Abstract

The recent results reported in reference [1] have produced an increased interest in explaining deviations from the ideal behavior of the energetic variation of the diffraction efficiency of holographic gratings. This ideal behavior occurs when uniform gratings are recorded, and the index modulation is proportional to the energetic exposure. As a result, a typical sin2 curve is obtained reaching a maximum diffraction efficiency and saturation at or below this value. However, linear deviations are experimentally observed when the first maximum on the curve is lower than the second. This effect does not correspond to overmodulation and recently in PVA/acrylamide photopolymers of high thickness it has been explained by the dye concentration in the layer and the resulting molecular weight of the polymer chains generated in the polymerization process. In this work, new insights into these deviations are gained from the analysis of the non-uniform gratings recorded. Therefore, we show that deviations from the linear response can be explained by taking into account the energetic evolution of the index modulation as well as the fringe bending in the grating.

©2009 Optical Society of America

Full Article  |  PDF Article
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References

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  1. M. Ortuño, C. Neipp, S. Gallego, and A. Beléndez, “Linear response deviations during recording of diffraction gratings in photopolymers,” Opt. Express 17, 13,193–13,201 (2009).
  2. D. A. Waldman, C. J. Butler, and D. H. Raguin, “CROP holographic storage media for optical data storage at greater than 100 bits/μm 2,” in Organic Holographic Materials and Applications, K. Meerholz, ed., Proc. SPIE 5216, 178–191 (2003).
  3. W. L. Wilson, K. R. Curtis, K. Anderson, M. C. Tackitt, A. J. Hill, M. Pane, C. Stanhope, T. Earhart, W. Loechel, C. Bergman, K. Wolfgang, C. Shuman, G. Hertrich, K. Pharris, K. Malang, B. Riley, and M. Ayres, “Realization of high performance holographic data storage: The InPhase Technologies demonstration platform,” in Organic Holographic Materials and Aplications, K. Meerholz, ed., Proc. SPIE 5216, 78–191 (2003).
  4. L. Dhar, “High-performance polymer recording materials for holographic data storage,” MRS Bulletin 31, 324–328 (2006).
    [Crossref]
  5. S. Orlic, E. Dietz, T. Feid, S. Frohmann, and C. Mueller, “Optical investigation of photopolymer systems for microholographic storage,” J. Opt. A 11(2), 024,014 (2009).
  6. R. A. Lessard, R. Changkakoti, and G. Mannivanan, Holographic recording materials, chap. Processes in pho-toreactive polymers, (Chapman and Hall, New York,1995) pp. 307–367.
  7. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell. Sys. Tech. J. 48(9), 2909–2945 (1969).
  8. A. Belé;ndez, A. Fimia, L. Carretero, and F. Mateos, “Self-induced phase gratings due to the inhomogeneous structure of acrylamide photopolymer systems used as holographic recording material,” Appl. Phys. Lett. 67(26), 3856–3858 (1995).
    [Crossref]
  9. S. Blaya, P. Acebal, L. Carretero, and A. Fimia, “Pyrromethene-HEMA-based photopolymerizable holographic recording material,” Opt. Commun. 228, 55–61 (2003).
    [Crossref]
  10. 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]
  11. T. Kubota, “The bending of interference fringes inside a hologram,” Optica Acta 26, 731–743 (1979).
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  14. L. Carretero, A. Murciano, S. Blaya, M. Ulibarrena, and A. Fimia, “Acrylamide-N,N’-methylenebisacrylamide silica glass holographic recording material,” Opt. Express 12(8), 1780–1787 (2004).
    [Crossref] [PubMed]
  15. A. Costela, I. García-Moreno, and R. Sastre, “Materials for solid-state dye lasers,” in Handbook of Advanced Electronic and Photonic Materials and Devices, H. S. Nalwa, ed., (Academic Press, San Diego, 2001) Vol. 7, Chap. 4, pp. 161–208.
    [Crossref]
  16. M. Canva, P. Georges, J.-F. Perelgritz, A. Brun, F. Chaput, and J.-P. Boilot, “Perylene-and pyrromethene-doped xerogel for a pulsed laser,” Appl. Opt. 34(3), 428–431 (1995).
    [Crossref] [PubMed]
  17. S. Noppakundilograt, S. Suzuki, T. Urano, N. Miyagawa, S. Takahara, and T. Yamaoka, “Vis-sensitive photopolymer containing vinyl ether compound and pyrromethene dye,” Polym. Adv. Technol. 13, 527–533 (2002).
    [Crossref]
  18. S. Suzuki, T. Urano, K. Ito, T. Murayama, I. Hotta, S. Takahara, and T. Yamaoka, “Pyrromethene dye sensitized photopolymer and the application to visible laser direct imaging,” J. Photopolym. Sci. Technol. 17(1), 125–129 (2004).
    [Crossref]
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    [Crossref]
  20. S. Suzuki, J. Iwaki, T. Urano, S. Takahara, and T. Yamaoka, “Pyrromethene dye sensitized photopolymer-photochemical behavior in polymer matrix and application to photoresist for printed circuit board,” Polym. Adv. Technol. 17, 348–353 (2006).
    [Crossref]
  21. T. Urano, H. Ito, and T. Yamaoka, “Sensitization mechanisms form excited-singlet state of pyrromethene dye to a radical-generating reagent in a poly(methylmethacrylate) film,” Polym. Adv. Technol. 10, 321–328 (1999).
    [Crossref]
  22. O. García, A. Costela, I. García-Moreno, and R. Sastre, “Pyrromethene 567 dye as visible light photoinitiator for free radical polymerization,” Macromol. Chem. Phys. 204(18), 2233–2239 (2003).
    [Crossref]
  23. T. Kojima and Y. Tomita, “Characterization of index and surface-relief gratings formed in methacrylate photopolymers,” Opt. Rev. 9(5), 222–226 (2002).
    [Crossref]
  24. Y. Tomita and H. Nishibirakie, “Improvement of holographic recording sensitivities in the green in SiO2 nanoparticle-dispersed methacrylate photopolymers doped with pyrromethene dyes,” Appl. Phys. Lett. 83(3), 410–412 (2003).
    [Crossref]
  25. M. Ortuño, A. Márquez, S. Gallego, C. Neipp, and E. Fernández, “Pyrromethene dye and non-redox initiator system in a hydrophilic binder photopolymer,” Opt. Mat. 30, 227–230 (2007).
    [Crossref]
  26. M. M. Wang and S. Esener, “Three dimensional optical data storage in a fluorescent dye-doped photopolymer,” Appl. Opt. 39(11), 1826–1834 (2000).
    [Crossref]
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    [Crossref]

2009 (2)

M. Ortuño, C. Neipp, S. Gallego, and A. Beléndez, “Linear response deviations during recording of diffraction gratings in photopolymers,” Opt. Express 17, 13,193–13,201 (2009).

