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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 12 — Jun. 4, 2012
  • pp: 13326–13336
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Small-polaron based holograms in LiNbO3 in the visible spectrum

H. Brüning, V. Dieckmann, B. Schoke, K.-M. Voit, M. Imlau, G. Corradi, and C. Merschjann  »View Author Affiliations


Optics Express, Vol. 20, Issue 12, pp. 13326-13336 (2012)
http://dx.doi.org/10.1364/OE.20.013326


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Abstract

Diffraction efficiency, relaxation behavior and dependence on pump-beam intensity of small-polaron based holograms are studied in thermally reduced, nominally undoped lithium niobate in the visible spectrum (λ = 488 nm). The pronounced phase gratings with diffraction efficiency up to η = (10.8 ± 1.0)% appeared upon irradiation by single ns-laser pulses (λ = 532 nm) and are comprehensively assigned to the optical formation of spatially modulated densities of small bound Nb Li 4 + electron polarons, Nb Li 4 + : Nb Nb 4 + electron bipolarons, and O hole polarons. A remarkable quadratic dependence on the pump-beam intensity is discovered for the recording configuration K || c-axis and can be explained by the electro-optic contribution of the optically generated small bound polarons. We discuss the build-up of local space-charge fields via small-polaron based bulk photovoltaic currents.

© 2012 OSA

1. Introduction

So far, we have probed the polaron-based hologram features in the near-infrared spectrum (λ = 785 nm). This allowed us to uncover the dominating role of small bound NbLi4+ polarons (GP) in the appearance of mixed absorption and index volume gratings.

In this work, we focus on hologram features at a probing light wavelength of λ = 488 nm, i.e., a spectral range that is of utmost importance for a variety of modern holographic applications of LiNbO3 such as real-time holographic displays [9

9. S. Tay, P.-A. Blanche, R. Voorakaranam, A. V. Tunc, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451, 694–698 (2008). [CrossRef] [PubMed]

]. The interest in the blue spectrum is particularly driven by our findings that hologram recording can be performed within a single 8 ns laser pulse while thermally-driven hologram self-decay takes place in the range of a few milliseconds at room temperature. Thus, thermally reduced LiNbO3 represents a photosensitive, re-recordable hologram medium that is updatable at kHz frequencies.

From the point of view of small polarons, the blue spectrum is dominated by the presence of NbLi4+:NbNb4+ electron bipolarons (BP, absorption maximum at λ ≃ 500 nm) [7

7. 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]

] and small O hole polarons (HP, λ ≃ 500 nm) [8

8. O. F. Schirmer, “O Bound small polarons in oxide materials,” J. Phys.: Condens. Matter 18, R667–R704 (2006). [CrossRef]

]. These two kinds of polarons exhibit essentially different features with respect to light-matter-interaction: Bipolarons stable at room temperature, are dissociated (gated) optically by light exposure within a one-photon absorption process. The maximum addressable BP number density is determined by the respective number density in the ground state. In contrast, short-lived small bound hole polarons are generated via two-photon absorption. Their number density grows until all possible O2− lattice sites, one in the vicinity of each Li vacancy, are saturated [8

8. O. F. Schirmer, “O Bound small polarons in oxide materials,” J. Phys.: Condens. Matter 18, R667–R704 (2006). [CrossRef]

]. These processes can be easily distinguished experimentally by the study of the grating efficiency as a function of the pump-beam intensity.

With these results and our earlier findings [1

1. M. Imlau, H. Brüning, B. Schoke, R.-S. Hardt, D. Conradi, and C. Merschjann, “Hologram recording via spatial density modulation of NbLi4+/5+ antisites in lithium niobate,” Opt. Express 19, 15322–15338 (2011). [CrossRef] [PubMed]

], the recording of polaron-based holograms with ns-laser pulses in LiNbO3 is demonstrated over a broad range in the visible spectrum. Further impact of the work is revealed by considering the possibility of recording with fs- and ps-laser pulses, thus enabling fs-holography. Also, we like to point to the possible transfer of the polaron concept for hologram recording to other oxide crystals like KNbO3 [11

11. 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]

].

