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Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 4 — Feb. 20, 2006
  • pp: 1533–1540
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Long-living currents induced by nanosecond light pulses in LiNbO3 crystals

O. Beyer, C. von Korff Schmising, M. Luennemann, K. Buse, and B. Sturman  »View Author Affiliations


Optics Express, Vol. 14, Issue 4, pp. 1533-1540 (2006)
http://dx.doi.org/10.1364/OE.14.001533


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Abstract

We have obtained first solid evidence of strong charge separation that is caused by relaxing localized electrons in a polar medium: Space-charge gratings induced in highly-doped LiNbO3:Fe crystals by interfering nanosecond light pulses at 532 nm show a highly peculiar long-term behavior (buildup or/and decay) in the dark. It depends strongly on the applied electric field E0 (ranging from -140 to +640 kV/cm) and occurs on a time scale of (1 – 100) s which is much larger than the relaxation time of photo-electrons and smaller than the dark dielectric relaxation time. All peculiarities observed are fully described by a charge-transport model that incorporates the energy relaxation of electrons within a band of localized Fe2+ states and a long-living, field-gradient-independent “polar current” directed along the polar axis.

© 2006 Optical Society of America

1. Introduction

Ferroelectric lithium niobate (LiNbO3) was the first material where the bulk photovoltaic effect — the generation of photo-currents caused by the absence of inversion symmetry — was discovered [1

1. 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]

]. Later this effect was detected and investigated in tens of noncentrosymmet-ric optical materials, ferro and piezoelectrics, yielding numerous publications [2

2. B. I. Sturman and V. M. Fridkin, The Photovoltaic and Photorefractive Effects in Noncentrosymmetric Materials, Gordon and Breach, Philadelphia (1992).

]. In contrast to the conventional drift and diffusion currents, the photovoltaic current density is non-zero even in the absence of macroscopic driving fields and gradients. Moreover, investigation of the mechanisms of the bulk photovoltaic effect has lead to the striking general prediction: Any thermodynamically non-equilibrium state of a macroscopically uniform polar medium has to be accompanied by fluxes of different physical quantities, e.g., charge carriers, particles, or energy [2

2. B. I. Sturman and V. M. Fridkin, The Photovoltaic and Photorefractive Effects in Noncentrosymmetric Materials, Gordon and Breach, Philadelphia (1992).

]. The studies of macroscopic and mesoscopic polar transport phenomena experience nowadays a new upsurge [3

3. L. DiCarlo, C. M. Marcus, and J. S. Harris Jr., “Photocurrent, Rectification, and Magnetic Field Symmetry of Induced Current through Quantum Dots,” Phys. Rev. Lett. 91, 246804 (2003). [CrossRef] [PubMed]

, 4

4. S. D. Ganichev, V. V. Bel’kov, L. E. Golub, E. L. Ivchenko, P. Schneider, S. Giglberger, J. Eroms, J. De Boeck, G. Borghs, W. Wegscheider, D. Weiss, and W. Prettl, “Experimental Separation of Rashba and Dresselhaus Spin Splittings in Semiconductor Quantum Wells,” Phys. Rev. Lett. 92, 256601 (2004). [CrossRef] [PubMed]

].

The bulk photovoltaic effect is extremely strong in LiNbO3 crystals. It generates space-charge fields of the order of 100 kV/cm [1

1. 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]

, 2

2. B. I. Sturman and V. M. Fridkin, The Photovoltaic and Photorefractive Effects in Noncentrosymmetric Materials, Gordon and Breach, Philadelphia (1992).

] and serves as the main mechanism of photorefrac-tion, i.e., the refractive index changes owing to charge separation and the linear electro-optic effect [5

5. L. Solymar, D. J. Webb, and A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials, Clarendon, Oxford (1996).

, 6

6. K. Buse, “Light-Induced Charge Transport Processes in Photorefractive Crystals II: Materials,” Appl. Phys. B 64, 391 (1997). [CrossRef]

]. Large values of the photovoltaic field are caused by the combination of pretty large polar displacements of photo-excited electrons, ~1 Å, with low photo-conductivity.