S. Orlic, E. Dietz, T. Feid, S. Frohmann, and C. Mueller, “Optical investigation of photopolymer systems for microholographic storage,” J. Opt. A 11(2), 024,014 (2009).

2007 (1)

M. Ortuño, A. Márquez, S. Gallego, C. Neipp, and E. Fernández, “Pyrromethene dye and non-redox initiator system in a hydrophilic binder photopolymer,” Opt. Mat. 30, 227–230 (2007).
[Crossref]

2006 (3)

L. Dhar, “High-performance polymer recording materials for holographic data storage,” MRS Bulletin 31, 324–328 (2006).
[Crossref]

S. Suzuki, X. Allonas, J.-P. Fouassier, T. Urano, S. Takahara, and T. Yamaoka, “Interaction mechanism in pyrromethene dye/photoacid generator photosensitive system for high-speed photopolymer,” J. Photochem. Pho-tobiol. A 181, 60–66 (2006).
[Crossref]

S. Suzuki, J. Iwaki, T. Urano, S. Takahara, and T. Yamaoka, “Pyrromethene dye sensitized photopolymer-photochemical behavior in polymer matrix and application to photoresist for printed circuit board,” Polym. Adv. Technol. 17, 348–353 (2006).
[Crossref]

2004 (2)

S. Suzuki, T. Urano, K. Ito, T. Murayama, I. Hotta, S. Takahara, and T. Yamaoka, “Pyrromethene dye sensitized photopolymer and the application to visible laser direct imaging,” J. Photopolym. Sci. Technol. 17(1), 125–129 (2004).
[Crossref]

L. Carretero, A. Murciano, S. Blaya, M. Ulibarrena, and A. Fimia, “Acrylamide-N,N’-methylenebisacrylamide silica glass holographic recording material,” Opt. Express 12(8), 1780–1787 (2004).
[Crossref] [PubMed]

2003 (5)

Y. Tomita and H. Nishibirakie, “Improvement of holographic recording sensitivities in the green in SiO2 nanoparticle-dispersed methacrylate photopolymers doped with pyrromethene dyes,” Appl. Phys. Lett. 83(3), 410–412 (2003).
[Crossref]

O. García, A. Costela, I. García-Moreno, and R. Sastre, “Pyrromethene 567 dye as visible light photoinitiator for free radical polymerization,” Macromol. Chem. Phys. 204(18), 2233–2239 (2003).
[Crossref]

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

D. A. Waldman, C. J. Butler, and D. H. Raguin, “CROP holographic storage media for optical data storage at greater than 100 bits/μm 2,” in Organic Holographic Materials and Applications, K. Meerholz, ed., Proc. SPIE 5216, 178–191 (2003).

W. L. Wilson, K. R. Curtis, K. Anderson, M. C. Tackitt, A. J. Hill, M. Pane, C. Stanhope, T. Earhart, W. Loechel, C. Bergman, K. Wolfgang, C. Shuman, G. Hertrich, K. Pharris, K. Malang, B. Riley, and M. Ayres, “Realization of high performance holographic data storage: The InPhase Technologies demonstration platform,” in Organic Holographic Materials and Aplications, K. Meerholz, ed., Proc. SPIE 5216, 78–191 (2003).

2002 (2)

T. Kojima and Y. Tomita, “Characterization of index and surface-relief gratings formed in methacrylate photopolymers,” Opt. Rev. 9(5), 222–226 (2002).
[Crossref]

S. Noppakundilograt, S. Suzuki, T. Urano, N. Miyagawa, S. Takahara, and T. Yamaoka, “Vis-sensitive photopolymer containing vinyl ether compound and pyrromethene dye,” Polym. Adv. Technol. 13, 527–533 (2002).
[Crossref]

2000 (1)

1999 (1)

T. Urano, H. Ito, and T. Yamaoka, “Sensitization mechanisms form excited-singlet state of pyrromethene dye to a radical-generating reagent in a poly(methylmethacrylate) film,” Polym. Adv. Technol. 10, 321–328 (1999).
[Crossref]

1997 (1)

D. A. Waldman, H.-Y. S. Li, and M. G. Horner, “Volume shrinkage in slant fringe gratings of a cationic ring-opening volume hologram recording material,” J. Imaging. Sci. Tecnol. 41(5), 497–514 (1997).

1995 (2)

M. Canva, P. Georges, J.-F. Perelgritz, A. Brun, F. Chaput, and J.-P. Boilot, “Perylene-and pyrromethene-doped xerogel for a pulsed laser,” Appl. Opt. 34(3), 428–431 (1995).
[Crossref] [PubMed]

A. Belé;ndez, A. Fimia, L. Carretero, and F. Mateos, “Self-induced phase gratings due to the inhomogeneous structure of acrylamide photopolymer systems used as holographic recording material,” Appl. Phys. Lett. 67(26), 3856–3858 (1995).
[Crossref]

1994 (1)

1979 (1)

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

1973 (1)

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]

1971 (1)

E. L. Simmons, “The photochemistry of solid layers. Reaction rates.” J. Phys. Chem. 75, 588–590 (1971).
[Crossref]

1969 (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell. Sys. Tech. J. 48(9), 2909–2945 (1969).

Acebal, P.

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

Allonas, X.

S. Suzuki, X. Allonas, J.-P. Fouassier, T. Urano, S. Takahara, and T. Yamaoka, “Interaction mechanism in pyrromethene dye/photoacid generator photosensitive system for high-speed photopolymer,” J. Photochem. Pho-tobiol. A 181, 60–66 (2006).
[Crossref]

Anderson, K.

