Abstract

The photosensitive properties of a centrosymmetric gadolinium gallium garnet crystal doped with calcium are investigated at room temperature. Elementary holograms can be recorded over a wide range of wavelengths in the visible spectral range. The photosensitive properties are studied experimentally using beam coupling and angular response experiments. Mixed absorption and refractive-index gratings are observed and their amplitudes and relative phases determined. Moreover, the candidate centers that are responsible for the photorefractive effect are discussed.

© 2006 Optical Society of America

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  2. A. S. Yurov, A. N. Karpov, V. K. Raev, G. E. Khodenkov, and M. P. Shorygin, “Displacement of a magnetic bubble by a Rayleigh surface wave in an iron garnet film containing bismuth,” Tech. Phys. Lett. 12, 83–4 (1986).
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    [CrossRef]
  4. C. S. Tsai, “Wideband tunable microwave devices using ferromagnetic film-gallium arsenide material structures,” J. Magn. Magn. Mater. 209, 10–14 (2000).
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  8. A. A. Danilov, E. Y. Nikirui, V. V. Osiko, V. G. Polushkin, S. N. Sorokin, and M. I. Timoshechkin, “Efficient laser with a rectangular active element,” Sov. J. Quantum Electron. 21, 264–6 (1991).
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    [CrossRef]
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  20. B. Crosignani, A. Degasperis, E. DelRe, P. Di-Porto, and A. J. Agranat, “Nonlinear Optical Diffraction Effects and Solitons Due to Anisotropic Charge-Diffusion-Based Self-Interaction,” Phys. Rev. Lett. 82, 1664–7 (1999).
    [CrossRef]
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  24. M. Pardavi-Horvath, J. Paitz, I. Földvari, I. Fellegvari, and L. Gosztonyi, “Spectroscopic Properties of Ca2+ -doped GGG,” Phys. Status Solidi (a) 84, 540–2 (1984).
    [CrossRef]
  25. M. Fally, M. Imlau, R. A. Rupp, M. A. Ellabban, and T. Woike, “Specific recording kinetics as a general property of unconventional photorefractive media,” Phys. Rev. Lett. 93(24), 243,903 (2004).
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    [CrossRef]
  28. A. Matkovskii, D. Sugak, S. Ubizskii, and I. Kityk, “Spectroscopy and radiation defects of the Gd3Ga5O12 single crystals,” Opto-Electron. Rev. 3, 41–53 (1995).
  29. E. Guibelalde, “Coupled wave analysis for out-of-phase mixed thick hologram gratings,” Opt. Quantum Electron. 16, 173 (1984).
    [CrossRef]
  30. V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, and M. S. Soskin, “Dynamic self-diffraction of coherent light beams,” Sov. Phys. Usp. 22, 742–756 (1979).
    [CrossRef]
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    [PubMed]

2004 (2)

A. Matkovskii, P. Potera, D. Sugak, L. Grigorjeva, D. Millers, V. Pankratov, and A. Suchocki, “Stable and transient color centers in Gd3Ga5O12 crystals,” Cryst. Res. Technol. 39, 788–795 (2004).
[CrossRef]

M. Fally, M. Imlau, R. A. Rupp, M. A. Ellabban, and T. Woike, “Specific recording kinetics as a general property of unconventional photorefractive media,” Phys. Rev. Lett. 93(24), 243,903 (2004).
[CrossRef]

2002 (1)

2000 (1)

C. S. Tsai, “Wideband tunable microwave devices using ferromagnetic film-gallium arsenide material structures,” J. Magn. Magn. Mater. 209, 10–14 (2000).
[CrossRef]

1999 (3)

M. Imlau, S. Haussühl, T. Woike, R. Schieder, V. Angelov, R. A. Rupp, and K. Schwarz, “Holographic Recording by Excitation of Metastable Electronic States in Na2[Fe(CN)5NO]∙2H2O: a new photorefractive effect,” Appl. Phys. B 68, 877–85 (1999).
[CrossRef]

B. Crosignani, A. Degasperis, E. DelRe, P. Di-Porto, and A. J. Agranat, “Nonlinear Optical Diffraction Effects and Solitons Due to Anisotropic Charge-Diffusion-Based Self-Interaction,” Phys. Rev. Lett. 82, 1664–7 (1999).
[CrossRef]

M. Imlau, T. Woike, R. Schieder, and R. A. Rupp, “Holographic Scattering in Centrosymmetric Na2[Fe(CN)5NO]∙2H2O,” Phys. Rev. Lett. 82, 2860–3 (1999).
[CrossRef]

1997 (1)

1995 (2)

B. Sugg, H. Nürge, B. Faust, E. Ruza, R. Niehüser, H. J. Reyher, R. A. Rupp, and L. Ackermann, “The Photorefractive Effect in Terbium Gallium Garnet,” Opt. Mat. 4, 343–7 (1995).
[CrossRef]

A. Matkovskii, D. Sugak, S. Ubizskii, and I. Kityk, “Spectroscopy and radiation defects of the Gd3Ga5O12 single crystals,” Opto-Electron. Rev. 3, 41–53 (1995).

1994 (1)

1993 (1)

1992 (2)

R. Hofmeister, A. Yariv, S. Yagi, and A. Agranat, “New Photorefractive Mechanism in Centrosymmetric Crystals: A Strain-Coordinated Jahn-Teller Relaxation,” Phys. Rev. Lett. 69, 1459–62 (1992).
[CrossRef] [PubMed]

R. Wolfe, “Thin films for non-reciprocal magneto-optic devices,” Thin Solid Films 216, 184–8 (1992).
[CrossRef]

1991 (4)

A. A. Danilov, E. Y. Nikirui, V. V. Osiko, V. G. Polushkin, S. N. Sorokin, and M. I. Timoshechkin, “Efficient laser with a rectangular active element,” Sov. J. Quantum Electron. 21, 264–6 (1991).
[CrossRef]

J. Dong and K. Lu, “Noncubic symmetry in garnet structures studied using extended x-ray-absorption fine-structure spectra,” Phys. Rev. B 43, 8808 (1991).
[CrossRef]

G. J. Pogatshnik, L. S. Cain, Y. Chen, and B. D. Evans, “Optical Properties of Color Centers in Calcium-Stabilized Gadolinium Gallium Garnets,” Phys. Rev. B 43, 1787–94 (1991).
[CrossRef]

