Abstract

Hologram recording is studied in thermally reduced, nominally undoped lithium niobate in the time domain from 10 ns to 100 s by means of intense ns pump laser pulses (λ = 532 nm) and continuous-wave probe light (λ = 785 nm). It is shown that mixed absorption and phase gratings can be recorded within 8 ns that feature diffraction efficiencies up to 23 % with non-exponential relaxation and lifetimes in the ms-regime. The results are explained comprehensively in the frame of the optical generation of a spatial density modulation of NbLi4+/5+ antisites and the related optical features, i.e. absorption as well as index changes mutually related via the Kramers-Kronig-relation. Implications of our findings, such as the electrooptical properties of small bound NbLi4+ polarons, the optical features of NbLi4+:NbNb4+ bipolarons, NbNb4+ free polarons and O hole-polarons, the impact of light polarization of pump and probe beams as well as of the polaron density are discussed.

© 2011 OSA

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  7. J. Shi, H. Fritze, G. Borchardt, and K. D. Becker, “Defect chemistry, redox kinetics, and chemical diffusion of lithium deficient lithium niobate,” Phys. Chem. Chem. Phys. 13, 6925 (2011)
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  32. S. Torbruegge, M. Imlau, B. Schoke, C. Merschjann, O. F. Schirmer, S. Vernay, A. Gross, V. Wesemann, and D. Rytz, “Optically generated small electron and hole polarons in nominally undoped and Fe-doped KNbO3 investigated by transient absorption spectroscopy,” Phys. Rev. B 78, 125112 (2008).
    [CrossRef]
  33. D. Conradi, C. Merschjann, B. Schoke, M. Imlau, G. Corradi, and K. Polgár, “Influence of Mg doping on the behaviour of polaronic light-induced absorption in LiNbO3,” Phys. Stat. Sol. RRL 2, 284 (2008).
    [CrossRef]
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  35. O. F. Schirmer and D. von der Linde, “Two-photon and X–Ray–Induced Nb4+ and O− small polarons in LiNbO3,” Appl. Phys. Lett. 33, 35 (1978).
    [CrossRef]
  36. B. Faust, H. Müller, and O. F. Schirmer, “Free small polarons in LiNbO3,” Ferroelectrics 153, 297 (1994).
    [CrossRef]
  37. H. Kurz, E. Krätzig, W. Keune, H. Engelmann, U. Gonser, B. Dischler, and A. Räuber, “Photorefractive centers in LiNbO3, studied by optical–, Mössbauer– and EPR–methods,” Appl. Phys. 12, 355 (1977).
    [CrossRef]
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    [CrossRef]
  40. B. Schoke, M. Imlau, H. Brüning, C. Merschjann, G. Corradi, K. Polgár, and I. I. Naumova, “Transient light-induced absorption in periodically poled lithium niobate: small polaron hopping in the presence of a spatially modulated defect concentration,” Phys. Rev. B 81, 132301 (2010).
    [CrossRef]
  41. I. G. Austin and N. F. Mott, “Polarons in crystalline and non-crystalline materials,” Adv. Phys. 18, 41 (1969).
    [CrossRef]
  42. M. Jazbinsek and M. Zgonik, “Material tensor parameters of LiNbO3 relevant for electro- and elasto-optics,” Appl. Phys. B 74, 407 (2002).
    [CrossRef]
  43. T. Fujiwara, M. Takahasi, M. Ohama, A. J. Ikushima, Y. Furukawa, and K. Kitamura, “Comparison of electrooptic effect between stoichiometric and congruent LiNbO3,” Electron. Lett. 35, 499 (1999).
    [CrossRef]
  44. S. Fries and S. Bauschulte, “Wavelength dependence of the electrooptic coefficients in LiNbO3:Fe,” Phys. Status Solidi A 125, 369 (1991).
    [CrossRef]
  45. A. M. Glass, D. von der Linde, and T. J. Negran, “High-voltage bulk photovoltaic effect and the photorefractive process in LiNbO3,” Appl. Phys. Lett. 25, 233 (1974).
    [CrossRef]
  46. O. F. Schirmer, S. Juppe, and J. Koppitz, “ESR–, optical and photovoltaic studies of reduced undoped LiNbO3,” Cryst. Lattice Defects Amorphous Mater. 16, 353 (1987).
  47. N. V. Kukhtarev, “Kinetics of hologram recording and erasure in electrooptic crystals,” Sov. Tech. Phys. Lett. 2, 438 (1976).