W. L. Wilson, K. R. Curtis, K. Anderson, M. C. Tackitt, A. J. Hill, M. Pane, C. Stanhope, T. Earhart, W. Loechel, C. Bergman, K. Wolfgang, C. Shuman, G. Hertrich, K. Pharris, K. Malang, B. Riley, and M. Ayres, “Realization of high performance holographic data storage: The InPhase Technologies demonstration platform,” in Organic Holographic Materials and Aplications, K. Meerholz, ed., Proc. SPIE 5216, 78–191 (2003).

Ayres, M.

W. L. Wilson, K. R. Curtis, K. Anderson, M. C. Tackitt, A. J. Hill, M. Pane, C. Stanhope, T. Earhart, W. Loechel, C. Bergman, K. Wolfgang, C. Shuman, G. Hertrich, K. Pharris, K. Malang, B. Riley, and M. Ayres, “Realization of high performance holographic data storage: The InPhase Technologies demonstration platform,” in Organic Holographic Materials and Aplications, K. Meerholz, ed., Proc. SPIE 5216, 78–191 (2003).

Belé;ndez, A.

A. Belé;ndez, A. Fimia, L. Carretero, and F. Mateos, “Self-induced phase gratings due to the inhomogeneous structure of acrylamide photopolymer systems used as holographic recording material,” Appl. Phys. Lett. 67(26), 3856–3858 (1995).
[Crossref]

Beléndez, A.

M. Ortuño, C. Neipp, S. Gallego, and A. Beléndez, “Linear response deviations during recording of diffraction gratings in photopolymers,” Opt. Express 17, 13,193–13,201 (2009).

Bergman, C.

W. L. Wilson, K. R. Curtis, K. Anderson, M. C. Tackitt, A. J. Hill, M. Pane, C. Stanhope, T. Earhart, W. Loechel, C. Bergman, K. Wolfgang, C. Shuman, G. Hertrich, K. Pharris, K. Malang, B. Riley, and M. Ayres, “Realization of high performance holographic data storage: The InPhase Technologies demonstration platform,” in Organic Holographic Materials and Aplications, K. Meerholz, ed., Proc. SPIE 5216, 78–191 (2003).

Blaya, S.

L. Carretero, A. Murciano, S. Blaya, M. Ulibarrena, and A. Fimia, “Acrylamide-N,N’-methylenebisacrylamide silica glass holographic recording material,” Opt. Express 12(8), 1780–1787 (2004).
[Crossref] [PubMed]

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

Boilot, J.-P.

Brun, A.

Butler, C. J.

D. A. Waldman, C. J. Butler, and D. H. Raguin, “CROP holographic storage media for optical data storage at greater than 100 bits/μm 2,” in Organic Holographic Materials and Applications, K. Meerholz, ed., Proc. SPIE 5216, 178–191 (2003).

Canva, M.

Carretero, L.

L. Carretero, A. Murciano, S. Blaya, M. Ulibarrena, and A. Fimia, “Acrylamide-N,N’-methylenebisacrylamide silica glass holographic recording material,” Opt. Express 12(8), 1780–1787 (2004).
[Crossref] [PubMed]

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

A. Belé;ndez, A. Fimia, L. Carretero, and F. Mateos, “Self-induced phase gratings due to the inhomogeneous structure of acrylamide photopolymer systems used as holographic recording material,” Appl. Phys. Lett. 67(26), 3856–3858 (1995).
[Crossref]

Changkakoti, R.

R. A. Lessard, R. Changkakoti, and G. Mannivanan, Holographic recording materials, chap. Processes in pho-toreactive polymers, (Chapman and Hall, New York,1995) pp. 307–367.

Chaput, F.

Costela, A.

O. García, A. Costela, I. García-Moreno, and R. Sastre, “Pyrromethene 567 dye as visible light photoinitiator for free radical polymerization,” Macromol. Chem. Phys. 204(18), 2233–2239 (2003).
[Crossref]

A. Costela, I. García-Moreno, and R. Sastre, “Materials for solid-state dye lasers,” in Handbook of Advanced Electronic and Photonic Materials and Devices, H. S. Nalwa, ed., (Academic Press, San Diego, 2001) Vol. 7, Chap. 4, pp. 161–208.
[Crossref]

Curtis, K. R.

W. L. Wilson, K. R. Curtis, K. Anderson, M. C. Tackitt, A. J. Hill, M. Pane, C. Stanhope, T. Earhart, W. Loechel, C. Bergman, K. Wolfgang, C. Shuman, G. Hertrich, K. Pharris, K. Malang, B. Riley, and M. Ayres, “Realization of high performance holographic data storage: The InPhase Technologies demonstration platform,” in Organic Holographic Materials and Aplications, K. Meerholz, ed., Proc. SPIE 5216, 78–191 (2003).

Dhar, L.

L. Dhar, “High-performance polymer recording materials for holographic data storage,” MRS Bulletin 31, 324–328 (2006).
[Crossref]

Dietz, E.

S. Orlic, E. Dietz, T. Feid, S. Frohmann, and C. Mueller, “Optical investigation of photopolymer systems for microholographic storage,” J. Opt. A 11(2), 024,014 (2009).

Earhart, T.

W. L. Wilson, K. R. Curtis, K. Anderson, M. C. Tackitt, A. J. Hill, M. Pane, C. Stanhope, T. Earhart, W. Loechel, C. Bergman, K. Wolfgang, C. Shuman, G. Hertrich, K. Pharris, K. Malang, B. Riley, and M. Ayres, “Realization of high performance holographic data storage: The InPhase Technologies demonstration platform,” in Organic Holographic Materials and Aplications, K. Meerholz, ed., Proc. SPIE 5216, 78–191 (2003).

Esener, S.

Feid, T.

S. Orlic, E. Dietz, T. Feid, S. Frohmann, and C. Mueller, “Optical investigation of photopolymer systems for microholographic storage,” J. Opt. A 11(2), 024,014 (2009).

Fernández, E.

M. Ortuño, A. Márquez, S. Gallego, C. Neipp, and E. Fernández, “Pyrromethene dye and non-redox initiator system in a hydrophilic binder photopolymer,” Opt. Mat. 30, 227–230 (2007).
[Crossref]

Fimia, A.