A. O. Matkovskii, D. Y. Sugak, S. B. Ubizskii, U. A. Ulmanis, and A. P. Shakhov, “Radiation-Stimulated Processes in Gadolinium Gallium Garnet Single Crystals,” Phys. Status Solidi (a) 128, 21–29 (1991).
[CrossRef]

1990 (2)

D. L. Wood and K. Nassau, “Optical Properties of Gadolinium Gallium Garnet,” Appl. Opt. 29, 3704–7 (1990).
[CrossRef] [PubMed]

A. E. Krumins, R. A. Rupp, and J. A. Seglins, “Hologram Recording in PLZT Ceramics in the Vicinity of its Diffused Phase Transition,” Ferroelectrics 107, 53–8 (1990).
[CrossRef]

1989 (1)

L. Antos, M. Pardavi-Horvath, A. Cziraki, J. Fidler, and P. Skalicky, “Microstructure of Yttrium Iron Garnet Thin Films and of Gadolinium Gallium Garnet Single Crystals,” J. Cryst. Growth 94, 197–02 (1989).
[CrossRef]

1986 (1)

A. S. Yurov, A. N. Karpov, V. K. Raev, G. E. Khodenkov, and M. P. Shorygin, “Displacement of a magnetic bubble by a Rayleigh surface wave in an iron garnet film containing bismuth,” Tech. Phys. Lett. 12, 83–4 (1986).

1985 (1)

J. Marion, “Strengthened solid-state laser materials,” Appl. Phys. Lett. 47, 694–6 (1985).
[CrossRef]

1984 (2)

M. Pardavi-Horvath, J. Paitz, I. Földvari, I. Fellegvari, and L. Gosztonyi, “Spectroscopic Properties of Ca2+ -doped GGG,” Phys. Status Solidi (a) 84, 540–2 (1984).
[CrossRef]

E. Guibelalde, “Coupled wave analysis for out-of-phase mixed thick hologram gratings,” Opt. Quantum Electron. 16, 173 (1984).
[CrossRef]

1983 (1)

M. Pardavi-Horvath and M. Osvay, “Thermoluminescent Properties of Gadolinium Gallium Garnet Crystals Containing Ca2+ Impurity,” Phys. Status Solidi (a) 80, K183–5 (1983).
[CrossRef]

1982 (1)

E. Zharikov, N. Il’ichev, V. Laptev, A. Malyutin, V. Ostroumov, P. Pashinin, and I. Shcherbakov, “Sensitization of neodymium ion luminescence by chromium ions in a Gd3Ga5O12 crystal,” Sov. J. Quantum Electron. 12, 338–41 (1982).
[CrossRef]

1979 (1)

V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, and M. S. Soskin, “Dynamic self-diffraction of coherent light beams,” Sov. Phys. Usp. 22, 742–756 (1979).
[CrossRef]

1976 (2)

S. Yamamoto and T. Makimoto, “Design considerations for nonreciprocal integrated optical devices,” J. Appl. Phys. 47, 4056–60 (1976).
[CrossRef]

R. Metselaar, J. P. M. Damen, P. K. Larsen, and M. A. H. Huyberts, “Investigation of Colour Centres in Gadolinium Gallium Garnet Crystals,” Phys. Status Solidi (a) 34, 665–70 (1976).
[CrossRef]

1967 (1)

H. Brusset, H. Giller-Prandraud, and J. L. Bordot, “Investigations on Gallates of Rare Earth Metals and of Yttrium,” B. Soc. Chim. Fr. 4, 1206 (1967).

Ackermann, L.

B. Sugg, H. Nürge, B. Faust, E. Ruza, R. Niehüser, H. J. Reyher, R. A. Rupp, and L. Ackermann, “The Photorefractive Effect in Terbium Gallium Garnet,” Opt. Mat. 4, 343–7 (1995).
[CrossRef]

Agranat, A.

R. Hofmeister, A. Yariv, S. Yagi, and A. Agranat, “New Photorefractive Mechanism in Centrosymmetric Crystals: A Strain-Coordinated Jahn-Teller Relaxation,” Phys. Rev. Lett. 69, 1459–62 (1992).
[CrossRef] [PubMed]

Agranat, A. J.

B. Crosignani, A. Degasperis, E. DelRe, P. Di-Porto, and A. J. Agranat, “Nonlinear Optical Diffraction Effects and Solitons Due to Anisotropic Charge-Diffusion-Based Self-Interaction,” Phys. Rev. Lett. 82, 1664–7 (1999).
[CrossRef]

Angelov, V.

M. Imlau, S. Haussühl, T. Woike, R. Schieder, V. Angelov, R. A. Rupp, and K. Schwarz, “Holographic Recording by Excitation of Metastable Electronic States in Na2[Fe(CN)5NO]∙2H2O: a new photorefractive effect,” Appl. Phys. B 68, 877–85 (1999).
[CrossRef]

Antos, L.

L. Antos, M. Pardavi-Horvath, A. Cziraki, J. Fidler, and P. Skalicky, “Microstructure of Yttrium Iron Garnet Thin Films and of Gadolinium Gallium Garnet Single Crystals,” J. Cryst. Growth 94, 197–02 (1989).
[CrossRef]

Becla, P.

Beléndez, A.

Bordot, J. L.

H. Brusset, H. Giller-Prandraud, and J. L. Bordot, “Investigations on Gallates of Rare Earth Metals and of Yttrium,” B. Soc. Chim. Fr. 4, 1206 (1967).

Brusset, H.

H. Brusset, H. Giller-Prandraud, and J. L. Bordot, “Investigations on Gallates of Rare Earth Metals and of Yttrium,” B. Soc. Chim. Fr. 4, 1206 (1967).

Cain, L. S.

G. J. Pogatshnik, L. S. Cain, Y. Chen, and B. D. Evans, “Optical Properties of Color Centers in Calcium-Stabilized Gadolinium Gallium Garnets,” Phys. Rev. B 43, 1787–94 (1991).
[CrossRef]

Chadi, J.

Chen, Y.

G. J. Pogatshnik, L. S. Cain, Y. Chen, and B. D. Evans, “Optical Properties of Color Centers in Calcium-Stabilized Gadolinium Gallium Garnets,” Phys. Rev. B 43, 1787–94 (1991).
[CrossRef]

Chuang, E.

Crosignani, B.

B. Crosignani, A. Degasperis, E. DelRe, P. Di-Porto, and A. J. Agranat, “Nonlinear Optical Diffraction Effects and Solitons Due to Anisotropic Charge-Diffusion-Based Self-Interaction,” Phys. Rev. Lett. 82, 1664–7 (1999).
[CrossRef]

Cziraki, A.