2011

J. Shi, H. Fritze, G. Borchardt, and K. D. Becker, “Defect chemistry, redox kinetics, and chemical diffusion of lithium deficient lithium niobate,” Phys. Chem. Chem. Phys. 13, 6925 (2011)
[CrossRef] [PubMed]

O. F. Schirmer, M. Imlau, and C. Merschjann, “Bulk photovoltaic effect of LiNbO3:Fe and its small-polaron-based microscopic interpretation,” Phys. Rev. B 83, 165106 (2011).
[CrossRef]

2010

B. Schoke, M. Imlau, H. Brüning, C. Merschjann, G. Corradi, K. Polgár, and I. I. Naumova, “Transient light-induced absorption in periodically poled lithium niobate: small polaron hopping in the presence of a spatially modulated defect concentration,” Phys. Rev. B 81, 132301 (2010).
[CrossRef]

2009

C. Merschjann, B. Schoke, D. Conradi, M. Imlau, G. Corradi, and K. Polgar, “Absorption cross sections and number densities of electron and hole polarons in congruently melting LiNbO3,” J. Phys.: Condens. Matter 21, 015906 (2009).
[CrossRef]

O. F. Schirmer, M. Imlau, C. Merschjann, and B. Schoke, “Electron small polarons and bipolarons in LiNbO3,” J. Phys.: Condens. Matter 21, 123201 (2009).
[CrossRef]

S. Sasamoto, J. Hirohashi, and S. Ashihara, “Polaron dynamics in lithium niobate upon femtosecond pulse irradiation: influence of magnesium doping and stoichiometry control,” J. Appl. Phys. 105, 083102 (2009).
[CrossRef]

2008

S. Torbruegge, M. Imlau, B. Schoke, C. Merschjann, O. F. Schirmer, S. Vernay, A. Gross, V. Wesemann, and D. Rytz, “Optically generated small electron and hole polarons in nominally undoped and Fe-doped KNbO3 investigated by transient absorption spectroscopy,” Phys. Rev. B 78, 125112 (2008).
[CrossRef]

D. Conradi, C. Merschjann, B. Schoke, M. Imlau, G. Corradi, and K. Polgár, “Influence of Mg doping on the behaviour of polaronic light-induced absorption in LiNbO3,” Phys. Stat. Sol. RRL 2, 284 (2008).
[CrossRef]

2007

C. Merschjann, B. Schoke, and M. Imlau, “Influence of chemical reduction on the particular number densities of light-induced small electron and hole polarons in nominally pure LiNbO3,” Phys. Rev. B 76, 085114 (2007).
[CrossRef]

2006

O. F. Schirmer, “O− bound small polarons in oxide materials,” J. Phys.: Condens. Matter 18, R667 (2006).
[CrossRef]

O. Beyer, D. Maxein, Th. Woike, and K. Buse, “Generation of small bound polarons in lithium niobate crystals on the subpicosecond time scale,” Appl. Phys. B 83, 527 (2006).
[CrossRef]

2005

P. Herth, T. Granzow, D. Schaniel, Th. Woike, M. Imlau, and E. Krätzig, “Evidence for light-induced hole polarons in LiNbO3,” Phys. Rev. Lett. 95, 067404 (2005).
[CrossRef] [PubMed]

Y. Qiu, K. B. Ucer, and R. T. Williams, “Formation time of a small electron polaron in LiNbO3: measurements and interpretation,” Phys. Status Solidi C 2, 232 (2005).
[CrossRef]

J. Carnicero, M. Carrascosa, G. García, and F. Agulló-López, “Site correlation effects in the dynamics of iron impurities Fe2+/Fe3+ and antisite defects NbLi4+/NbLi5+ after a short-pulse excitation in LiNbO3,” Phys. Rev. B 72, 245108 (2005).
[CrossRef]