L. Carretero, A. Murciano, S. Blaya, M. Ulibarrena, and A. Fimia, “Acrylamide-N,N’-methylenebisacrylamide silica glass holographic recording material,” Opt. Express 12(8), 1780–1787 (2004).
[Crossref] [PubMed]

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

A. Belé;ndez, A. Fimia, L. Carretero, and F. Mateos, “Self-induced phase gratings due to the inhomogeneous structure of acrylamide photopolymer systems used as holographic recording material,” Appl. Phys. Lett. 67(26), 3856–3858 (1995).
[Crossref]

Fouassier, J.-P.

S. Suzuki, X. Allonas, J.-P. Fouassier, T. Urano, S. Takahara, and T. Yamaoka, “Interaction mechanism in pyrromethene dye/photoacid generator photosensitive system for high-speed photopolymer,” J. Photochem. Pho-tobiol. A 181, 60–66 (2006).
[Crossref]

Frohmann, S.

S. Orlic, E. Dietz, T. Feid, S. Frohmann, and C. Mueller, “Optical investigation of photopolymer systems for microholographic storage,” J. Opt. A 11(2), 024,014 (2009).

Gallego, S.

M. Ortuño, C. Neipp, S. Gallego, and A. Beléndez, “Linear response deviations during recording of diffraction gratings in photopolymers,” Opt. Express 17, 13,193–13,201 (2009).

M. Ortuño, A. Márquez, S. Gallego, C. Neipp, and E. Fernández, “Pyrromethene dye and non-redox initiator system in a hydrophilic binder photopolymer,” Opt. Mat. 30, 227–230 (2007).
[Crossref]

Gallo, J. T.

García, O.

O. García, A. Costela, I. García-Moreno, and R. Sastre, “Pyrromethene 567 dye as visible light photoinitiator for free radical polymerization,” Macromol. Chem. Phys. 204(18), 2233–2239 (2003).
[Crossref]

García-Moreno, I.

O. García, A. Costela, I. García-Moreno, and R. Sastre, “Pyrromethene 567 dye as visible light photoinitiator for free radical polymerization,” Macromol. Chem. Phys. 204(18), 2233–2239 (2003).
[Crossref]

A. Costela, I. García-Moreno, and R. Sastre, “Materials for solid-state dye lasers,” in Handbook of Advanced Electronic and Photonic Materials and Devices, H. S. Nalwa, ed., (Academic Press, San Diego, 2001) Vol. 7, Chap. 4, pp. 161–208.
[Crossref]

Georges, P.

Hertrich, G.

W. L. Wilson, K. R. Curtis, K. Anderson, M. C. Tackitt, A. J. Hill, M. Pane, C. Stanhope, T. Earhart, W. Loechel, C. Bergman, K. Wolfgang, C. Shuman, G. Hertrich, K. Pharris, K. Malang, B. Riley, and M. Ayres, “Realization of high performance holographic data storage: The InPhase Technologies demonstration platform,” in Organic Holographic Materials and Aplications, K. Meerholz, ed., Proc. SPIE 5216, 78–191 (2003).

Hill, A. J.

W. L. Wilson, K. R. Curtis, K. Anderson, M. C. Tackitt, A. J. Hill, M. Pane, C. Stanhope, T. Earhart, W. Loechel, C. Bergman, K. Wolfgang, C. Shuman, G. Hertrich, K. Pharris, K. Malang, B. Riley, and M. Ayres, “Realization of high performance holographic data storage: The InPhase Technologies demonstration platform,” in Organic Holographic Materials and Aplications, K. Meerholz, ed., Proc. SPIE 5216, 78–191 (2003).

Horner, M. G.

D. A. Waldman, H.-Y. S. Li, and M. G. Horner, “Volume shrinkage in slant fringe gratings of a cationic ring-opening volume hologram recording material,” J. Imaging. Sci. Tecnol. 41(5), 497–514 (1997).

Hotta, I.

S. Suzuki, T. Urano, K. Ito, T. Murayama, I. Hotta, S. Takahara, and T. Yamaoka, “Pyrromethene dye sensitized photopolymer and the application to visible laser direct imaging,” J. Photopolym. Sci. Technol. 17(1), 125–129 (2004).
[Crossref]

Ito, H.

T. Urano, H. Ito, and T. Yamaoka, “Sensitization mechanisms form excited-singlet state of pyrromethene dye to a radical-generating reagent in a poly(methylmethacrylate) film,” Polym. Adv. Technol. 10, 321–328 (1999).
[Crossref]

Ito, K.

S. Suzuki, T. Urano, K. Ito, T. Murayama, I. Hotta, S. Takahara, and T. Yamaoka, “Pyrromethene dye sensitized photopolymer and the application to visible laser direct imaging,” J. Photopolym. Sci. Technol. 17(1), 125–129 (2004).
[Crossref]

Iwaki, J.

S. Suzuki, J. Iwaki, T. Urano, S. Takahara, and T. Yamaoka, “Pyrromethene dye sensitized photopolymer-photochemical behavior in polymer matrix and application to photoresist for printed circuit board,” Polym. Adv. Technol. 17, 348–353 (2006).
[Crossref]

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell. Sys. Tech. J. 48(9), 2909–2945 (1969).

Kojima, T.

T. Kojima and Y. Tomita, “Characterization of index and surface-relief gratings formed in methacrylate photopolymers,” Opt. Rev. 9(5), 222–226 (2002).
[Crossref]

Kubota, T.

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

Lessard, R. A.

R. A. Lessard, R. Changkakoti, and G. Mannivanan, Holographic recording materials, chap. Processes in pho-toreactive polymers, (Chapman and Hall, New York,1995) pp. 307–367.

Li, H.-Y. S.

D. A. Waldman, H.-Y. S. Li, and M. G. Horner, “Volume shrinkage in slant fringe gratings of a cationic ring-opening volume hologram recording material,” J. Imaging. Sci. Tecnol. 41(5), 497–514 (1997).

Loechel, W.

W. L. Wilson, K. R. Curtis, K. Anderson, M. C. Tackitt, A. J. Hill, M. Pane, C. Stanhope, T. Earhart, W. Loechel, C. Bergman, K. Wolfgang, C. Shuman, G. Hertrich, K. Pharris, K. Malang, B. Riley, and M. Ayres, “Realization of high performance holographic data storage: The InPhase Technologies demonstration platform,” in Organic Holographic Materials and Aplications, K. Meerholz, ed., Proc. SPIE 5216, 78–191 (2003).

Malang, K.