L. Antos, M. Pardavi-Horvath, A. Cziraki, J. Fidler, and P. Skalicky, “Microstructure of Yttrium Iron Garnet Thin Films and of Gadolinium Gallium Garnet Single Crystals,” J. Cryst. Growth 94, 197–02 (1989).
[CrossRef]

Damen, J. P. M.

R. Metselaar, J. P. M. Damen, P. K. Larsen, and M. A. H. Huyberts, “Investigation of Colour Centres in Gadolinium Gallium Garnet Crystals,” Phys. Status Solidi (a) 34, 665–70 (1976).
[CrossRef]

Danilov, A. A.

A. A. Danilov, E. Y. Nikirui, V. V. Osiko, V. G. Polushkin, S. N. Sorokin, and M. I. Timoshechkin, “Efficient laser with a rectangular active element,” Sov. J. Quantum Electron. 21, 264–6 (1991).
[CrossRef]

Degasperis, A.

B. Crosignani, A. Degasperis, E. DelRe, P. Di-Porto, and A. J. Agranat, “Nonlinear Optical Diffraction Effects and Solitons Due to Anisotropic Charge-Diffusion-Based Self-Interaction,” Phys. Rev. Lett. 82, 1664–7 (1999).
[CrossRef]

DelRe, E.

B. Crosignani, A. Degasperis, E. DelRe, P. Di-Porto, and A. J. Agranat, “Nonlinear Optical Diffraction Effects and Solitons Due to Anisotropic Charge-Diffusion-Based Self-Interaction,” Phys. Rev. Lett. 82, 1664–7 (1999).
[CrossRef]

Devlin, G.

Di-Porto, P.

B. Crosignani, A. Degasperis, E. DelRe, P. Di-Porto, and A. J. Agranat, “Nonlinear Optical Diffraction Effects and Solitons Due to Anisotropic Charge-Diffusion-Based Self-Interaction,” Phys. Rev. Lett. 82, 1664–7 (1999).
[CrossRef]

Dong, J.

J. Dong and K. Lu, “Noncubic symmetry in garnet structures studied using extended x-ray-absorption fine-structure spectra,” Phys. Rev. B 43, 8808 (1991).
[CrossRef]

Ellabban, M. A.

M. Fally, M. Imlau, R. A. Rupp, M. A. Ellabban, and T. Woike, “Specific recording kinetics as a general property of unconventional photorefractive media,” Phys. Rev. Lett. 93(24), 243,903 (2004).
[CrossRef]

Evans, B. D.

G. J. Pogatshnik, L. S. Cain, Y. Chen, and B. D. Evans, “Optical Properties of Color Centers in Calcium-Stabilized Gadolinium Gallium Garnets,” Phys. Rev. B 43, 1787–94 (1991).
[CrossRef]

Fally, M.

M. Fally, M. Imlau, R. A. Rupp, M. A. Ellabban, and T. Woike, “Specific recording kinetics as a general property of unconventional photorefractive media,” Phys. Rev. Lett. 93(24), 243,903 (2004).
[CrossRef]

Faust, B.

B. Sugg, H. Nürge, B. Faust, E. Ruza, R. Niehüser, H. J. Reyher, R. A. Rupp, and L. Ackermann, “The Photorefractive Effect in Terbium Gallium Garnet,” Opt. Mat. 4, 343–7 (1995).
[CrossRef]

Fellegvari, I.

M. Pardavi-Horvath, J. Paitz, I. Földvari, I. Fellegvari, and L. Gosztonyi, “Spectroscopic Properties of Ca2+ -doped GGG,” Phys. Status Solidi (a) 84, 540–2 (1984).
[CrossRef]

Fidler, J.

L. Antos, M. Pardavi-Horvath, A. Cziraki, J. Fidler, and P. Skalicky, “Microstructure of Yttrium Iron Garnet Thin Films and of Gadolinium Gallium Garnet Single Crystals,” J. Cryst. Growth 94, 197–02 (1989).
[CrossRef]

Földvari, I.

M. Pardavi-Horvath, J. Paitz, I. Földvari, I. Fellegvari, and L. Gosztonyi, “Spectroscopic Properties of Ca2+ -doped GGG,” Phys. Status Solidi (a) 84, 540–2 (1984).
[CrossRef]

Giller-Prandraud, H.

H. Brusset, H. Giller-Prandraud, and J. L. Bordot, “Investigations on Gallates of Rare Earth Metals and of Yttrium,” B. Soc. Chim. Fr. 4, 1206 (1967).

Gosztonyi, L.

M. Pardavi-Horvath, J. Paitz, I. Földvari, I. Fellegvari, and L. Gosztonyi, “Spectroscopic Properties of Ca2+ -doped GGG,” Phys. Status Solidi (a) 84, 540–2 (1984).
[CrossRef]

Grigorjeva, L.

A. Matkovskii, P. Potera, D. Sugak, L. Grigorjeva, D. Millers, V. Pankratov, and A. Suchocki, “Stable and transient color centers in Gd3Ga5O12 crystals,” Cryst. Res. Technol. 39, 788–795 (2004).
[CrossRef]

Guibelalde, E.

E. Guibelalde, “Coupled wave analysis for out-of-phase mixed thick hologram gratings,” Opt. Quantum Electron. 16, 173 (1984).
[CrossRef]

Haussühl, S.

M. Imlau, S. Haussühl, T. Woike, R. Schieder, V. Angelov, R. A. Rupp, and K. Schwarz, “Holographic Recording by Excitation of Metastable Electronic States in Na2[Fe(CN)5NO]∙2H2O: a new photorefractive effect,” Appl. Phys. B 68, 877–85 (1999).
[CrossRef]

Hofmeister, R.

R. Hofmeister, A. Yariv, S. Yagi, and A. Agranat, “New Photorefractive Mechanism in Centrosymmetric Crystals: A Strain-Coordinated Jahn-Teller Relaxation,” Phys. Rev. Lett. 69, 1459–62 (1992).
[CrossRef] [PubMed]

Huyberts, M. A. H.

R. Metselaar, J. P. M. Damen, P. K. Larsen, and M. A. H. Huyberts, “Investigation of Colour Centres in Gadolinium Gallium Garnet Crystals,” Phys. Status Solidi (a) 34, 665–70 (1976).
[CrossRef]

Il’ichev, N.