Charge transport properties of lithium niobate, including the photovoltaic properties, have been the subject of many studies in connection with photorefraction and its applications. It is established for the most important dopants Fe and Cu that the ions Fe2+/Fe3+ and Cu+/Cu2+ serve as sources/traps during photo-excitation/recombination of electrons in/from the conduction band [7

7. P. Günter and J. -P. Huignard, eds., Photorefractive Materials and Their Applications, I, Vol. 61 of Topics in Applied Physics, Springer-Verlag, Berlin (1988). [CrossRef]

]. The characteristic transport lengths and relaxation times for photo-electrons have been measured [8

8. 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 (2000). [CrossRef]

]. Hopping dark conductivity caused by tunnelling to nearest free Fe or Cu centers is found to become important in heavily doped samples [9

9. I. Nee, M. Müller, K. Buse, and E. Krätzig, “Role of Iron in Lithium-Niobate Crystals for the Dark-Storage Time of Holograms,” J. Appl. Phys. 88, 4282 (2000). [CrossRef]

, 10

10. K. Peithmann, K. Buse, and E. Krätzig, “Dark Conductivity in Copper-Doped Lithium Niobate Crystals,” Appl. Phys. B 74, 549 (2002). [CrossRef]

].

2. Experimental methods and results

Using an experimental setup, that allows application of extremely large non-screened electric fields [11

11. M. Luennemann, U. Hartwig, and K. Buse, “Improvements of Sensitivity and Refractive-Index Changes in Pho-torefractive Iron-Doped Lithium-Niobate Crystals by Application of Extremely Large External Electrical Fields,” J. Opt. Soc. Am. B 20, 1643 (2003). [CrossRef]

, 12

12. M. Luennemann, U. Hartwig, G. Panotopoulos, and K. Buse, “Electrooptic Properties of Lithium Niobate Crystals for Extremly High External Electric Fields,” Appl. Phys. B 76, 403 (2003). [CrossRef]

], for nanosecond recording of space-charge gratings in LiNbO3:Fe crystals, we encountered a new striking polar charge-transport phenomenon. It occurs in the dark and accompanies the relaxation of electrons inside the band of localized Fe2+/Fe3+ states.

The experimental arrangement is depicted in Fig. 1. Two single nanosecond light pulses of equal intensity are incident simultaneously and almost normally onto the opposite faces of a z-cut iron-doped LiNbO3 sample to record a reflection index grating (temporal pulse width 15 ns; peak intensity 2.4 × 107 W/cm2; recording wavelength λr = 532 nm; grating vector K ≈ 5.4 × 105 cm-1; grating period 117 nm). The electric field E 0, applied through liquid electrodes, ranges from -140 to +640 kV/cm; larger negative fields would invert the spontaneous polarization [11

11. M. Luennemann, U. Hartwig, and K. Buse, “Improvements of Sensitivity and Refractive-Index Changes in Pho-torefractive Iron-Doped Lithium-Niobate Crystals by Application of Extremely Large External Electrical Fields,” J. Opt. Soc. Am. B 20, 1643 (2003). [CrossRef]

]. The recorded grating is probed by a weak continuous-wave Bragg-matched beam of wavelength λt = 543.5 nm and its diffraction efficiency η = I diff/(I trans + I diff) is measured as a function of time. The total concentration of Fe ions, N Fe = NFe2+ + NFe3+, ranges from ≈ 2 to 6 × 1019 cm-3; the concentration ratio NFe2+/NFe3+ is varied by thermal treatments. Thin samples with the thickness d = 0.22 mm are used.

Fig. 1. Experimental configuration; c is the polar axis, K is the grating vector, U 0 is the applied voltage, and I diff and I trans are the intensities of diffracted and transmitted beams.