W. L. Wilson, K. R. Curtis, K. Anderson, M. C. Tackitt, A. J. Hill, M. Pane, C. Stanhope, T. Earhart, W. Loechel, C. Bergman, K. Wolfgang, C. Shuman, G. Hertrich, K. Pharris, K. Malang, B. Riley, and M. Ayres, “Realization of high performance holographic data storage: The InPhase Technologies demonstration platform,” in Organic Holographic Materials and Aplications, K. Meerholz, ed., Proc. SPIE 5216, 78–191 (2003).

Mannivanan, G.

R. A. Lessard, R. Changkakoti, and G. Mannivanan, Holographic recording materials, chap. Processes in pho-toreactive polymers, (Chapman and Hall, New York,1995) pp. 307–367.

Márquez, A.

M. Ortuño, A. Márquez, S. Gallego, C. Neipp, and E. Fernández, “Pyrromethene dye and non-redox initiator system in a hydrophilic binder photopolymer,” Opt. Mat. 30, 227–230 (2007).
[Crossref]

Mateos, F.

A. Belé;ndez, A. Fimia, L. Carretero, and F. Mateos, “Self-induced phase gratings due to the inhomogeneous structure of acrylamide photopolymer systems used as holographic recording material,” Appl. Phys. Lett. 67(26), 3856–3858 (1995).
[Crossref]

Miyagawa, N.

S. Noppakundilograt, S. Suzuki, T. Urano, N. Miyagawa, S. Takahara, and T. Yamaoka, “Vis-sensitive photopolymer containing vinyl ether compound and pyrromethene dye,” Polym. Adv. Technol. 13, 527–533 (2002).
[Crossref]

Mueller, C.

S. Orlic, E. Dietz, T. Feid, S. Frohmann, and C. Mueller, “Optical investigation of photopolymer systems for microholographic storage,” J. Opt. A 11(2), 024,014 (2009).

Murayama, T.

S. Suzuki, T. Urano, K. Ito, T. Murayama, I. Hotta, S. Takahara, and T. Yamaoka, “Pyrromethene dye sensitized photopolymer and the application to visible laser direct imaging,” J. Photopolym. Sci. Technol. 17(1), 125–129 (2004).
[Crossref]

Murciano, A.

Neipp, C.

M. Ortuño, C. Neipp, S. Gallego, and A. Beléndez, “Linear response deviations during recording of diffraction gratings in photopolymers,” Opt. Express 17, 13,193–13,201 (2009).

M. Ortuño, A. Márquez, S. Gallego, C. Neipp, and E. Fernández, “Pyrromethene dye and non-redox initiator system in a hydrophilic binder photopolymer,” Opt. Mat. 30, 227–230 (2007).
[Crossref]

Nishibirakie, H.

Y. Tomita and H. Nishibirakie, “Improvement of holographic recording sensitivities in the green in SiO2 nanoparticle-dispersed methacrylate photopolymers doped with pyrromethene dyes,” Appl. Phys. Lett. 83(3), 410–412 (2003).
[Crossref]

Noppakundilograt, S.

S. Noppakundilograt, S. Suzuki, T. Urano, N. Miyagawa, S. Takahara, and T. Yamaoka, “Vis-sensitive photopolymer containing vinyl ether compound and pyrromethene dye,” Polym. Adv. Technol. 13, 527–533 (2002).
[Crossref]

Orlic, S.

S. Orlic, E. Dietz, T. Feid, S. Frohmann, and C. Mueller, “Optical investigation of photopolymer systems for microholographic storage,” J. Opt. A 11(2), 024,014 (2009).

Ortuño, M.

M. Ortuño, C. Neipp, S. Gallego, and A. Beléndez, “Linear response deviations during recording of diffraction gratings in photopolymers,” Opt. Express 17, 13,193–13,201 (2009).

M. Ortuño, A. Márquez, S. Gallego, C. Neipp, and E. Fernández, “Pyrromethene dye and non-redox initiator system in a hydrophilic binder photopolymer,” Opt. Mat. 30, 227–230 (2007).
[Crossref]

Pane, M.

W. L. Wilson, K. R. Curtis, K. Anderson, M. C. Tackitt, A. J. Hill, M. Pane, C. Stanhope, T. Earhart, W. Loechel, C. Bergman, K. Wolfgang, C. Shuman, G. Hertrich, K. Pharris, K. Malang, B. Riley, and M. Ayres, “Realization of high performance holographic data storage: The InPhase Technologies demonstration platform,” in Organic Holographic Materials and Aplications, K. Meerholz, ed., Proc. SPIE 5216, 78–191 (2003).

Perelgritz, J.-F.

Pharris, K.

W. L. Wilson, K. R. Curtis, K. Anderson, M. C. Tackitt, A. J. Hill, M. Pane, C. Stanhope, T. Earhart, W. Loechel, C. Bergman, K. Wolfgang, C. Shuman, G. Hertrich, K. Pharris, K. Malang, B. Riley, and M. Ayres, “Realization of high performance holographic data storage: The InPhase Technologies demonstration platform,” in Organic Holographic Materials and Aplications, K. Meerholz, ed., Proc. SPIE 5216, 78–191 (2003).

Raguin, D. H.

D. A. Waldman, C. J. Butler, and D. H. Raguin, “CROP holographic storage media for optical data storage at greater than 100 bits/μm 2,” in Organic Holographic Materials and Applications, K. Meerholz, ed., Proc. SPIE 5216, 178–191 (2003).

Riley, B.

W. L. Wilson, K. R. Curtis, K. Anderson, M. C. Tackitt, A. J. Hill, M. Pane, C. Stanhope, T. Earhart, W. Loechel, C. Bergman, K. Wolfgang, C. Shuman, G. Hertrich, K. Pharris, K. Malang, B. Riley, and M. Ayres, “Realization of high performance holographic data storage: The InPhase Technologies demonstration platform,” in Organic Holographic Materials and Aplications, K. Meerholz, ed., Proc. SPIE 5216, 78–191 (2003).

Sastre, R.