E. Zharikov, N. Il’ichev, V. Laptev, A. Malyutin, V. Ostroumov, P. Pashinin, and I. Shcherbakov, “Sensitization of neodymium ion luminescence by chromium ions in a Gd3Ga5O12 crystal,” Sov. J. Quantum Electron. 12, 338–41 (1982).
[CrossRef]

Imlau, M.

M. Fally, M. Imlau, R. A. Rupp, M. A. Ellabban, and T. Woike, “Specific recording kinetics as a general property of unconventional photorefractive media,” Phys. Rev. Lett. 93(24), 243,903 (2004).
[CrossRef]

M. Imlau, T. Woike, R. Schieder, and R. A. Rupp, “Holographic Scattering in Centrosymmetric Na2[Fe(CN)5NO]∙2H2O,” Phys. Rev. Lett. 82, 2860–3 (1999).
[CrossRef]

M. Imlau, S. Haussühl, T. Woike, R. Schieder, V. Angelov, R. A. Rupp, and K. Schwarz, “Holographic Recording by Excitation of Metastable Electronic States in Na2[Fe(CN)5NO]∙2H2O: a new photorefractive effect,” Appl. Phys. B 68, 877–85 (1999).
[CrossRef]

Kahmann, F.

Karpov, A. N.

A. S. Yurov, A. N. Karpov, V. K. Raev, G. E. Khodenkov, and M. P. Shorygin, “Displacement of a magnetic bubble by a Rayleigh surface wave in an iron garnet film containing bismuth,” Tech. Phys. Lett. 12, 83–4 (1986).

Khodenkov, G. E.

A. S. Yurov, A. N. Karpov, V. K. Raev, G. E. Khodenkov, and M. P. Shorygin, “Displacement of a magnetic bubble by a Rayleigh surface wave in an iron garnet film containing bismuth,” Tech. Phys. Lett. 12, 83–4 (1986).

Kityk, I.

A. Matkovskii, D. Sugak, S. Ubizskii, and I. Kityk, “Spectroscopy and radiation defects of the Gd3Ga5O12 single crystals,” Opto-Electron. Rev. 3, 41–53 (1995).

Krumins, A. E.

A. E. Krumins, R. A. Rupp, and J. A. Seglins, “Hologram Recording in PLZT Ceramics in the Vicinity of its Diffused Phase Transition,” Ferroelectrics 107, 53–8 (1990).
[CrossRef]

Kukhtarev, N. V.

V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, and M. S. Soskin, “Dynamic self-diffraction of coherent light beams,” Sov. Phys. Usp. 22, 742–756 (1979).
[CrossRef]

Lam, J. F.

G. C. Valley and J. F. Lam, Theory of Photorefractive Effects in Electro-Optic Crystals, vol. 61 of Topics in Applied Physics, chap. 3, pp. 75–98 (Springer-Verlag, Berlin, 1988).

Laptev, V.

E. Zharikov, N. Il’ichev, V. Laptev, A. Malyutin, V. Ostroumov, P. Pashinin, and I. Shcherbakov, “Sensitization of neodymium ion luminescence by chromium ions in a Gd3Ga5O12 crystal,” Sov. J. Quantum Electron. 12, 338–41 (1982).
[CrossRef]

Larsen, P. K.

R. Metselaar, J. P. M. Damen, P. K. Larsen, and M. A. H. Huyberts, “Investigation of Colour Centres in Gadolinium Gallium Garnet Crystals,” Phys. Status Solidi (a) 34, 665–70 (1976).
[CrossRef]

Linke, R.

Lu, K.

J. Dong and K. Lu, “Noncubic symmetry in garnet structures studied using extended x-ray-absorption fine-structure spectra,” Phys. Rev. B 43, 8808 (1991).
[CrossRef]

MacDonald, R.

Makimoto, T.

S. Yamamoto and T. Makimoto, “Design considerations for nonreciprocal integrated optical devices,” J. Appl. Phys. 47, 4056–60 (1976).
[CrossRef]

Malyutin, A.

E. Zharikov, N. Il’ichev, V. Laptev, A. Malyutin, V. Ostroumov, P. Pashinin, and I. Shcherbakov, “Sensitization of neodymium ion luminescence by chromium ions in a Gd3Ga5O12 crystal,” Sov. J. Quantum Electron. 12, 338–41 (1982).
[CrossRef]

Marion, J.

J. Marion, “Strengthened solid-state laser materials,” Appl. Phys. Lett. 47, 694–6 (1985).
[CrossRef]

Matkovskii, A.

A. Matkovskii, P. Potera, D. Sugak, L. Grigorjeva, D. Millers, V. Pankratov, and A. Suchocki, “Stable and transient color centers in Gd3Ga5O12 crystals,” Cryst. Res. Technol. 39, 788–795 (2004).
[CrossRef]

A. Matkovskii, D. Sugak, S. Ubizskii, and I. Kityk, “Spectroscopy and radiation defects of the Gd3Ga5O12 single crystals,” Opto-Electron. Rev. 3, 41–53 (1995).

Matkovskii, A. O.

A. O. Matkovskii, D. Y. Sugak, S. B. Ubizskii, U. A. Ulmanis, and A. P. Shakhov, “Radiation-Stimulated Processes in Gadolinium Gallium Garnet Single Crystals,” Phys. Status Solidi (a) 128, 21–29 (1991).
[CrossRef]

Metselaar, R.

R. Metselaar, J. P. M. Damen, P. K. Larsen, and M. A. H. Huyberts, “Investigation of Colour Centres in Gadolinium Gallium Garnet Crystals,” Phys. Status Solidi (a) 34, 665–70 (1976).
[CrossRef]

Millers, D.

A. Matkovskii, P. Potera, D. Sugak, L. Grigorjeva, D. Millers, V. Pankratov, and A. Suchocki, “Stable and transient color centers in Gd3Ga5O12 crystals,” Cryst. Res. Technol. 39, 788–795 (2004).
[CrossRef]

Nassau, K.

Neipp, C.

Niehüser, R.

B. Sugg, H. Nürge, B. Faust, E. Ruza, R. Niehüser, H. J. Reyher, R. A. Rupp, and L. Ackermann, “The Photorefractive Effect in Terbium Gallium Garnet,” Opt. Mat. 4, 343–7 (1995).
[CrossRef]

Nikirui, E. Y.

A. A. Danilov, E. Y. Nikirui, V. V. Osiko, V. G. Polushkin, S. N. Sorokin, and M. I. Timoshechkin, “Efficient laser with a rectangular active element,” Sov. J. Quantum Electron. 21, 264–6 (1991).
[CrossRef]

Nürge, H.