The diffraction efficiency in question is expressed by η ≃ (πno3 r 13 EKd/2λt)2 [5

5. L. Solymar, D. J. Webb, and A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials, Clarendon, Oxford (1996).

,7

7. P. Günter and J. -P. Huignard, eds., Photorefractive Materials and Their Applications, I, Vol. 61 of Topics in Applied Physics, Springer-Verlag, Berlin (1988). [CrossRef]

], where n o is the ordinary refractive index, r 13 is the electro-optic coefficient, and E K is the space-charge field amplitude. All parameters entering this relation, except E K, are known [6

6. K. Buse, “Light-Induced Charge Transport Processes in Photorefractive Crystals II: Materials,” Appl. Phys. B 64, 391 (1997). [CrossRef]

]. In particular, πno3 r 13 d/2λt ≈ 0.8 × 10-5 cm/V. A value of η = 1% corresponds to the grating amplitude E K ≈ 12 kV/cm.

Figure 2 shows the evolution of the diffraction efficiency on the scale (1 – 100) s for N Fe = 5.6 × 1019 cm-3, NFe2+/NFe3+ = 0.23, and several values of E 0. This temporal evolution and its field-induced changes are reproducible and highly peculiar:

  • For E 0 ≲ 50 kV/cm the efficiency decreases monotonously (on the scale of ~ 10 s) tending to a slightly lower value, curves 1–3.
  • With increasing E 0, the initial value η(t = 0) is decreasing while the relative drop of η(t) during the shown stage of relaxation is increasing. A non-exponential character of the relaxation is well pronounced at this stage.
  • The initial value η(t = 0,E 0) is minimal at E 0 ≈ 230kV/cm, curve 4. The dependence η(t) is characterized here by a narrow peak followed by a weak increase on the scale of a few minutes.
  • For E 0 ≳ 300 kV/cm the function η(t) shows a monotonous growth, curves 5 – 8. It is essentially non-exponential, initially fast and then pretty slow. The values of η achieved during this dark buildup are as high as (2–4)%; they are increasing with E 0 . At E 0 ≈ 640 kV/cm, the space-charge field growth in the dark is as high as ≈ 25 kV/cm.

On a larger time scale (~ 1 hour) the diffraction efficiency exhibits a mono-exponential decay. The inset in Fig. 2 gives a representative example of the long-term evolution. The rate of the final decay is ≈ 2σ d/εε 0, where σ d is the dark conductivity of the sample and e is the longitudinal dielectric constant of LiNbO3. It corresponds to the dark Maxwell relaxation of the space-charge field. The time difference between the fast buildup and final decay processes exceeds two orders of magnitude.

The dots in Fig. 3 represent our experimental data on the field dependence η max(E 0). This dependence is characterized by a clear minimum at E 0 ≈ 230 kV/cm.

Variation of the concentration ratio NFe2+/NFe3+ does not affect strongly the presented regularities. A decrease of the total concentration N Fe results in a rapid increase of the buildup time.

Fig. 2. Diffraction efficiency η versus post-pulse relaxation time t. Curves 1–8 are plotted for E 0 = -136, -45, 45, 227, 318, 455, 500, and 590 kV/cm. The inset shows the long-term behavior for E 0 = 364 kV/cm.
Fig. 3. Maximum value of η(t) versus E 0; the dots are experimental data and the solid line is a theoretical fit.

3. Macroscopic model

Now we consider a macroscopic model of the dark buildup and relaxation, its microscopic aspects will be discussed below. First, we represent the total electric field as E = E 0 + E Kcos(Kz). The grating amplitude EK obeys the general evolution equation

dEKdt=jKεε0,
(1)

where j K is the Fourier component of the current density j.

j=σ(E+ER),
(2)

where E R is a new characteristic field and σ is the conductivity. This relation means that, apart from the usual drift component σE, there is an additional (polar) current component σE R which is fully due to the polar symmetry of the crystal. This component is absent under the conditions of thermodynamic equilibrium, σ = σ d, but it is present when the electron system is far from equilibrium, σσ d. The polar relaxation current is similar to the photovoltaic current and the characteristic field E R is similar in nature to the photovoltaic field E pv.