P. Herth, D. Schaniel, Th. Woike, T. Granzow, M. Imlau, and E. Krätzig, “Polarons generated by laser pulses in doped LiNbO3,” Phys. Rev. B 71, 125128 (2005).
[CrossRef]

2004

L. Arizmendi, “Photonic applications of lithium niobate crystals,” Phys. Status Solidi A 201, 253 (2004).
[CrossRef]

2003

M. M. Chirila, N. Y. Garces, L. E. Halliburton, S. G. Demos, T. A. Land, and H. B. Radousky, “Production and thermal decay of radiation-induced point defects in KD2PO4 crystals,” J. Appl. Phys. 94, 6456 (2003).
[CrossRef]

W. Hong, L. E. Halliburton, K. T. Stevens, D. Perlov, G. C. Catella, R. K. Route, and R. S. Feigelson, “Electron paramagnetic resoncance study of electron and hole traps in β-BaB2O4 crystals,” J. Appl. Phys 94, 2510 (2003).
[CrossRef]

2002

M. Jazbinsek and M. Zgonik, “Material tensor parameters of LiNbO3 relevant for electro- and elasto-optics,” Appl. Phys. B 74, 407 (2002).
[CrossRef]

2000

D. Berben, K. Buse, S. Wevering, P. Herth, M. Imlau, and Th. Woike, “Lifetime of small polarons in iron-doped lithium–niobate crystals,” J. Appl. Phys. 87, 1034–1041 (2000).
[CrossRef]

1999

T. Fujiwara, M. Takahasi, M. Ohama, A. J. Ikushima, Y. Furukawa, and K. Kitamura, “Comparison of electrooptic effect between stoichiometric and congruent LiNbO3,” Electron. Lett. 35, 499 (1999).
[CrossRef]

1998

L. Hesselink, S. S. Orlov, A. Lie, A. Akella, D. Lande, and R. R. Neurgaonkar, “Photorefractive materials for nonvolatile volume holographic data storage,” Science 282, 1089 (1998).
[CrossRef] [PubMed]

K. Buse, A. Adibi, and D. Psaltis, “Non-volatile holographic storage in doubly doped lithium niobate crystals,” Nature 393, 665 (1998).
[CrossRef]

1994

F. Jermann and K. Buse, “Light-induced thermal gratings in LiNbO3:Fe,” Appl. Phys. B 59, 437 (1994).
[CrossRef]

B. Faust, H. Müller, and O. F. Schirmer, “Free small polarons in LiNbO3,” Ferroelectrics 153, 297 (1994).
[CrossRef]

1993

F. Jermann and J. Otten, “Light-induced charge transport in LiNbO3:Fe at high light intensities,” J. Opt. Soc. Am. B 10, 2085 (1993).
[CrossRef]

D. Emin, “Optical properties of large and small polarons and bipolarons,” Phys. Rev. B 48, 13691 (1993).
[CrossRef]

1991

S. Fries and S. Bauschulte, “Wavelength dependence of the electrooptic coefficients in LiNbO3:Fe,” Phys. Status Solidi A 125, 369 (1991).
[CrossRef]

1987

O. F. Schirmer, S. Juppe, and J. Koppitz, “ESR–, optical and photovoltaic studies of reduced undoped LiNbO3,” Cryst. Lattice Defects Amorphous Mater. 16, 353 (1987).

J. Koppitz, O. F. Schirmer, and A. I. Kuznetsov, “Thermal dissociation of bipolarons in reduced undoped LiNbO3,” Europhys. Lett. 4, 1055 (1987).
[CrossRef]

1985

R. S. Weis and T. K. Gaylord, “Lithium niobate: summery of physical properties and crystal structure,” Appl. Phys. A 37, 191–203 (1985).
[CrossRef]

1983

K. L. Sweeney and L. E. Halliburton, “Oxygen vacancies in lithium niobate,” Appl. Phys. Lett 43, 336 (1983).
[CrossRef]

1978

O. F. Schirmer and D. von der Linde, “Two-photon and X–Ray–Induced Nb4+ and O− small polarons in LiNbO3,” Appl. Phys. Lett. 33, 35 (1978).
[CrossRef]

1977

H. Kurz, E. Krätzig, W. Keune, H. Engelmann, U. Gonser, B. Dischler, and A. Räuber, “Photorefractive centers in LiNbO3, studied by optical–, Mössbauer– and EPR–methods,” Appl. Phys. 12, 355 (1977).
[CrossRef]

1976

D. S. Smith, H. D. Riccius, and R. P. Edwin, “Refractive indices of lithium niobate,” Opt. Commun. 17, 332 (1976).
[CrossRef]

N. V. Kukhtarev, “Kinetics of hologram recording and erasure in electrooptic crystals,” Sov. Tech. Phys. Lett. 2, 438 (1976).