B. Sugg, H. Nürge, B. Faust, E. Ruza, R. Niehüser, H. J. Reyher, R. A. Rupp, and L. Ackermann, “The Photorefractive Effect in Terbium Gallium Garnet,” Opt. Mat. 4, 343–7 (1995).
[CrossRef]

Odulov, S. G.

V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, and M. S. Soskin, “Dynamic self-diffraction of coherent light beams,” Sov. Phys. Usp. 22, 742–756 (1979).
[CrossRef]

Osiko, V. V.

A. A. Danilov, E. Y. Nikirui, V. V. Osiko, V. G. Polushkin, S. N. Sorokin, and M. I. Timoshechkin, “Efficient laser with a rectangular active element,” Sov. J. Quantum Electron. 21, 264–6 (1991).
[CrossRef]

Ostroumov, V.

E. Zharikov, N. Il’ichev, V. Laptev, A. Malyutin, V. Ostroumov, P. Pashinin, and I. Shcherbakov, “Sensitization of neodymium ion luminescence by chromium ions in a Gd3Ga5O12 crystal,” Sov. J. Quantum Electron. 12, 338–41 (1982).
[CrossRef]

Osvay, M.

M. Pardavi-Horvath and M. Osvay, “Thermoluminescent Properties of Gadolinium Gallium Garnet Crystals Containing Ca2+ Impurity,” Phys. Status Solidi (a) 80, K183–5 (1983).
[CrossRef]

Paitz, J.

M. Pardavi-Horvath, J. Paitz, I. Földvari, I. Fellegvari, and L. Gosztonyi, “Spectroscopic Properties of Ca2+ -doped GGG,” Phys. Status Solidi (a) 84, 540–2 (1984).
[CrossRef]

Pankratov, V.

A. Matkovskii, P. Potera, D. Sugak, L. Grigorjeva, D. Millers, V. Pankratov, and A. Suchocki, “Stable and transient color centers in Gd3Ga5O12 crystals,” Cryst. Res. Technol. 39, 788–795 (2004).
[CrossRef]

Pardavi-Horvath, M.

L. Antos, M. Pardavi-Horvath, A. Cziraki, J. Fidler, and P. Skalicky, “Microstructure of Yttrium Iron Garnet Thin Films and of Gadolinium Gallium Garnet Single Crystals,” J. Cryst. Growth 94, 197–02 (1989).
[CrossRef]

M. Pardavi-Horvath, J. Paitz, I. Földvari, I. Fellegvari, and L. Gosztonyi, “Spectroscopic Properties of Ca2+ -doped GGG,” Phys. Status Solidi (a) 84, 540–2 (1984).
[CrossRef]

M. Pardavi-Horvath and M. Osvay, “Thermoluminescent Properties of Gadolinium Gallium Garnet Crystals Containing Ca2+ Impurity,” Phys. Status Solidi (a) 80, K183–5 (1983).
[CrossRef]

Pascual, I.

Pashinin, P.

E. Zharikov, N. Il’ichev, V. Laptev, A. Malyutin, V. Ostroumov, P. Pashinin, and I. Shcherbakov, “Sensitization of neodymium ion luminescence by chromium ions in a Gd3Ga5O12 crystal,” Sov. J. Quantum Electron. 12, 338–41 (1982).
[CrossRef]

Pogatshnik, G. J.

G. J. Pogatshnik, L. S. Cain, Y. Chen, and B. D. Evans, “Optical Properties of Color Centers in Calcium-Stabilized Gadolinium Gallium Garnets,” Phys. Rev. B 43, 1787–94 (1991).
[CrossRef]

Polushkin, V. G.

A. A. Danilov, E. Y. Nikirui, V. V. Osiko, V. G. Polushkin, S. N. Sorokin, and M. I. Timoshechkin, “Efficient laser with a rectangular active element,” Sov. J. Quantum Electron. 21, 264–6 (1991).
[CrossRef]

Potera, P.

A. Matkovskii, P. Potera, D. Sugak, L. Grigorjeva, D. Millers, V. Pankratov, and A. Suchocki, “Stable and transient color centers in Gd3Ga5O12 crystals,” Cryst. Res. Technol. 39, 788–795 (2004).
[CrossRef]

Psaltis, D.

Raev, V. K.

A. S. Yurov, A. N. Karpov, V. K. Raev, G. E. Khodenkov, and M. P. Shorygin, “Displacement of a magnetic bubble by a Rayleigh surface wave in an iron garnet film containing bismuth,” Tech. Phys. Lett. 12, 83–4 (1986).

Redmond, I.

Reyher, H. J.

B. Sugg, H. Nürge, B. Faust, E. Ruza, R. Niehüser, H. J. Reyher, R. A. Rupp, and L. Ackermann, “The Photorefractive Effect in Terbium Gallium Garnet,” Opt. Mat. 4, 343–7 (1995).
[CrossRef]

Rupp, R. A.

M. Fally, M. Imlau, R. A. Rupp, M. A. Ellabban, and T. Woike, “Specific recording kinetics as a general property of unconventional photorefractive media,” Phys. Rev. Lett. 93(24), 243,903 (2004).
[CrossRef]

M. Imlau, T. Woike, R. Schieder, and R. A. Rupp, “Holographic Scattering in Centrosymmetric Na2[Fe(CN)5NO]∙2H2O,” Phys. Rev. Lett. 82, 2860–3 (1999).
[CrossRef]

M. Imlau, S. Haussühl, T. Woike, R. Schieder, V. Angelov, R. A. Rupp, and K. Schwarz, “Holographic Recording by Excitation of Metastable Electronic States in Na2[Fe(CN)5NO]∙2H2O: a new photorefractive effect,” Appl. Phys. B 68, 877–85 (1999).
[CrossRef]

B. Sugg, H. Nürge, B. Faust, E. Ruza, R. Niehüser, H. J. Reyher, R. A. Rupp, and L. Ackermann, “The Photorefractive Effect in Terbium Gallium Garnet,” Opt. Mat. 4, 343–7 (1995).
[CrossRef]

A. E. Krumins, R. A. Rupp, and J. A. Seglins, “Hologram Recording in PLZT Ceramics in the Vicinity of its Diffused Phase Transition,” Ferroelectrics 107, 53–8 (1990).
[CrossRef]

Ruza, E.