Inline with the above specifications and the experimental conditions, we assume furthermore that

σ=σ0f(vt)[1+cos(Kz)],
(3)

where σ 0 is the initial value of the non-equilibrium conductivity, f(vt) is a decay function decreasing from 1 to 0 when the relaxation time t is increasing from 0 to ∞, and v is the relaxation rate. The choice of a unit value for the spatial contrast of σ(z) is dictated by a unit value of the light intensity contrast and by the smallness of migration lengths of photo-electrons in lithium niobate as compared to the grating period [6

6. K. Buse, “Light-Induced Charge Transport Processes in Photorefractive Crystals II: Materials,” Appl. Phys. B 64, 391 (1997). [CrossRef]

]. Expression (3) implies that the spatially modulated conductivity decreases during a relaxation process involving transitions between Fe centers and that the equilibrium dark conductivity σ d is still negligible.

Now we consider the consequences of this model for the post-pulse relaxation dynamics. Combining Eqs. (1) – (3), we obtain for the grating amplitude:

dEKdt=γ0f(vt)(E0+ER+EK),
(4)

where γ 0 = σ 0/εε 0 is the initial rate of dielectric relaxation. The initial condition is E K(t = 0) = EK0, where EK0 is determined by the pulse recording process prior to relaxation. Then the solution of Eq. (4) is

EK=(EK0+E0+ER)exp[γ0v0vtf(s)ds]E0ER.
(5)

As one can see, the relaxation law is non-exponential even for a single-exponential decay function f(vt). In the limit vt ≪ 1 we obtain for the time-saturated value of the grating amplitude: EK = (EK0 + E 0 + E R) exp(- 0/v) -E 0 - E R with c = 0 f(s)ds being of the order of one.

To describe the field dependence of the initial value η(t = 0), which is controlled by the photovoltaic charge transport during the pulse recording, we set EK0 = -q 0(E 0 - E pv) with the photovoltaic field E pv = 340 kV/cm and q 0 =0.05. Smallness of q 0 means that the charge separation is not saturated during the recording; the accepted high value of E pv is within the reasonable range for high intensities and iron concentrations [11

11. M. Luennemann, U. Hartwig, and K. Buse, “Improvements of Sensitivity and Refractive-Index Changes in Pho-torefractive Iron-Doped Lithium-Niobate Crystals by Application of Extremely Large External Electrical Fields,” J. Opt. Soc. Am. B 20, 1643 (2003). [CrossRef]

, 13

13. 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]

]. To describe the saturated value of η(t), which is achieved during the post-illumination relaxation, we set E R = 160 kV/cm, and 0/v = 0.018. The direction of the relaxation current, σE R, is opposite to that of the photovoltaic current during recording.

For the above indicated parameters we have η(t)]max = max{η(0), η(∞)} for the maximum value of the diffraction efficiency. The solid line in Fig. 3 shows the field dependence of this important characteristic; it is in good agreement with the experimental data.

In accordance with Eq. (4) and the above assumptions, the initial rate of changes of the grating amplitude, [dE K/dt]t=0, is ≃ -γ 0(E 0 + E R) and the initial rate of changes of the diffraction efficiency, [d η/dt]t=0, is proportional to (E 0 + E R)(E 0 - E pv). This expression explains qualitatively the experimentally observed strong dependence of the slope [/dt]t=0 on the external field E 0 (Fig. 2).

