positioned at Bragg’s angle for this wavelength. Once the hologram was recorded, angular response measurements were made using a probe beam from the He-Ne laser. In order to do so, the sample was mounted on a monitorized rotation stage and the angle of the sample plane relative to Bragg’s angle was computer controlled via a DC motor control (OWIS), with an angular resolution of 0.01 degrees. It has been recorded more than 30 diffraction gratings with each composition and at each experimental condition (intensity and exposure time). Therefore, it will be shown the main results obtained in each case.

3. Results and discussion

Fig. 1. Experimental and theoretical angular selectivity curves of holographic gratings obtained in a silica glass photopolymerizable material at different energetic exposures (mJ/cm 2). Composition A and a total intensity of 1160 mW/cm 2 were used to record the hologram.

In order to characterize the performance of the material and to obtain quantitative information on the experimental curves shown in Fig. 1, we used a modified model of Uchida [19

19. N. Uchida, “Calculation of diffraction efficiency in hologram gratings attenuated along the direction perpendicular to the grating vector,” J. Opt. Soc. Am 63, 280–287 (1973). [CrossRef]

] introducing the possibility of bending of the fringe planes [18

18. T. Kubota, “The bending of interference fringes inside a hologram,” Optica Acta 26, 731–743 (1979). [CrossRef]

]. The model takes into account that the grating planes are perpendicular to the y plane (plane of incidence of the beam), with the grating vector K⃗ forming an angle ϕ with the z axis (propagation direction) (Fig. 2). It is assumed that the modulation of the grating exponentially decreases with the attenuation coefficient αg in the y plane parallel to the grating fringes and the fringes are bent. Using the treatment developed by Uchida in order to obtain the derived coupled-wave equations [19

19. N. Uchida, “Calculation of diffraction efficiency in hologram gratings attenuated along the direction perpendicular to the grating vector,” J. Opt. Soc. Am 63, 280–287 (1973). [CrossRef]

], two waves with the same polarization are inside the material (R[z] and S[z]), where θ is the angle of incidence measured inside the medium, θ 0 is the Bragg’s angle, λ is the wavelength, d is the thickness of the grating, k is 2π/λ and the spatial modulation of the refractive index (n) and absorption coefficient (α) are considered. With this model the coupled-wave equations are

given by:

c0dR[z]dz+αR[z]=jκ0eαgzsin(ϕ)ej(Δkzz+ξ)S[z]
(1)

and

c1dS[z]dz+αS[z]=jκ0eαgzsin(ϕ)ej(Δkzz+ξ)R[z]
(2)

where

c0=cos(θ)
c1=cos(2ϕ2θ0+θ)
Δk=K[cos(ϕθ0+θ)cos(ϕ)]
(3)

and

κ0=(kn1+jα1)2
(4)

Δkz is the z component of the wave-vector mismatch Δk⃗ given by:

k1=k0KΔk
(5)

where k0 and k1 are the wave vectors of the incident (R[z]) and first order diffracted waves (S[z]) in the medium, respectively. The constant κ 0 is the coupling constant, which represents the coupling of both waves which is a function of the spatial modulations of the refractive index and absorption coefficient n 1 and α 1, respectively. Finally, the term ξ is the phase term of the grating due to the bending and we assumed that it is represented by a polynomial of up to the third order of l (l=z/d) [18

18. T. Kubota, “The bending of interference fringes inside a hologram,” Optica Acta 26, 731–743 (1979). [CrossRef]

]:

ξ=2πn(a0+a1l+a2l(2l)+a3l(33l+l2))
(6)
Fig. 2. Scheme of the grating used for the analysis.
Fig. 3. Experimental and theoretical angular selectivity curves of holographic gratings obtained in a silica glass photopolymerizable material for the different compositions used. The energetic exposure is in mJ/cm 2 and the total intensity used to record the hologram is 1160 mW/cm 2.