1975

D. Emin, “Phonon-assisted transition rates I. optical-phonon-assisted hopping in solids,” Adv. Phys. 24, 305 (1975).
[CrossRef]

1974

D. Redfield and W. J. Burke, “Optical absorption edge of LiNbO3,” J. Appl. Phys. 45, 4566 (1974)
[CrossRef]

A. M. Glass, D. von der Linde, and T. J. Negran, “High-voltage bulk photovoltaic effect and the photorefractive process in LiNbO3,” Appl. Phys. Lett. 25, 233 (1974).
[CrossRef]

1970

G. Williams and D. C. Watts, “Non–symmetrical dielectric relaxation behaviour arising from a simple empirical decay function,” Trans. Faraday Soc 66, 80 (1970).
[CrossRef]

1969

I. G. Austin and N. F. Mott, “Polarons in crystalline and non-crystalline materials,” Adv. Phys. 18, 41 (1969).
[CrossRef]

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

1864

C. Merschjann, D. Berben, M. Imlau, and M. Wöhlecke, “Evidence for two-path recombination of photoinduced small polarons in reduced LiNbO3,” Phys. Rev. Lett. 96, 186404 (2006).

Adibi, A.

K. Buse, A. Adibi, and D. Psaltis, “Non-volatile holographic storage in doubly doped lithium niobate crystals,” Nature 393, 665 (1998).
[CrossRef]

Agulló-López, F.

J. Carnicero, M. Carrascosa, G. García, and F. Agulló-López, “Site correlation effects in the dynamics of iron impurities Fe2+/Fe3+ and antisite defects NbLi4+/NbLi5+ after a short-pulse excitation in LiNbO3,” Phys. Rev. B 72, 245108 (2005).
[CrossRef]

Akella, A.

L. Hesselink, S. S. Orlov, A. Lie, A. Akella, D. Lande, and R. R. Neurgaonkar, “Photorefractive materials for nonvolatile volume holographic data storage,” Science 282, 1089 (1998).
[CrossRef] [PubMed]

Arizmendi, L.

L. Arizmendi, “Photonic applications of lithium niobate crystals,” Phys. Status Solidi A 201, 253 (2004).
[CrossRef]

Ashihara, S.

S. Sasamoto, J. Hirohashi, and S. Ashihara, “Polaron dynamics in lithium niobate upon femtosecond pulse irradiation: influence of magnesium doping and stoichiometry control,” J. Appl. Phys. 105, 083102 (2009).
[CrossRef]

Austin, I. G.

I. G. Austin and N. F. Mott, “Polarons in crystalline and non-crystalline materials,” Adv. Phys. 18, 41 (1969).
[CrossRef]

Bauschulte, S.

S. Fries and S. Bauschulte, “Wavelength dependence of the electrooptic coefficients in LiNbO3:Fe,” Phys. Status Solidi A 125, 369 (1991).
[CrossRef]

Becker, K. D.

J. Shi, H. Fritze, G. Borchardt, and K. D. Becker, “Defect chemistry, redox kinetics, and chemical diffusion of lithium deficient lithium niobate,” Phys. Chem. Chem. Phys. 13, 6925 (2011)
[CrossRef] [PubMed]

Berben, D.

D. Berben, K. Buse, S. Wevering, P. Herth, M. Imlau, and Th. Woike, “Lifetime of small polarons in iron-doped lithium–niobate crystals,” J. Appl. Phys. 87, 1034–1041 (2000).
[CrossRef]

C. Merschjann, D. Berben, M. Imlau, and M. Wöhlecke, “Evidence for two-path recombination of photoinduced small polarons in reduced LiNbO3,” Phys. Rev. Lett. 96, 186404 (2006).