B. Sugg, H. Nürge, B. Faust, E. Ruza, R. Niehüser, H. J. Reyher, R. A. Rupp, and L. Ackermann, “The Photorefractive Effect in Terbium Gallium Garnet,” Opt. Mat. 4, 343–7 (1995).
[CrossRef]

Schieder, R.

M. Imlau, S. Haussühl, T. Woike, R. Schieder, V. Angelov, R. A. Rupp, and K. Schwarz, “Holographic Recording by Excitation of Metastable Electronic States in Na2[Fe(CN)5NO]∙2H2O: a new photorefractive effect,” Appl. Phys. B 68, 877–85 (1999).
[CrossRef]

M. Imlau, T. Woike, R. Schieder, and R. A. Rupp, “Holographic Scattering in Centrosymmetric Na2[Fe(CN)5NO]∙2H2O,” Phys. Rev. Lett. 82, 2860–3 (1999).
[CrossRef]

Schwarz, K.

M. Imlau, S. Haussühl, T. Woike, R. Schieder, V. Angelov, R. A. Rupp, and K. Schwarz, “Holographic Recording by Excitation of Metastable Electronic States in Na2[Fe(CN)5NO]∙2H2O: a new photorefractive effect,” Appl. Phys. B 68, 877–85 (1999).
[CrossRef]

Seglins, J. A.

A. E. Krumins, R. A. Rupp, and J. A. Seglins, “Hologram Recording in PLZT Ceramics in the Vicinity of its Diffused Phase Transition,” Ferroelectrics 107, 53–8 (1990).
[CrossRef]

Shakhov, A. P.

A. O. Matkovskii, D. Y. Sugak, S. B. Ubizskii, U. A. Ulmanis, and A. P. Shakhov, “Radiation-Stimulated Processes in Gadolinium Gallium Garnet Single Crystals,” Phys. Status Solidi (a) 128, 21–29 (1991).
[CrossRef]

Shcherbakov, I.

E. Zharikov, N. Il’ichev, V. Laptev, A. Malyutin, V. Ostroumov, P. Pashinin, and I. Shcherbakov, “Sensitization of neodymium ion luminescence by chromium ions in a Gd3Ga5O12 crystal,” Sov. J. Quantum Electron. 12, 338–41 (1982).
[CrossRef]

Shorygin, M. P.

A. S. Yurov, A. N. Karpov, V. K. Raev, G. E. Khodenkov, and M. P. Shorygin, “Displacement of a magnetic bubble by a Rayleigh surface wave in an iron garnet film containing bismuth,” Tech. Phys. Lett. 12, 83–4 (1986).

Skalicky, P.

L. Antos, M. Pardavi-Horvath, A. Cziraki, J. Fidler, and P. Skalicky, “Microstructure of Yttrium Iron Garnet Thin Films and of Gadolinium Gallium Garnet Single Crystals,” J. Cryst. Growth 94, 197–02 (1989).
[CrossRef]

Sorokin, S. N.

A. A. Danilov, E. Y. Nikirui, V. V. Osiko, V. G. Polushkin, S. N. Sorokin, and M. I. Timoshechkin, “Efficient laser with a rectangular active element,” Sov. J. Quantum Electron. 21, 264–6 (1991).
[CrossRef]

Soskin, M. S.

V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, and M. S. Soskin, “Dynamic self-diffraction of coherent light beams,” Sov. Phys. Usp. 22, 742–756 (1979).
[CrossRef]

Suchocki, A.

A. Matkovskii, P. Potera, D. Sugak, L. Grigorjeva, D. Millers, V. Pankratov, and A. Suchocki, “Stable and transient color centers in Gd3Ga5O12 crystals,” Cryst. Res. Technol. 39, 788–795 (2004).
[CrossRef]

Sugak, D.

A. Matkovskii, P. Potera, D. Sugak, L. Grigorjeva, D. Millers, V. Pankratov, and A. Suchocki, “Stable and transient color centers in Gd3Ga5O12 crystals,” Cryst. Res. Technol. 39, 788–795 (2004).
[CrossRef]

A. Matkovskii, D. Sugak, S. Ubizskii, and I. Kityk, “Spectroscopy and radiation defects of the Gd3Ga5O12 single crystals,” Opto-Electron. Rev. 3, 41–53 (1995).

Sugak, D. Y.

A. O. Matkovskii, D. Y. Sugak, S. B. Ubizskii, U. A. Ulmanis, and A. P. Shakhov, “Radiation-Stimulated Processes in Gadolinium Gallium Garnet Single Crystals,” Phys. Status Solidi (a) 128, 21–29 (1991).
[CrossRef]

Sugg, B.

B. Sugg, H. Nürge, B. Faust, E. Ruza, R. Niehüser, H. J. Reyher, R. A. Rupp, and L. Ackermann, “The Photorefractive Effect in Terbium Gallium Garnet,” Opt. Mat. 4, 343–7 (1995).
[CrossRef]

Thio, T.

Timoshechkin, M. I.

A. A. Danilov, E. Y. Nikirui, V. V. Osiko, V. G. Polushkin, S. N. Sorokin, and M. I. Timoshechkin, “Efficient laser with a rectangular active element,” Sov. J. Quantum Electron. 21, 264–6 (1991).
[CrossRef]

Tsai, C. S.

C. S. Tsai, “Wideband tunable microwave devices using ferromagnetic film-gallium arsenide material structures,” J. Magn. Magn. Mater. 209, 10–14 (2000).
[CrossRef]

Ubizskii, S.

A. Matkovskii, D. Sugak, S. Ubizskii, and I. Kityk, “Spectroscopy and radiation defects of the Gd3Ga5O12 single crystals,” Opto-Electron. Rev. 3, 41–53 (1995).

Ubizskii, S. B.

A. O. Matkovskii, D. Y. Sugak, S. B. Ubizskii, U. A. Ulmanis, and A. P. Shakhov, “Radiation-Stimulated Processes in Gadolinium Gallium Garnet Single Crystals,” Phys. Status Solidi (a) 128, 21–29 (1991).
[CrossRef]

Ulmanis, U. A.

A. O. Matkovskii, D. Y. Sugak, S. B. Ubizskii, U. A. Ulmanis, and A. P. Shakhov, “Radiation-Stimulated Processes in Gadolinium Gallium Garnet Single Crystals,” Phys. Status Solidi (a) 128, 21–29 (1991).
[CrossRef]

Valley, G. C.