The diffraction efficiency η is defined as c1c0S[z]S*[z] where S*[z] is the complex conjugate of the wave S[z]. By numerically solving the coupled differential equations 1 and 2, the angular selectivity curves shown in Fig. 1 can be fitted. To do so, the experimental conditions described above were taken into account, the refractive index of the silica glass (n=1.4) was used, and α=α 1=0 (due to the low absorption at the reconstruction wavelength (633 nm)). The free parameters used were a 0, a 1, a 2, a 3, αg, n 1 and d (thickness of the grating), and as can be seen in Fig. 1 good agreement between theory and experiment was obtained (with regression coefficients better than 0.99). However, in some cases larger deviations than the experimental error in the side lobes are observed, but the central lobe, uplift of the nulls, asymmetrical behavior and the angular deviations are well fitted in most of the cases. If the Kogelnik theory [21

21. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell. Sys. Tech. J. 48, 2909–2945 (1969).

] is used the central lobe and far edges can be fitted but the uplift of the nulls, asymmetrical response and the angular deviations can not be explained. In Table 2 the values of the parameters of interest are shown for different experimental conditions and compositions. As can be seen in Table 2, from the data obtained with composition A, in order to record the hologram in the whole thickness it is necessary to work with high intensities and diffraction efficiencies of 65 % are obtained. However, higher diffraction efficiencies at these conditions can not be reached due to the formation of noise gratings [20

20. L. Carretero, S. Blaya, R. Mallavia, R. F. Madrigal, and A. Fimia, “A theoretical model for noise gratings recorded in acrylamide photopolymer materials used in real-time holography,” J. Mod. Opt. 45, 2345–2354 (1998). [CrossRef]

]. Table 2 also shows the results obtained with compositions B and C, whose angular selectivity curves are represented in Fig. 3. In the case of composition B the highest diffraction efficiency was obtained, at both high and low intensity, and the best energetic sensitivity was 10 mJ/cm 2. This value is similar to that obtained in PVA compositions [17

17. S. Blaya, L. Carretero, A. Fimia, R. Mallavia, R. F. Madrigal, R. Sastre, and F. Amat-Guerri, “Optimal composition of an acrylamide and N,N’-methylenebisacrylamide holographic recording material,” J. Mod. Opt. 45, 2573–2584 (1998).

] and more than one order of magnitude less than that reported in other sol-gel derivative materials [12

12. G. Ramos, A. Álvarez-Herrero, T. Belenguer, D. Levy, and F. del Monte, “Photopolymerizable hybrid sol-gel material for holographic recording,” in Organic holographic materials and applications, vol. 5216, pp. 116–125, SPIE (SPIE, San Diego, 2003).

]. Also, as with the A composition, the influence of the exposure time is very important in this material. As the exposure time increases the effective thickness is higher, however lower values than in composition A are reached. Also, it is very important to point out that only a short exposure time is needed to form the holographic grating in all compositions; in the slowest case, at low intensity (20 mW/cm 2) the grating is formed in 500 ms. Finally, with composition C high diffraction efficiency and effective thickness with low energetic exposure are obtained. In this case, with 20 ms of exposure the grating is formed (23 mJ/cm 2 of energetic sensitivity), giving a diffraction efficiency of 68 % and an effective thickness of 350 µm. Also with 30 ms of exposure a thickness of 670 µm is recorded with a diffraction efficiency of 72 %. Due to the high thickness and energetic sensitivity obtained in these materials, we multiplexed several diffraction gratings at different angles as can be seen in Fig. 4. For these initial results, we used composition D multiplexed 9 holograms with diffraction efficiencies between 5 and 12 %, being the angular increment between exposures of 1°. We used high intensities, being the first exposure time 40 ms, 20 ms for the second and 10 ms for the rest. The behavior of this material when hologram multiplexing is realized is different than when an unique hologram is recorded, in fact it is observed in all the studied cases that the two initial holograms need more energetic exposure than the rest. At the same time, except the two initial holograms the others need lower exposure than if an unique hologram were recorded as it is deduced from the exposure times used. Therefore it is demonstrated the possibility to use this photopolymerizable silica glass for holographic data storage and the optimization of the composition and the procedure (energetic sensitivities) the performance will improved.

Table 2. Results of the fittings of the holographic gratings recorded at different experimental conditions

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Fig. 4. Experimental diffraction efficiency scan of the 9 angular multiplexed holograms recorded with composition D. The exposure times were 40 ms for the first grating, 20 ms for the second and 10 ms for the rest. The total intensity used to record the hologram was 1160 mW/cm 2. and θ is the angle of reconstruction where 0 refers to the used to record one hologram in the symmetrical setup.