O. García, A. Costela, I. García-Moreno, and R. Sastre, “Pyrromethene 567 dye as visible light photoinitiator for free radical polymerization,” Macromol. Chem. Phys. 204(18), 2233–2239 (2003).
[Crossref]

A. Costela, I. García-Moreno, and R. Sastre, “Materials for solid-state dye lasers,” in Handbook of Advanced Electronic and Photonic Materials and Devices, H. S. Nalwa, ed., (Academic Press, San Diego, 2001) Vol. 7, Chap. 4, pp. 161–208.
[Crossref]

Sen, A.

A. Sen and M. Srivastava, Regresion analysis. Theory, methods, and applications (Springer, New York, 1997).

Shuman, C.

W. L. Wilson, K. R. Curtis, K. Anderson, M. C. Tackitt, A. J. Hill, M. Pane, C. Stanhope, T. Earhart, W. Loechel, C. Bergman, K. Wolfgang, C. Shuman, G. Hertrich, K. Pharris, K. Malang, B. Riley, and M. Ayres, “Realization of high performance holographic data storage: The InPhase Technologies demonstration platform,” in Organic Holographic Materials and Aplications, K. Meerholz, ed., Proc. SPIE 5216, 78–191 (2003).

Simmons, E. L.

E. L. Simmons, “The photochemistry of solid layers. Reaction rates.” J. Phys. Chem. 75, 588–590 (1971).
[Crossref]

Srivastava, M.

A. Sen and M. Srivastava, Regresion analysis. Theory, methods, and applications (Springer, New York, 1997).

Stanhope, C.

W. L. Wilson, K. R. Curtis, K. Anderson, M. C. Tackitt, A. J. Hill, M. Pane, C. Stanhope, T. Earhart, W. Loechel, C. Bergman, K. Wolfgang, C. Shuman, G. Hertrich, K. Pharris, K. Malang, B. Riley, and M. Ayres, “Realization of high performance holographic data storage: The InPhase Technologies demonstration platform,” in Organic Holographic Materials and Aplications, K. Meerholz, ed., Proc. SPIE 5216, 78–191 (2003).

Suzuki, S.

S. Suzuki, X. Allonas, J.-P. Fouassier, T. Urano, S. Takahara, and T. Yamaoka, “Interaction mechanism in pyrromethene dye/photoacid generator photosensitive system for high-speed photopolymer,” J. Photochem. Pho-tobiol. A 181, 60–66 (2006).
[Crossref]

S. Suzuki, J. Iwaki, T. Urano, S. Takahara, and T. Yamaoka, “Pyrromethene dye sensitized photopolymer-photochemical behavior in polymer matrix and application to photoresist for printed circuit board,” Polym. Adv. Technol. 17, 348–353 (2006).
[Crossref]

S. Suzuki, T. Urano, K. Ito, T. Murayama, I. Hotta, S. Takahara, and T. Yamaoka, “Pyrromethene dye sensitized photopolymer and the application to visible laser direct imaging,” J. Photopolym. Sci. Technol. 17(1), 125–129 (2004).
[Crossref]

S. Noppakundilograt, S. Suzuki, T. Urano, N. Miyagawa, S. Takahara, and T. Yamaoka, “Vis-sensitive photopolymer containing vinyl ether compound and pyrromethene dye,” Polym. Adv. Technol. 13, 527–533 (2002).
[Crossref]

Tackitt, M. C.

W. L. Wilson, K. R. Curtis, K. Anderson, M. C. Tackitt, A. J. Hill, M. Pane, C. Stanhope, T. Earhart, W. Loechel, C. Bergman, K. Wolfgang, C. Shuman, G. Hertrich, K. Pharris, K. Malang, B. Riley, and M. Ayres, “Realization of high performance holographic data storage: The InPhase Technologies demonstration platform,” in Organic Holographic Materials and Aplications, K. Meerholz, ed., Proc. SPIE 5216, 78–191 (2003).

Takahara, S.

S. Suzuki, J. Iwaki, T. Urano, S. Takahara, and T. Yamaoka, “Pyrromethene dye sensitized photopolymer-photochemical behavior in polymer matrix and application to photoresist for printed circuit board,” Polym. Adv. Technol. 17, 348–353 (2006).
[Crossref]

S. Suzuki, X. Allonas, J.-P. Fouassier, T. Urano, S. Takahara, and T. Yamaoka, “Interaction mechanism in pyrromethene dye/photoacid generator photosensitive system for high-speed photopolymer,” J. Photochem. Pho-tobiol. A 181, 60–66 (2006).
[Crossref]

S. Suzuki, T. Urano, K. Ito, T. Murayama, I. Hotta, S. Takahara, and T. Yamaoka, “Pyrromethene dye sensitized photopolymer and the application to visible laser direct imaging,” J. Photopolym. Sci. Technol. 17(1), 125–129 (2004).
[Crossref]

S. Noppakundilograt, S. Suzuki, T. Urano, N. Miyagawa, S. Takahara, and T. Yamaoka, “Vis-sensitive photopolymer containing vinyl ether compound and pyrromethene dye,” Polym. Adv. Technol. 13, 527–533 (2002).
[Crossref]

Tomita, Y.

Y. Tomita and H. Nishibirakie, “Improvement of holographic recording sensitivities in the green in SiO2 nanoparticle-dispersed methacrylate photopolymers doped with pyrromethene dyes,” Appl. Phys. Lett. 83(3), 410–412 (2003).
[Crossref]

T. Kojima and Y. Tomita, “Characterization of index and surface-relief gratings formed in methacrylate photopolymers,” Opt. Rev. 9(5), 222–226 (2002).
[Crossref]

Uchida, N.

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]

Ulibarrena, M.

Urano, T.

S. Suzuki, X. Allonas, J.-P. Fouassier, T. Urano, S. Takahara, and T. Yamaoka, “Interaction mechanism in pyrromethene dye/photoacid generator photosensitive system for high-speed photopolymer,” J. Photochem. Pho-tobiol. A 181, 60–66 (2006).
[Crossref]

S. Suzuki, J. Iwaki, T. Urano, S. Takahara, and T. Yamaoka, “Pyrromethene dye sensitized photopolymer-photochemical behavior in polymer matrix and application to photoresist for printed circuit board,” Polym. Adv. Technol. 17, 348–353 (2006).
[Crossref]

S. Suzuki, T. Urano, K. Ito, T. Murayama, I. Hotta, S. Takahara, and T. Yamaoka, “Pyrromethene dye sensitized photopolymer and the application to visible laser direct imaging,” J. Photopolym. Sci. Technol. 17(1), 125–129 (2004).
[Crossref]

S. Noppakundilograt, S. Suzuki, T. Urano, N. Miyagawa, S. Takahara, and T. Yamaoka, “Vis-sensitive photopolymer containing vinyl ether compound and pyrromethene dye,” Polym. Adv. Technol. 13, 527–533 (2002).
[Crossref]

T. Urano, H. Ito, and T. Yamaoka, “Sensitization mechanisms form excited-singlet state of pyrromethene dye to a radical-generating reagent in a poly(methylmethacrylate) film,” Polym. Adv. Technol. 10, 321–328 (1999).
[Crossref]

Verber, C. M.