To fit the whole temporal behavior, we suppose that the decay function obeys a stretched-exponential law, f(s) = exp(-s 1/2), which is typical for disordered systems (see, e.g., [14

14. J. C. Phillips, “Stretched Exponential Relaxation in Molecular and Electronic Glasses,” Rep. Prog. Phys. 59, 1133 (1996). [CrossRef]

]); this gives c = 2. Figure 4 shows the calculated dependences η(t) for the rate coefficients v = 0.5 s_1, γ 0 = 4.5 × 10-3 s-1, and several representative values of E 0 (E 0 < E R, curves 1–3; E RE 0E pv, curves 4, 5; E 0 > E pv, curves 6 – 8). The theoretical dependences reproduce perfectly well all experimental field-induced changes in the dynamics of η (t) shown in Fig. 2. Our macroscopic model catches thus the main features of charge transport during the post-pulse relaxation.

Fig. 4. Modification of the dark evolution of the diffraction efficiency η with increasing field E 0. Curves 1 – 8 are plotted for E 0 = -150, -70, 30, 250, 320, 420, 500, and 600 kV/cm.

4. Discussion

Turning to justification and discussion of our model, we first narrow the possibilities for explanations:

  • Recombination of photo-excited electrons from the conduction band to Fe centers occurs on the sub-μs time scale in LiNbO3:Fe [8

    8. 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 (2000). [CrossRef]

    , 15

    15. P. Herth, T. Granzow, D. Schaniel, Th. Woike, M. Imlau, and E. Krätzig, “Evidence for Light-Induced Hole Polarons in LiNbO3,” Phys. Rev. Lett. 67404 (2005). [CrossRef]

    ].
  • Thermal and pyroelectric gratings decay on approximately the same time scale [16

    16. H. J. Eichler, P. Günter, and D. W. Pohl, Laser-Induced Dynamic Gratings, Springer-Verlag, N.Y. (1986).

    ].
  • Diffusion of carriers is negligible because the diffusion field E D = Kk B T/e ≈ 14 kV/cm (k B T is the thermal energy and e is the elementary charge) is small as compared to the other characteristic fields.

It is worth mentioning that our physical situation and basic observations are entirely different from those relevant to the known cases of dark diffusion buildup of space-charge gratings [17

17. I. Biaggio, M. Zgonik, and P. Günter, “Build-Up and Dark Decay of Transient Photorefractive Gratings in Reduced KNbO3,” Opt. Commun. 77, 312 (1990); K. Buse, J. Frejlich, G. Kuper, and E. Krätzig, ”Dark Build-Up of Holograms in BaTiO3 after Recording,” Appl. Phys. A 57, 437 (1993). [CrossRef]

]. The latter deal neither with heavily doped crystals nor with large applied fields and comply with the diffusion transport and elementary two-center models.

Having excluded the above possibilities, we are certain that the introduced polar relaxation current is the necessary ingredient for explanation of the experimental results. The major remaining problem is to interpret our model [Eqs. (2) and (3)] on the microscopic level.

The first open question is about the reason for the high initial conductivity s0 which is attributed to hops of electrons over Fe sites. The density of localized electronic states as a function of the energy possesses a peak nearby the Fermi level in iron-doped samples, (Fig. 5); its width is expected to be of the order of 0.1 eV. In the thermodynamic equilibrium, electrons on Fe2+ sites occupy the levels well below the energy peak, (Fig. 5a). Most of them experience at least one excitation-recombination cycle at the pulse recording; this is consistent with the values of pulse energy, concentration NFe2+, and absorption coefficient (≈ 40 cm-1 at 532 nm). After recombination, electrons populate first the Fe levels nearby the peak of the density of localized states, (Fig. 5b), because the number of such states is relatively large. The hopping mobility of these non-equilibrium electrons is much higher than the mobility of electrons occupying the energy tail because of a much greater probability to find a close neighbor with a lower energy [18

18. N. F. Mott and E. A. Davis, Electron Processes in Non-Crystalline Materials, Clarendon Press, Oxford (1979).

]. The non-equilibrium conductivity is attributed to these electrons. The rate v can thus be identified with the inverse relaxation time of the non-equilibrium electrons.

Fig. 5. Expected density of localized states (solid curves) and distributions of electrons (grayscale) over these states in the equilibrium (a) and non-equilibrium (b) states. The arrows show the energy flow during relaxation.