Beyer, O.

O. Beyer, D. Maxein, Th. Woike, and K. Buse, “Generation of small bound polarons in lithium niobate crystals on the subpicosecond time scale,” Appl. Phys. B 83, 527 (2006).
[CrossRef]

Borchardt, G.

J. Shi, H. Fritze, G. Borchardt, and K. D. Becker, “Defect chemistry, redox kinetics, and chemical diffusion of lithium deficient lithium niobate,” Phys. Chem. Chem. Phys. 13, 6925 (2011)
[CrossRef] [PubMed]

Brüning, H.

B. Schoke, M. Imlau, H. Brüning, C. Merschjann, G. Corradi, K. Polgár, and I. I. Naumova, “Transient light-induced absorption in periodically poled lithium niobate: small polaron hopping in the presence of a spatially modulated defect concentration,” Phys. Rev. B 81, 132301 (2010).
[CrossRef]

Burke, W. J.

D. Redfield and W. J. Burke, “Optical absorption edge of LiNbO3,” J. Appl. Phys. 45, 4566 (1974)
[CrossRef]

Buse, K.

O. Beyer, D. Maxein, Th. Woike, and K. Buse, “Generation of small bound polarons in lithium niobate crystals on the subpicosecond time scale,” Appl. Phys. B 83, 527 (2006).
[CrossRef]

D. Berben, K. Buse, S. Wevering, P. Herth, M. Imlau, and Th. Woike, “Lifetime of small polarons in iron-doped lithium–niobate crystals,” J. Appl. Phys. 87, 1034–1041 (2000).
[CrossRef]

K. Buse, A. Adibi, and D. Psaltis, “Non-volatile holographic storage in doubly doped lithium niobate crystals,” Nature 393, 665 (1998).
[CrossRef]

F. Jermann and K. Buse, “Light-induced thermal gratings in LiNbO3:Fe,” Appl. Phys. B 59, 437 (1994).
[CrossRef]

Carnicero, J.

J. Carnicero, M. Carrascosa, G. García, and F. Agulló-López, “Site correlation effects in the dynamics of iron impurities Fe2+/Fe3+ and antisite defects NbLi4+/NbLi5+ after a short-pulse excitation in LiNbO3,” Phys. Rev. B 72, 245108 (2005).
[CrossRef]

Carrascosa, M.

J. Carnicero, M. Carrascosa, G. García, and F. Agulló-López, “Site correlation effects in the dynamics of iron impurities Fe2+/Fe3+ and antisite defects NbLi4+/NbLi5+ after a short-pulse excitation in LiNbO3,” Phys. Rev. B 72, 245108 (2005).
[CrossRef]

Catella, G. C.

W. Hong, L. E. Halliburton, K. T. Stevens, D. Perlov, G. C. Catella, R. K. Route, and R. S. Feigelson, “Electron paramagnetic resoncance study of electron and hole traps in β-BaB2O4 crystals,” J. Appl. Phys 94, 2510 (2003).
[CrossRef]

Chirila, M. M.

M. M. Chirila, N. Y. Garces, L. E. Halliburton, S. G. Demos, T. A. Land, and H. B. Radousky, “Production and thermal decay of radiation-induced point defects in KD2PO4 crystals,” J. Appl. Phys. 94, 6456 (2003).
[CrossRef]

Conradi, D.

C. Merschjann, B. Schoke, D. Conradi, M. Imlau, G. Corradi, and K. Polgar, “Absorption cross sections and number densities of electron and hole polarons in congruently melting LiNbO3,” J. Phys.: Condens. Matter 21, 015906 (2009).
[CrossRef]

D. Conradi, C. Merschjann, B. Schoke, M. Imlau, G. Corradi, and K. Polgár, “Influence of Mg doping on the behaviour of polaronic light-induced absorption in LiNbO3,” Phys. Stat. Sol. RRL 2, 284 (2008).
[CrossRef]

Corradi, G.