4. Conclusions

Stable holographic gratings were recorded in photopolymeric silica glass materials containing acrylamide and N,N’-methylenebisacrylamide as monomers. Three different compositions were studied, and a diffraction efficiency of 83 % was reached with high energetic sensitivity (10 mJ/cm 2). Also, the response time is very short, 500 ms and 20 ms using an intensity of 20 mW/cm 2 and 1160 mW/cm 2 respectively. Finally, gratings of high effective thickness can be obtained with these compositions (1.1 mm), this fact implies that a high dynamic range could be recorded in these materials. Therefore, this material has interesting properties that suggest it may be suitable for use as a holographic storage medium once the optimal composition has been obtained as it was demonstrated in Fig. 4, where 9 holograms with an exposure time shorter than 150 ms and diffraction efficiencies between 6 and 12 % being multiplexed, obtaining a dynamic range of M/#=2.4.

Acknowledgments

This work was financially supported by the Comisión Interministerial de Ciencia y Tecnología (CICYT) of Spain (project MAT2002-01690).

References and links

1.

L. Dhar, K. R. Curtis, M. L. Schilling, M. Schnoes, M. Tackitt, S. Campbell, W. L. Wilson, and A. Hill, “Digital holographic data storage in photopolymer systems,” in Advanced optical memories and interfaces to computer storage, vol. 3468, pp. 40–42 (SPIE, San Diego, 1998).

2.

H. J. Coufal and G. T. Sincerbox, Holographic data storage (Springer, Berlin, 2000). [CrossRef]

3.

G. J. Steckman, V. Shelkovnikov, V. Berezhnaya, T. G. nd I. Solomatine, and D. Psaltis, “Holographic recording in a photopolymer by optically induced detachment of chromophores,” Opt. Lett. 25, 607–609 (2000). [CrossRef]

4.

D. A. Waldman, C. J. Butler, and D. H. Raguin, “CROP holographic storage media for optical data storage at greater than 100 bits/µm2,” in Organic Holographic Materials and Applications, vol. 5216 (SPIE, San Diego, 2003).

5.

S. Blaya, L. Carretero, R. F. Madrigal, and A. Fimia, “Study of the optimization of a photopolymerizable holographic recording material based on polyvinylalcohol using angular responses,” Opt. Mater. 23, 529–538 (2003). [CrossRef]

6.

S. Blaya, L. Carretero, R. Madrigal, and A. Fimia, “Study of effect of bifunctional crosslinking agent in polyvinylalcohol-based photopolymerizable holographic recording material using angular responses,” Jpn. J. Appl. Phys. Part 1 - Regul. Pap. Short Notes Rev. Pap. 41, 3730–3736 (2002).

7.

S. Blaya, R. Mallavia, L. Carretero, A. Fimia, and R. F. Madrigal, “Highly sensitive photopolymerizable dry film for use in real time holography,” Appl. Phys. Lett. 73, 1628–1630 (1998). [CrossRef]

8.

C. García, A. Fimia, and I. Pascual, “Holographic behavior of a photopolymer at high thicknesses and high monomer concentrations: mechanism of photopolymerization,” Appl. Phys. B 72, 311–316 (2000). [CrossRef]

9.

S. Blaya, L. Carretero, R. F. Madrigal, M. Ulibarrena, and A. Fimia, “New photopolymerizable holographic recording material based on polyvinylalcohol and 2-hydroxiethylmethacrylate (HEMA),” Appl. Phys. B-Lasers Opt. 74, 603–605 (2002). [CrossRef]

10.

P. Cheben, T. Belenguer, A. Nuńez, F. del Monte, and D. Levy, “Holographic diffraction gratings recording in organically modified silica gels,” Opt. Lett. 21, 1857–1859 (1996). [CrossRef] [PubMed]

11.

P. Cheben and M. L. Calvo, “A photopolymerizable glass with diffraction efficiency near 100 % for holographic storage,” Appl. Phys. Lett. 78, 1490–1492 (2001). [CrossRef]

12.