Waldman, D. A.

D. A. Waldman, C. J. Butler, and D. H. Raguin, “CROP holographic storage media for optical data storage at greater than 100 bits/μm 2,” in Organic Holographic Materials and Applications, K. Meerholz, ed., Proc. SPIE 5216, 178–191 (2003).

D. A. Waldman, H.-Y. S. Li, and M. G. Horner, “Volume shrinkage in slant fringe gratings of a cationic ring-opening volume hologram recording material,” J. Imaging. Sci. Tecnol. 41(5), 497–514 (1997).

Wang, M. M.

Wilson, W. L.

W. L. Wilson, K. R. Curtis, K. Anderson, M. C. Tackitt, A. J. Hill, M. Pane, C. Stanhope, T. Earhart, W. Loechel, C. Bergman, K. Wolfgang, C. Shuman, G. Hertrich, K. Pharris, K. Malang, B. Riley, and M. Ayres, “Realization of high performance holographic data storage: The InPhase Technologies demonstration platform,” in Organic Holographic Materials and Aplications, K. Meerholz, ed., Proc. SPIE 5216, 78–191 (2003).

Wolfgang, K.

W. L. Wilson, K. R. Curtis, K. Anderson, M. C. Tackitt, A. J. Hill, M. Pane, C. Stanhope, T. Earhart, W. Loechel, C. Bergman, K. Wolfgang, C. Shuman, G. Hertrich, K. Pharris, K. Malang, B. Riley, and M. Ayres, “Realization of high performance holographic data storage: The InPhase Technologies demonstration platform,” in Organic Holographic Materials and Aplications, K. Meerholz, ed., Proc. SPIE 5216, 78–191 (2003).

Yamaoka, T.

S. Suzuki, J. Iwaki, T. Urano, S. Takahara, and T. Yamaoka, “Pyrromethene dye sensitized photopolymer-photochemical behavior in polymer matrix and application to photoresist for printed circuit board,” Polym. Adv. Technol. 17, 348–353 (2006).
[Crossref]

S. Suzuki, X. Allonas, J.-P. Fouassier, T. Urano, S. Takahara, and T. Yamaoka, “Interaction mechanism in pyrromethene dye/photoacid generator photosensitive system for high-speed photopolymer,” J. Photochem. Pho-tobiol. A 181, 60–66 (2006).
[Crossref]

S. Suzuki, T. Urano, K. Ito, T. Murayama, I. Hotta, S. Takahara, and T. Yamaoka, “Pyrromethene dye sensitized photopolymer and the application to visible laser direct imaging,” J. Photopolym. Sci. Technol. 17(1), 125–129 (2004).
[Crossref]

S. Noppakundilograt, S. Suzuki, T. Urano, N. Miyagawa, S. Takahara, and T. Yamaoka, “Vis-sensitive photopolymer containing vinyl ether compound and pyrromethene dye,” Polym. Adv. Technol. 13, 527–533 (2002).
[Crossref]

T. Urano, H. Ito, and T. Yamaoka, “Sensitization mechanisms form excited-singlet state of pyrromethene dye to a radical-generating reagent in a poly(methylmethacrylate) film,” Polym. Adv. Technol. 10, 321–328 (1999).
[Crossref]

Appl. Opt. (3)

Appl. Phys. Lett. (2)

Y. Tomita and H. Nishibirakie, “Improvement of holographic recording sensitivities in the green in SiO2 nanoparticle-dispersed methacrylate photopolymers doped with pyrromethene dyes,” Appl. Phys. Lett. 83(3), 410–412 (2003).
[Crossref]

A. Belé;ndez, A. Fimia, L. Carretero, and F. Mateos, “Self-induced phase gratings due to the inhomogeneous structure of acrylamide photopolymer systems used as holographic recording material,” Appl. Phys. Lett. 67(26), 3856–3858 (1995).
[Crossref]

Bell. Sys. Tech. J. (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell. Sys. Tech. J. 48(9), 2909–2945 (1969).

J. Imaging. Sci. Tecnol. (1)

D. A. Waldman, H.-Y. S. Li, and M. G. Horner, “Volume shrinkage in slant fringe gratings of a cationic ring-opening volume hologram recording material,” J. Imaging. Sci. Tecnol. 41(5), 497–514 (1997).

J. Opt. A (1)

S. Orlic, E. Dietz, T. Feid, S. Frohmann, and C. Mueller, “Optical investigation of photopolymer systems for microholographic storage,” J. Opt. A 11(2), 024,014 (2009).

J. Opt. Soc. Am (1)

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]

J. Photochem. Pho-tobiol. A (1)

S. Suzuki, X. Allonas, J.-P. Fouassier, T. Urano, S. Takahara, and T. Yamaoka, “Interaction mechanism in pyrromethene dye/photoacid generator photosensitive system for high-speed photopolymer,” J. Photochem. Pho-tobiol. A 181, 60–66 (2006).
[Crossref]

J. Photopolym. Sci. Technol. (1)

S. Suzuki, T. Urano, K. Ito, T. Murayama, I. Hotta, S. Takahara, and T. Yamaoka, “Pyrromethene dye sensitized photopolymer and the application to visible laser direct imaging,” J. Photopolym. Sci. Technol. 17(1), 125–129 (2004).
[Crossref]

J. Phys. Chem. (1)

E. L. Simmons, “The photochemistry of solid layers. Reaction rates.” J. Phys. Chem. 75, 588–590 (1971).
[Crossref]

Macromol. Chem. Phys. (1)

O. García, A. Costela, I. García-Moreno, and R. Sastre, “Pyrromethene 567 dye as visible light photoinitiator for free radical polymerization,” Macromol. Chem. Phys. 204(18), 2233–2239 (2003).
[Crossref]

MRS Bulletin (1)

L. Dhar, “High-performance polymer recording materials for holographic data storage,” MRS Bulletin 31, 324–328 (2006).
[Crossref]

Opt. Commun. (1)

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

Opt. Express (2)

M. Ortuño, C. Neipp, S. Gallego, and A. Beléndez, “Linear response deviations during recording of diffraction gratings in photopolymers,” Opt. Express 17, 13,193–13,201 (2009).