G. C. Valley and J. F. Lam, Theory of Photorefractive Effects in Electro-Optic Crystals, vol. 61 of Topics in Applied Physics, chap. 3, pp. 75–98 (Springer-Verlag, Berlin, 1988).

Vinetskii, V. L.

V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, and M. S. Soskin, “Dynamic self-diffraction of coherent light beams,” Sov. Phys. Usp. 22, 742–756 (1979).
[CrossRef]

Woike, T.

M. Fally, M. Imlau, R. A. Rupp, M. A. Ellabban, and T. Woike, “Specific recording kinetics as a general property of unconventional photorefractive media,” Phys. Rev. Lett. 93(24), 243,903 (2004).
[CrossRef]

M. Imlau, T. Woike, R. Schieder, and R. A. Rupp, “Holographic Scattering in Centrosymmetric Na2[Fe(CN)5NO]∙2H2O,” Phys. Rev. Lett. 82, 2860–3 (1999).
[CrossRef]

M. Imlau, S. Haussühl, T. Woike, R. Schieder, V. Angelov, R. A. Rupp, and K. Schwarz, “Holographic Recording by Excitation of Metastable Electronic States in Na2[Fe(CN)5NO]∙2H2O: a new photorefractive effect,” Appl. Phys. B 68, 877–85 (1999).
[CrossRef]

Wolfe, R.

R. Wolfe, “Thin films for non-reciprocal magneto-optic devices,” Thin Solid Films 216, 184–8 (1992).
[CrossRef]

Wood, D. L.

Yagi, S.

R. Hofmeister, A. Yariv, S. Yagi, and A. Agranat, “New Photorefractive Mechanism in Centrosymmetric Crystals: A Strain-Coordinated Jahn-Teller Relaxation,” Phys. Rev. Lett. 69, 1459–62 (1992).
[CrossRef] [PubMed]

Yamamoto, S.

S. Yamamoto and T. Makimoto, “Design considerations for nonreciprocal integrated optical devices,” J. Appl. Phys. 47, 4056–60 (1976).
[CrossRef]

Yariv, A.

R. Hofmeister, A. Yariv, S. Yagi, and A. Agranat, “New Photorefractive Mechanism in Centrosymmetric Crystals: A Strain-Coordinated Jahn-Teller Relaxation,” Phys. Rev. Lett. 69, 1459–62 (1992).
[CrossRef] [PubMed]

Yurov, A. S.

A. S. Yurov, A. N. Karpov, V. K. Raev, G. E. Khodenkov, and M. P. Shorygin, “Displacement of a magnetic bubble by a Rayleigh surface wave in an iron garnet film containing bismuth,” Tech. Phys. Lett. 12, 83–4 (1986).

Zharikov, E.

E. Zharikov, N. Il’ichev, V. Laptev, A. Malyutin, V. Ostroumov, P. Pashinin, and I. Shcherbakov, “Sensitization of neodymium ion luminescence by chromium ions in a Gd3Ga5O12 crystal,” Sov. J. Quantum Electron. 12, 338–41 (1982).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

M. Imlau, S. Haussühl, T. Woike, R. Schieder, V. Angelov, R. A. Rupp, and K. Schwarz, “Holographic Recording by Excitation of Metastable Electronic States in Na2[Fe(CN)5NO]∙2H2O: a new photorefractive effect,” Appl. Phys. B 68, 877–85 (1999).
[CrossRef]

Appl. Phys. Lett. (1)

J. Marion, “Strengthened solid-state laser materials,” Appl. Phys. Lett. 47, 694–6 (1985).
[CrossRef]

B. Soc. Chim. Fr. (1)

H. Brusset, H. Giller-Prandraud, and J. L. Bordot, “Investigations on Gallates of Rare Earth Metals and of Yttrium,” B. Soc. Chim. Fr. 4, 1206 (1967).

Cryst. Res. Technol. (1)

A. Matkovskii, P. Potera, D. Sugak, L. Grigorjeva, D. Millers, V. Pankratov, and A. Suchocki, “Stable and transient color centers in Gd3Ga5O12 crystals,” Cryst. Res. Technol. 39, 788–795 (2004).
[CrossRef]

Ferroelectrics (1)

A. E. Krumins, R. A. Rupp, and J. A. Seglins, “Hologram Recording in PLZT Ceramics in the Vicinity of its Diffused Phase Transition,” Ferroelectrics 107, 53–8 (1990).
[CrossRef]

J. Appl. Phys. (1)

S. Yamamoto and T. Makimoto, “Design considerations for nonreciprocal integrated optical devices,” J. Appl. Phys. 47, 4056–60 (1976).
[CrossRef]

J. Cryst. Growth (1)

L. Antos, M. Pardavi-Horvath, A. Cziraki, J. Fidler, and P. Skalicky, “Microstructure of Yttrium Iron Garnet Thin Films and of Gadolinium Gallium Garnet Single Crystals,” J. Cryst. Growth 94, 197–02 (1989).
[CrossRef]

J. Magn. Magn. Mater. (1)

C. S. Tsai, “Wideband tunable microwave devices using ferromagnetic film-gallium arsenide material structures,” J. Magn. Magn. Mater. 209, 10–14 (2000).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Express (1)

Opt. Lett. (2)

Opt. Mat. (1)

B. Sugg, H. Nürge, B. Faust, E. Ruza, R. Niehüser, H. J. Reyher, R. A. Rupp, and L. Ackermann, “The Photorefractive Effect in Terbium Gallium Garnet,” Opt. Mat. 4, 343–7 (1995).
[CrossRef]

Opt. Quantum Electron. (1)

E. Guibelalde, “Coupled wave analysis for out-of-phase mixed thick hologram gratings,” Opt. Quantum Electron. 16, 173 (1984).
[CrossRef]

Opto-Electron. Rev. (1)

A. Matkovskii, D. Sugak, S. Ubizskii, and I. Kityk, “Spectroscopy and radiation defects of the Gd3Ga5O12 single crystals,” Opto-Electron. Rev. 3, 41–53 (1995).