G. Ramos, A. Álvarez-Herrero, T. Belenguer, D. Levy, and F. del Monte, “Photopolymerizable hybrid sol-gel material for holographic recording,” in Organic holographic materials and applications, vol. 5216, pp. 116–125, SPIE (SPIE, San Diego, 2003).

13.

C. Wang, Y. Zhang, Y. Lu, and Y. Wei, “A novel bulk sol-gel process to prepare monolithic silica materials,” J. Mater. Res. 14, 4098–4102 (1999). [CrossRef]

14.

S. Blaya, P. Acebal, L. Carretero, and A. Fimia, “Pyrromethene-HEMA-based photopolymerizable holographic recording material,” Opt. Commun. 228, 55–61 (2003). [CrossRef]

15.

S. Blaya, L. Carretero, R. F. Madrigal, M. Ulibarrena, P. Acebal, and A. Fimia, “Photopolymerization model for holographic gratings formation in photopolymers,” Appl. Phys. B-Lasers Opt. 77, 639–662 (2003). [CrossRef]

16.

S. Blaya, A. Murciano, P. Acebal, L. Carretero, M. Ulibarrena, and A. Fimia, “Diffraction gratings and diffusion coefficient determination of acrylamide and polyacrylami de in sol-gel glass.” Appl. Phys. Lett. Submitted (2004). [CrossRef]

17.

S. Blaya, L. Carretero, A. Fimia, R. Mallavia, R. F. Madrigal, R. Sastre, and F. Amat-Guerri, “Optimal composition of an acrylamide and N,N’-methylenebisacrylamide holographic recording material,” J. Mod. Opt. 45, 2573–2584 (1998).

18.

T. Kubota, “The bending of interference fringes inside a hologram,” Optica Acta 26, 731–743 (1979). [CrossRef]

19.

N. Uchida, “Calculation of diffraction efficiency in hologram gratings attenuated along the direction perpendicular to the grating vector,” J. Opt. Soc. Am 63, 280–287 (1973). [CrossRef]

20.

L. Carretero, S. Blaya, R. Mallavia, R. F. Madrigal, and A. Fimia, “A theoretical model for noise gratings recorded in acrylamide photopolymer materials used in real-time holography,” J. Mod. Opt. 45, 2345–2354 (1998). [CrossRef]

21.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell. Sys. Tech. J. 48, 2909–2945 (1969).

OCIS Codes
(050.7330) Diffraction and gratings : Volume gratings
(090.0090) Holography : Holography
(090.2900) Holography : Optical storage materials

ToC Category:
Research Papers

History
Original Manuscript: March 22, 2004
Revised Manuscript: April 8, 2004
Published: April 19, 2004

Citation
L. Carretero, A. Murciano, S. Blaya, M. Ulibarrena, and A. Fimia, "Acrylamide-N,N'-methylenebisacrylamide silica glass holographic recording material," Opt. Express 12, 1780-1787 (2004)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-8-1780