B. Schoke, M. Imlau, H. Brüning, C. Merschjann, G. Corradi, K. Polgár, and I. I. Naumova, “Transient light-induced absorption in periodically poled lithium niobate: small polaron hopping in the presence of a spatially modulated defect concentration,” Phys. Rev. B 81, 132301 (2010).
[CrossRef]

C. Merschjann, B. Schoke, D. Conradi, M. Imlau, G. Corradi, and K. Polgar, “Absorption cross sections and number densities of electron and hole polarons in congruently melting LiNbO3,” J. Phys.: Condens. Matter 21, 015906 (2009).
[CrossRef]

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P. Herth, T. Granzow, D. Schaniel, Th. Woike, M. Imlau, and E. Krätzig, “Evidence for light-induced hole polarons in LiNbO3,” Phys. Rev. Lett. 95, 067404 (2005).
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C. Merschjann, B. Schoke, D. Conradi, M. Imlau, G. Corradi, and K. Polgar, “Absorption cross sections and number densities of electron and hole polarons in congruently melting LiNbO3,” J. Phys.: Condens. Matter 21, 015906 (2009).
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D. Conradi, C. Merschjann, B. Schoke, M. Imlau, G. Corradi, and K. Polgár, “Influence of Mg doping on the behaviour of polaronic light-induced absorption in LiNbO3,” Phys. Stat. Sol. RRL 2, 284 (2008).
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H. Kurz, E. Krätzig, W. Keune, H. Engelmann, U. Gonser, B. Dischler, and A. Räuber, “Photorefractive centers in LiNbO3, studied by optical–, Mössbauer– and EPR–methods,” Appl. Phys. 12, 355 (1977).
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P. Herth, T. Granzow, D. Schaniel, Th. Woike, M. Imlau, and E. Krätzig, “Evidence for light-induced hole polarons in LiNbO3,” Phys. Rev. Lett. 95, 067404 (2005).
[CrossRef] [PubMed]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

C. Merschjann, B. Schoke, D. Conradi, M. Imlau, G. Corradi, and K. Polgar, “Absorption cross sections and number densities of electron and hole polarons in congruently melting LiNbO3,” J. Phys.: Condens. Matter 21, 015906 (2009).
[CrossRef]

O. F. Schirmer, M. Imlau, C. Merschjann, and B. Schoke, “Electron small polarons and bipolarons in LiNbO3,” J. Phys.: Condens. Matter 21, 123201 (2009).
[CrossRef]

D. Conradi, C. Merschjann, B. Schoke, M. Imlau, G. Corradi, and K. Polgár, “Influence of Mg doping on the behaviour of polaronic light-induced absorption in LiNbO3,” Phys. Stat. Sol. RRL 2, 284 (2008).
[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef] [PubMed]

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Figures (7)

Fig. 1
Fig. 1

Scheme of the experimental setup for hologram recording as described in the text. PP: electromechanical pulse picker, BS: 50% : 50% beam splitter, GP: Glan-Taylor prism, λ/2: half-wave plate, M1-M5: dielectric mirrors, DP: diaphragm, D1-D3: Si-PIN diodes, DS: optical delay stage, DSO: digital storage oscilloscope, FC: fiber collimator with wave plate and polarizer.

Fig. 2
Fig. 2

Temporal dynamics of the intensity of the first order diffracted beam I (1st) for (a) Kc-axis, e p || c-axis, s-polarization and (b) K || c-axis, e p || c-axis and p-polarization. Recording conditions: λ p = 532 nm, ΘB = 11.5°, spatial frequency Λ ≈ 1.3μm, I p = I R + I S = 380 GW/m2 and 230 GW/m2, respectively. Bragg-matched probing conditions: λ = 785 nm, e || c-axis with (a) s- and (b) p-polarization. The data are normalized to the intensity of the incoming probe beam I 0 and a logarithmic time scale is applied. The solid lines correspond to a fit of a stretched-exponential function Eq. (1) to the data set. The insets sketch the respective recording and probing configurations.

Fig. 3
Fig. 3

Angular dependence of the intensity of the normalized first order diffracted beam I (1st)/I 0 at t = 1μs after the pump pulse as a function of the deviation δΘ of the Bragg-angle ΘB (external values). The solid line represents the result of fitting Eq. (6) to the experimental data.