The second major question is about the nature of the post-pulse relaxation current. In accordance with the general principles of kinetic electron processes, relaxation to the thermodynamic equilibrium in macroscopically uniform polar media must be accompanied by an electrical current. Examples of microscopic mechanisms explaining such a current can be found in Ref 2. We suppose that “the driving force” for the relaxation current in our case is a polar correlation between the spatial and energy positions of neighboring localized states. The presence of such a correlation is not surprising when the migration length of a photo-excited electron is smaller than (or comparable with) the mean distance between Fe centers, ≈ 25 Å. It provides the necessary difference between the tunnelling distances in the ±c directions for non-equilibrium electrons.

Within our microscopic picture, the total relaxation charge 2 0 E R/v flowed through a unit surface element is ≈ eNFe2+ δR, where δR is an average polar displacement per one electron during the relaxation over Fe sites. Then we obtain a simple estimate, δR ≈ (γ 0/v)(2εε 0 E R/eNFe2+). With E R = 160 kV/cm, γ 0/v = 9 × 10-3, and NFe2+ = 1.3 × 1019 cm-3 it gives δR ≈ 0.5 Å. It is comparable with an average polar displacement per one photo-electron that characterizes the photovoltaic current in lithium niobate [1

1. 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]

,2

2. B. I. Sturman and V. M. Fridkin, The Photovoltaic and Photorefractive Effects in Noncentrosymmetric Materials, Gordon and Breach, Philadelphia (1992).

].

The last finding elucidates the microscopic mechanism of the bulk photovoltaic effect in this material: The distinct contributions to the steady-state photovoltaic current coming from the asymmetry of photo-excitation and recombination compensate partially each other. The photovoltaic charge separation can be enhanced by making use of a pulse excitation.

5. Conclusion

In conclusion, we have discovered a new polar charge-transport effect in highly doped LiNbO3:Fe crystals: Dark relaxation of localized non-equilibrium electrons, occupying Fe sites after a pulsed photo-excitation, is accompanied by a current flow in the direction of the polar axis. This non-drift and non-diffusion relaxation current is responsible for post-pulse buildup of strong (up to 25 kV/cm) gratings of space-charge fields and pronounced peculiarities in the long-term dynamics of the grating diffraction efficiency.

Acknowledgments

Financial support from the Deutsche Telekom AG and from the DFG (Award No. BU 913/13-1) is gratefully acknowledged.

References and links

1.

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]

2.

B. I. Sturman and V. M. Fridkin, The Photovoltaic and Photorefractive Effects in Noncentrosymmetric Materials, Gordon and Breach, Philadelphia (1992).

3.

L. DiCarlo, C. M. Marcus, and J. S. Harris Jr., “Photocurrent, Rectification, and Magnetic Field Symmetry of Induced Current through Quantum Dots,” Phys. Rev. Lett. 91, 246804 (2003). [CrossRef] [PubMed]

4.

S. D. Ganichev, V. V. Bel’kov, L. E. Golub, E. L. Ivchenko, P. Schneider, S. Giglberger, J. Eroms, J. De Boeck, G. Borghs, W. Wegscheider, D. Weiss, and W. Prettl, “Experimental Separation of Rashba and Dresselhaus Spin Splittings in Semiconductor Quantum Wells,” Phys. Rev. Lett. 92, 256601 (2004). [CrossRef] [PubMed]

5.

L. Solymar, D. J. Webb, and A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials, Clarendon, Oxford (1996).

6.

K. Buse, “Light-Induced Charge Transport Processes in Photorefractive Crystals II: Materials,” Appl. Phys. B 64, 391 (1997). [CrossRef]

7.

P. Günter and J. -P. Huignard, eds., Photorefractive Materials and Their Applications, I, Vol. 61 of Topics in Applied Physics, Springer-Verlag, Berlin (1988). [CrossRef]

8.

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 (2000). [CrossRef]

9.