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References

  1. L. Dhar, K. R. Curtis, M. L. Schilling, M. Schnoes, M. Tackitt, S. Campbell, W. L. Wilson, and A. Hill, �??Digital holographic data storage in photopolymer systems,�?? in Advanced optical memories and interfaces to computer storage, vol. 3468, pp. 40�??42 (SPIE, San Diego, 1998)
  2. H. J. Coufal and G. T. Sincerbox, Holographic data storage (Springer, Berlin, 2000) [CrossRef]
  3. G. J. Steckman, V. Shelkovnikov, V. Berezhnaya, T. G. nd I. Solomatine, and D. Psaltis, �??Holographic recording in a photopolymer by optically induced detachment of chromophores,�?? Opt. Lett. 25, 607�??609 (2000) [CrossRef]
  4. D. A. Waldman, C. J. Butler, and D. H. Raguin, �??CROP holographic storage media for optical data storage at greater than 100 bits/ µm2,�?? in Organic Holographic Materials and Applications, vol. 5216 (SPIE, San Diego, 2003)
  5. S. Blaya, L. Carretero, R. F. Madrigal, and A. Fimia, �??Study of the optimization of a photopolymerizable holographic recording material based on polyvinylalcohol using angular responses,�?? Opt. Mater. 23, 529�??538 (2003) [CrossRef]
  6. S. Blaya, L. Carretero, R. Madrigal, and A. Fimia, �??Study of effect of bifunctional crosslinking agent in polyvinylalcohol-based photopolymerizable holographic recording material using angular responses,�?? Jpn. J. Appl. Phys. Part 1 - Regul. Pap. Short Notes Rev. Pap. 41, 3730�??3736 (2002).
  7. S. Blaya, R. Mallavia, L. Carretero, A. Fimia, and R. F. Madrigal, �??Highly sensitive photopolymerizable dry film for use in real time holography,�?? Appl. Phys. Lett. 73, 1628�??1630 (1998) [CrossRef]
  8. C. Garcia, A. Fimia, and I. Pascual, �??Holographic behavior of a photopolymer at high thicknesses and high monomer concentrations: mechanism of photopolymerization,�?? Appl. Phys. B 72, 311�??316 (2000) [CrossRef]
  9. S. Blaya, L. Carretero, R. F. Madrigal, M. Ulibarrena, and A. Fimia, �??New photopolymerizable holographic recording material based on polyvinylalcohol and 2-hydroxiethylmethacrylate (HEMA),�?? Appl. Phys. B-Lasers Opt. 74, 603�??605 (2002) [CrossRef]
  10. P. Cheben, T. Belenguer, A. Nunez, F. del Monte, and D. Levy, �??Holographic diffraction gratings recording in organically modified silica gels,�?? Opt. Lett. 21, 1857�??1859 (1996) [CrossRef] [PubMed]
  11. P. Cheben and M. L. Calvo, �??A photopolymerizable glass with diffraction efficiency near 100 % for holographic storage,�?? Appl. Phys. Lett. 78, 1490�??1492 (2001) [CrossRef]
  12. G. Ramos, A. Alvarez-Herrero, T. Belenguer, D. Levy, and F. del Monte, �??Photopolymerizable hybrid sol-gel material for holographic recording,�?? in Organic holographic materials and applications, vol. 5216, pp. 116�??125, SPIE (SPIE, San Diego, 2003)
  13. C. Wang, Y. Zhang, Y. Lu, and Y. Wei, �??A novel bulk sol-gel process to prepare monolithic silica materials,�?? J. Mater. Res. 14, 4098�??4102 (1999) [CrossRef]
  14. S. Blaya, P. Acebal, L. Carretero, and A. Fimia, �??Pyrromethene-HEMA-based photopolymerizable holographic recording material,�?? Opt. Commun. 228, 55�??61 (2003) [CrossRef]
  15. S. Blaya, L. Carretero, R. F. Madrigal, M. Ulibarrena, P. Acebal, and A. Fimia, �??Photopolymerization model for holographic gratings formation in photopolymers,�?? Appl. Phys. B-Lasers Opt. 77, 639�??662 (2003) [CrossRef]
  16. S. Blaya, A. Murciano, P. Acebal, L. Carretero, M. Ulibarrena, and A. Fimia, �??Diffraction gratings and diffusion coefficient determination of acrylamide and polyacrylami de in sol-gel glass.�?? Appl. Phys. Lett. Submitted (2004) [CrossRef]
  17. S. Blaya, L. Carretero, A. Fimia, R. Mallavia, R. F. Madrigal, R. Sastre, and F. Amat-Guerri, �??Optimal composition of an acrylamide and N,N�??-methylenebisacrylamide holographic recording material,�?? J. Mod. Opt. 45, 2573�??2584 (1998)
  18. T. Kubota, �??The bending of interference fringes inside a hologram,�?? Optica Acta 26, 731�??743 (1979) [CrossRef]
  19. N. Uchida, �??Calculation of diffraction efficiency in hologram gratings attenuated along the direction perpendicular to the grating vector,�?? J. Opt. Soc. Am 63, 280�??287 (1973) [CrossRef]
  20. L. Carretero, S. Blaya, R. Mallavia, R. F. Madrigal, and A. Fimia, �??A theoretical model for noise gratings recorded in acrylamide photopolymer materials used in real-time holography,�?? J. Mod. Opt. 45, 2345�??2354 (1998) [CrossRef]
  21. H. Kogelnik, �??Coupled wave theory for thick hologram gratings,�?? Bell. Sys. Tech. J. 48, 2909�??2945 (1969)

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