Fig. 4
Fig. 4

The temporal dynamics of the light-induced absorption α li determined for the sample under study and for probing light at λ = 785 nm and λ = 488 nm. The intensity of the pump beam at λ p = 532 nm was I p = 760 GW/m2 with e p || e || c-axis and s-polarization. The solid lines are the results of fitting Eq. (2) to the experimental data sets. The inset sketches the experimental arrangement of pump and probe beams.

Fig. 5
Fig. 5

Polaron generation in thermally reduced lithium niobate upon exposure to ns laser pulses. Left: optical gating of Nb Li 4 + : Nb Nb 4 + bipolarons into small bound Nb Li 4 + and free Nb Nb 4 + polarons. Right: two-photon excitation yielding O hole as well as bound and free polarons. The valencies of the individual centers correspond to the sketched location of electrons and holes at the trap centers (left) and in the valence band (right).

Fig. 6
Fig. 6

(a) Sinusoidal intensity pattern I(x) applied for exposure in our experiments with average intensity I p = I R + I S and modulation depth unity, spatially periodic density modulations of small bound polarons N GP(x), hole polarons N HP(x) and bipolarons N BP(x). (b) Spatial modulation of the absorption coefficient α(x) with amplitude α 1 and average value of α + α 1. The overall absorption change in the maximum of the fringe pattern α li = 2α 1 is assembled from absorption changes of the individual polaron type: α li,GP, α li,HP and α li,BP. All absorption contributions are related to λ = 785 nm and extraordinary light polarization.

Fig. 7
Fig. 7

Spectral dependence of α li(λ) determined from the analysis of the experimentally determined light-induced absorption at 785 nm and 488 nm, the literature data on polaron absorption cross sections and the previously published experimental band shapes of small polarons. The dispersion n li(λ) is calculated from α li(λ) applying the Kramers-Kronig-relation, Eq. (6). For details see text.

Tables (6)

Tables Icon

Table 1 Dimension, Orientation, Fe Content and Thermal Pre-Treatment Parameters of the Lithium Niobate Sample under Study

Tables Icon

Table 2 Steady-State Absorption αo/e , Polaron Absorption Cross Section σo/e at λ = 488 nm and λ = 785 nm, as well as Polaron Number Densities N BP and N GP

Tables Icon

Table 3 Parameters Obtained by Fit of Eq. (1) to the Data of Fig. 1

Tables Icon

Table 4 Parameters Deduced from Fitting Eq. (2) to the Experimental Data in Fig. 4

Tables Icon

Table 5 Changes of the Number Densities of Light-Induced Bound Polarons N li,GP, Bipolarons N li,BP, and Hole Polarons N li,HP

Tables Icon

Table 6 Parameters Determined for an Estimate of I (1st)/I 0 via Eq. (3) for Hologram Recording with Kc-Axis, Light Polarization Parallel c-Axis and s-Polarization

Equations (9)

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

I ( 1 st) ( t ) I 0 = I ( 1 st ) ( t = 0 ) I 0 exp [ ( t / τ ) β ]
α li = α li 0 exp [ ( t / τ ) β ]
I ( 1 st ) I 0 = exp ( 2 ( α + α 1 ) d h cos Θ B ) × [ sin 2 ( π n 1 d h λ cos Θ B ) + sinh 2 ( α 1 d h 2 cos Θ B ) ]
α li ( λ ) = α li , GP ( λ ) + α li , HP ( λ ) + α li , BP ( λ ) = N li , GP σ GP ( λ ) + N li , HP σ HP ( λ ) + N li , BP σ BP ( λ )
N li , GP = ( 2 N li , BP + N li , HP )
n li ( ω ) = 2 π P 0 ω Δ κ ( ω ) ω 2 ω 2 d ω ,
I ( 1 st ) ( δ Θ ) I 0 = exp ( 2 ( α + α 1 ) d h cos Θ B ) sin 2 ( ν 2 + ξ 2 1 + ξ 2 / ν 2 )
ν = π n 1 d h cos ( 2 Θ B ) / ( λ cos Θ B ) , ξ = 2 δ Θ π n d h sin Θ B / λ .
n 1 ( λ ) = 1 2 n eff 3 ( λ ) r eff ( λ ) E

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