L. Carretero, A. Murciano, S. Blaya, M. Ulibarrena, and A. Fimia, “Acrylamide-N,N’-methylenebisacrylamide silica glass holographic recording material,” Opt. Express 12(8), 1780–1787 (2004).
[Crossref] [PubMed]

Opt. Mat. (1)

M. Ortuño, A. Márquez, S. Gallego, C. Neipp, and E. Fernández, “Pyrromethene dye and non-redox initiator system in a hydrophilic binder photopolymer,” Opt. Mat. 30, 227–230 (2007).
[Crossref]

Opt. Rev. (1)

T. Kojima and Y. Tomita, “Characterization of index and surface-relief gratings formed in methacrylate photopolymers,” Opt. Rev. 9(5), 222–226 (2002).
[Crossref]

Optica Acta (1)

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

Polym. Adv. Technol. (3)

S. Noppakundilograt, S. Suzuki, T. Urano, N. Miyagawa, S. Takahara, and T. Yamaoka, “Vis-sensitive photopolymer containing vinyl ether compound and pyrromethene dye,” Polym. Adv. Technol. 13, 527–533 (2002).
[Crossref]

S. Suzuki, J. Iwaki, T. Urano, S. Takahara, and T. Yamaoka, “Pyrromethene dye sensitized photopolymer-photochemical behavior in polymer matrix and application to photoresist for printed circuit board,” Polym. Adv. Technol. 17, 348–353 (2006).
[Crossref]

T. Urano, H. Ito, and T. Yamaoka, “Sensitization mechanisms form excited-singlet state of pyrromethene dye to a radical-generating reagent in a poly(methylmethacrylate) film,” Polym. Adv. Technol. 10, 321–328 (1999).
[Crossref]

Proc. SPIE (2)

D. A. Waldman, C. J. Butler, and D. H. Raguin, “CROP holographic storage media for optical data storage at greater than 100 bits/μm 2,” in Organic Holographic Materials and Applications, K. Meerholz, ed., Proc. SPIE 5216, 178–191 (2003).

W. L. Wilson, K. R. Curtis, K. Anderson, M. C. Tackitt, A. J. Hill, M. Pane, C. Stanhope, T. Earhart, W. Loechel, C. Bergman, K. Wolfgang, C. Shuman, G. Hertrich, K. Pharris, K. Malang, B. Riley, and M. Ayres, “Realization of high performance holographic data storage: The InPhase Technologies demonstration platform,” in Organic Holographic Materials and Aplications, K. Meerholz, ed., Proc. SPIE 5216, 78–191 (2003).

Other (3)

R. A. Lessard, R. Changkakoti, and G. Mannivanan, Holographic recording materials, chap. Processes in pho-toreactive polymers, (Chapman and Hall, New York,1995) pp. 307–367.

A. Costela, I. García-Moreno, and R. Sastre, “Materials for solid-state dye lasers,” in Handbook of Advanced Electronic and Photonic Materials and Devices, H. S. Nalwa, ed., (Academic Press, San Diego, 2001) Vol. 7, Chap. 4, pp. 161–208.
[Crossref]

A. Sen and M. Srivastava, Regresion analysis. Theory, methods, and applications (Springer, New York, 1997).

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Figures (4)

Fig. 1.
Fig. 1. Energetical variation of the diffraction efficiency (η) at different recording intensities.
Fig. 2.
Fig. 2. Theoretical (lines) and experimental (symbols) angular selectivity curves obtained at different recording intensities.
Fig. 3.
Fig. 3. Variation the index modulation (a) and fringe bending (b), versus the thickness of the grating. Data was obtained from the fitting of the angular selectivity curves.
Fig. 4.
Fig. 4. Experimental (symbols) and theoretical (lines) energetic variation of the diffraction efficiency (η) at different recording intensities

Tables (2)

Tables Icon

Table 1. Optimal parameters calculated from the fittings of the experimental angular selectivity curves obtained at different recording intensities. In all cases a0 = as = a= 0.

Tables Icon

Table 2. Theoretical parameters calculated from the fittings of the experimental energetic variations of the diffraction efficiency obtained at different recording intensities.

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

n x z = n 0 + n 1 ( z ) cos ( K x + Δφ ( z ) )
n 1 ( z ) = n 10 exp ( 2 α r z cos ( θ r ) )
Δφ ( z ) = 2 π n 0 ( a 0 + a 1 l + a 2 l ( 2 l ) + a 3 l ( 3 3 l + l 2 ) )
c R d R ( z ) d z + ( α + α s ) R ( z ) = F R S ( z )
c S d S ( z ) d z + ( α + α s ) S ( z ) = F S R ( z )
F R = i π λ r n 1 ( z ) exp ( i Δ φ ( z ) ) exp ( k z z )
F S = i π λ r n 1 ( z ) exp ( i Δ φ ( z ) ) exp ( i Δ k z z )
Δ k = k R k S K
Δ k z = K cos ( ϕ + θ r θ 0 )
c R = cos θ r
c S = cos ( 2 ϕ 2 θ 0 + θ r )
η = c S c R S ( d ) S * ( d )
n 10 ( E ) = n 10 f ( 1 exp ( β ( E E inh ) ) ) E > E inh n 10 ( E ) = 0 E < E inh
Δφ z E = 2 π n 0 ( a 0 + A 1 l + A 2 l ( 2 l ) + A 3 l ( 3 3 l + l 2 ) )
A 1 = a 1 ( 1 exp ( β 1 ( E E 0 ) ) ) E > E 0 A 2 = a 2 ( 1 exp ( β 2 ( E E 0 ) ) ) E > E 0 A 3 = a 3 ( 1 exp ( β 3 ( E E 0 ) ) ) E > E 0 A 1 = A 2 = A 3 = 0 E < E 0

Metrics