Phys. Rev. B (2)

J. Dong and K. Lu, “Noncubic symmetry in garnet structures studied using extended x-ray-absorption fine-structure spectra,” Phys. Rev. B 43, 8808 (1991).
[CrossRef]

G. J. Pogatshnik, L. S. Cain, Y. Chen, and B. D. Evans, “Optical Properties of Color Centers in Calcium-Stabilized Gadolinium Gallium Garnets,” Phys. Rev. B 43, 1787–94 (1991).
[CrossRef]

Phys. Rev. Lett. (4)

R. Hofmeister, A. Yariv, S. Yagi, and A. Agranat, “New Photorefractive Mechanism in Centrosymmetric Crystals: A Strain-Coordinated Jahn-Teller Relaxation,” Phys. Rev. Lett. 69, 1459–62 (1992).
[CrossRef] [PubMed]

B. Crosignani, A. Degasperis, E. DelRe, P. Di-Porto, and A. J. Agranat, “Nonlinear Optical Diffraction Effects and Solitons Due to Anisotropic Charge-Diffusion-Based Self-Interaction,” Phys. Rev. Lett. 82, 1664–7 (1999).
[CrossRef]

M. Imlau, T. Woike, R. Schieder, and R. A. Rupp, “Holographic Scattering in Centrosymmetric Na2[Fe(CN)5NO]∙2H2O,” Phys. Rev. Lett. 82, 2860–3 (1999).
[CrossRef]

M. Fally, M. Imlau, R. A. Rupp, M. A. Ellabban, and T. Woike, “Specific recording kinetics as a general property of unconventional photorefractive media,” Phys. Rev. Lett. 93(24), 243,903 (2004).
[CrossRef]

Phys. Status Solidi (a) (4)

M. Pardavi-Horvath and M. Osvay, “Thermoluminescent Properties of Gadolinium Gallium Garnet Crystals Containing Ca2+ Impurity,” Phys. Status Solidi (a) 80, K183–5 (1983).
[CrossRef]

M. Pardavi-Horvath, J. Paitz, I. Földvari, I. Fellegvari, and L. Gosztonyi, “Spectroscopic Properties of Ca2+ -doped GGG,” Phys. Status Solidi (a) 84, 540–2 (1984).
[CrossRef]

R. Metselaar, J. P. M. Damen, P. K. Larsen, and M. A. H. Huyberts, “Investigation of Colour Centres in Gadolinium Gallium Garnet Crystals,” Phys. Status Solidi (a) 34, 665–70 (1976).
[CrossRef]

A. O. Matkovskii, D. Y. Sugak, S. B. Ubizskii, U. A. Ulmanis, and A. P. Shakhov, “Radiation-Stimulated Processes in Gadolinium Gallium Garnet Single Crystals,” Phys. Status Solidi (a) 128, 21–29 (1991).
[CrossRef]

Sov. J. Quantum Electron. (2)

E. Zharikov, N. Il’ichev, V. Laptev, A. Malyutin, V. Ostroumov, P. Pashinin, and I. Shcherbakov, “Sensitization of neodymium ion luminescence by chromium ions in a Gd3Ga5O12 crystal,” Sov. J. Quantum Electron. 12, 338–41 (1982).
[CrossRef]

A. A. Danilov, E. Y. Nikirui, V. V. Osiko, V. G. Polushkin, S. N. Sorokin, and M. I. Timoshechkin, “Efficient laser with a rectangular active element,” Sov. J. Quantum Electron. 21, 264–6 (1991).
[CrossRef]

Sov. Phys. Usp. (1)

V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, and M. S. Soskin, “Dynamic self-diffraction of coherent light beams,” Sov. Phys. Usp. 22, 742–756 (1979).
[CrossRef]

Tech. Phys. Lett. (1)

A. S. Yurov, A. N. Karpov, V. K. Raev, G. E. Khodenkov, and M. P. Shorygin, “Displacement of a magnetic bubble by a Rayleigh surface wave in an iron garnet film containing bismuth,” Tech. Phys. Lett. 12, 83–4 (1986).

Thin Solid Films (1)

R. Wolfe, “Thin films for non-reciprocal magneto-optic devices,” Thin Solid Films 216, 184–8 (1992).
[CrossRef]

Other (1)

G. C. Valley and J. F. Lam, Theory of Photorefractive Effects in Electro-Optic Crystals, vol. 61 of Topics in Applied Physics, chap. 3, pp. 75–98 (Springer-Verlag, Berlin, 1988).

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Figures (6)

Fig. 1.
Fig. 1.

Schematic of the experimental setups for recording gratings, performing rocking curves and beam-coupling experiments.

Fig. 2.
Fig. 2.

Absorption spectra of as-grown pure and calcium doped single crystals of GGG at room temperature. Inset: difference δαd = αdoped - αpure of the absorption coefficient between the doped and the pure GGG sample as a function of wavelength.

Fig. 3.
Fig. 3.

Spectral dependence of the absorption coefficient of a GGG:Ca crystal illuminated with UV, visible light and after a heat treatment (a). The inset shows photographs of the sample in the bleached and the colored state, respectively. The absorption difference spectra (b) are obtained by subtraction of the spectrum for the heat-treated reference sample.

Fig. 4.
Fig. 4.

Kinetics of the diffraction efficiency η R of the R-beam during recording an elementary grating at room temperature for two different wavelengths λw =458 and 514 nm (left scale). The light-induced change of the mean absorption coefficient α 0 is also shown (right scale).

Fig. 5.
Fig. 5.

Angular dependence of the ±1st order diffraction efficiency η R,S around the Bragg incidence. The grating was recorded and read out at λw = λr = 458 nm.

Fig. 6.
Fig. 6.

Beam coupling analysis with an external displacement of the recorded elementary hologram along its grating vector. λw = λr = 458 nm. The grating spacing Λ is indicated. Note, that the intensities of the coupled beams are dephased.

Equations (5)

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η R , S = ( n 1 π λ ) 2 + ( α 1 2 ) 2 ± n 1 πα 1 λ sin ( Δ φ ) X 2 + Y 2 [ sin 2 ( Xd ) + sinh 2 ( Yd ) ] .
η R η S = ( n 1 π λ ) 2 + ( α 1 2 ) 2 + n 1 πα 1 λ sin ( Δ φ ) ( n 1 π λ ) 2 + ( α 1 2 ) 2 n 1 πα 1 λ sin ( Δ φ ) .
a R : = A R 2 R ̂ + R ̂ + * + A S 2 S ̂ S ̂ * a S : = A S 2 R ̂ + R ̂ + * + A R 2 S ̂ S ̂ *
b R : = 2 A R A S { R ̂ + * S ̂ e i Φ } b S : = 2 A R A S { R ̂ * S ̂ + * e i Φ }
c R : = 2 A R A S { R ̂ + * S ̂ ie i Φ } c S : = 2 A R A S { R ̂ - S ̂ + * ie i Φ } .

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