I. Nee, M. Müller, K. Buse, and E. Krätzig, “Role of Iron in Lithium-Niobate Crystals for the Dark-Storage Time of Holograms,” J. Appl. Phys. 88, 4282 (2000). [CrossRef]

10.

K. Peithmann, K. Buse, and E. Krätzig, “Dark Conductivity in Copper-Doped Lithium Niobate Crystals,” Appl. Phys. B 74, 549 (2002). [CrossRef]

11.

M. Luennemann, U. Hartwig, and K. Buse, “Improvements of Sensitivity and Refractive-Index Changes in Pho-torefractive Iron-Doped Lithium-Niobate Crystals by Application of Extremely Large External Electrical Fields,” J. Opt. Soc. Am. B 20, 1643 (2003). [CrossRef]

12.

M. Luennemann, U. Hartwig, G. Panotopoulos, and K. Buse, “Electrooptic Properties of Lithium Niobate Crystals for Extremly High External Electric Fields,” Appl. Phys. B 76, 403 (2003). [CrossRef]

13.

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]

14.

J. C. Phillips, “Stretched Exponential Relaxation in Molecular and Electronic Glasses,” Rep. Prog. Phys. 59, 1133 (1996). [CrossRef]

15.

P. Herth, T. Granzow, D. Schaniel, Th. Woike, M. Imlau, and E. Krätzig, “Evidence for Light-Induced Hole Polarons in LiNbO3,” Phys. Rev. Lett. 67404 (2005). [CrossRef]

16.

H. J. Eichler, P. Günter, and D. W. Pohl, Laser-Induced Dynamic Gratings, Springer-Verlag, N.Y. (1986).

17.

I. Biaggio, M. Zgonik, and P. Günter, “Build-Up and Dark Decay of Transient Photorefractive Gratings in Reduced KNbO3,” Opt. Commun. 77, 312 (1990); K. Buse, J. Frejlich, G. Kuper, and E. Krätzig, ”Dark Build-Up of Holograms in BaTiO3 after Recording,” Appl. Phys. A 57, 437 (1993). [CrossRef]

18.

N. F. Mott and E. A. Davis, Electron Processes in Non-Crystalline Materials, Clarendon Press, Oxford (1979).

OCIS Codes
(160.3730) Materials : Lithium niobate
(160.5320) Materials : Photorefractive materials

ToC Category:
Materials

History
Original Manuscript: November 8, 2005
Revised Manuscript: February 3, 2006
Manuscript Accepted: February 6, 2006
Published: February 20, 2006

Citation
O. Beyer, C. von Korff Schmising, M. Luennemann, K. Buse, and B. Sturman, "Long-living currents induced by nanosecond light pulses in LiNbO3 crystals," Opt. Express 14, 1533-1540 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-4-1533


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References

  1. 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]
  2. B. I. Sturman and V. M. Fridkin, The Photovoltaic and Photorefractive Effects in Noncentrosymmetric Materials, Gordon and Breach, Philadelphia (1992).
  3. L. DiCarlo, C. M. Marcus, and J. S. Harris, Jr., "Photocurrent, Rectification, and Magnetic Field Symmetry of Induced Current through Quantum Dots," Phys. Rev. Lett. 91, 246804 (2003). [CrossRef] [PubMed]
  4. S. D. Ganichev, V. V. Bel’kov, L. E. Golub, E. L. Ivchenko, P. Schneider, S. Giglberger, J. Eroms, J. De Boeck, G. Borghs, W. Wegscheider, D. Weiss, and W. Prettl, "Experimental Separation of Rashba and Dresselhaus Spin Splittings in Semiconductor Quantum Wells," Phys. Rev. Lett. 92, 256601 (2004). [CrossRef] [PubMed]
  5. L. Solymar, D. J. Webb, and A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials, Clarendon, Oxford (1996).
  6. K. Buse, "Light-Induced Charge Transport Processes in Photorefractive Crystals II: Materials," Appl. Phys. B 64, 391 (1997). [CrossRef]
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