2. Samples and experimental setup

Our studies were performed with single crystals of thermally reduced lithium niobate grown from a congruent, nominally undoped melt via Czochralski growth technique (Crystal Technology, Inc.). The sample under study (cf. Ref. [1

1. M. Imlau, H. Brüning, B. Schoke, R.-S. Hardt, D. Conradi, and C. Merschjann, “Hologram recording via spatial density modulation of NbLi4+/5+ antisites in lithium niobate,” Opt. Express 19, 15322–15338 (2011). [CrossRef] [PubMed]

]) with aperture (a × c) = (6.54 ± 0.01) × (5.69±0.01) mm2 and thickness d = (1.23±0.03) mm has been thermally pre-treated by heating it for 6 hours at T = (970 ± 10) K in a reducing atmosphere of p < 10−4 mbar. Thus, high densities of NbLi4+:NbNb4+ bipolarons (BP) and of small bound NbLi4+-polarons (GP) [12

12. 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]

, 13

13. J. Koppitz, O. F. Schirmer, and A. I. Kuznetsov, “Thermal dissociation of bipolarons in reduced undoped LiNbO3,” Europhys. Lett. 4, 1055–1059 (1987). [CrossRef]

] were generated that are stable at room temperature. We have calculated the number densities NBP and NGP using the steady-state absorption for extraordinary light polarization at λ = 488 nm and λ = 785 nm and the absorption cross sections published in Refs. [1

1. M. Imlau, H. Brüning, B. Schoke, R.-S. Hardt, D. Conradi, and C. Merschjann, “Hologram recording via spatial density modulation of NbLi4+/5+ antisites in lithium niobate,” Opt. Express 19, 15322–15338 (2011). [CrossRef] [PubMed]

, 14

14. 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]

]. All relevant parameters are summarized in Table 1.

Table 1. Absorption features and polaron number densities of the reduced lithium niobate sample under study in the steady state at room temperature. The sample is identical to the one used in Ref. [1].

table-icon
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Hologram recording and time-resolved detection of the hologram decay were performed in a two-beam interferometer setup. A single pulse of a frequency-doubled YAG:Nd-laser (Innolas Spitlight 600, λp = 532 nm and average pulse duration τFWHM ≈ 8 ns) was used for recording an unslanted volume grating (equal intensities IR = IS, parallel light polarization eR = eS, modulation depth m = 1, Bragg angle ΘB = 6.3°). The decay of the grating was probed in the blue-green spectral range with the Bragg-matched beam of a continuous-wave laser at λt = 488 nm (Coherent Sapphire, I0 = 10 kW/m2). Time-dependent data collection via a Si-PIN diode and digital storage oscilloscope was limited to the range 1μs – 100 s in order to suppress unwanted signal contributions from thermal gratings [15

15. F. Jermann and K. Buse, “Light-induced thermal gratings in LiNbO3:Fe,” Appl. Phys. B 59, 437–443 (1994). [CrossRef]

]. The sample temperature was adjusted by a PID-controlled thermoelectric element from room temperature up to 410 K.

3. Experimental results

Fig. 1 Semilogarithmic plot of the temporal dynamics of the normalized intensity of the first order diffracted beam I(1st)/I0 for (a) Kc-axis (s-polarization) and (b) K || c-axis (p-polarization). Recording conditions: λp = 532 nm, ep || c-axis and Bragg angle ΘB = 6.3°. Ip = IR + IS = 380 GW/m2. Bragg-matched probing conditions: λ = 488 nm, e || c-axis. The solid lines correspond to fits of Eq. (1) to the data. The insets sketch the respective recording and probing configurations.

Qualitatively, both gratings decay with a similar temporal dependence. The striking observation in the two spectra is the severely different starting amplitude at t = 1μs of the diffraction efficiency that is by a factor of approximately 500 larger in configuration (b) compared with (a). Fitting a stretched exponential function:
I(1st)(t)I0=I(1st)(t=0)I0exp[(tτ)β]
(1)
to the experimental data (solid lines) yields the starting amplitudes I(1st)(t = 1μs)/I0, the decay time constant τ and the stretching factor β as summarized in Table 2. We note that Eq. (1) accords with the empirical dielectric decay function introduced by Kohlrausch, Williams and Watts (KWW) [17

17. G. Williams and D. C. Watts, “Non–symmetrical dielectric relaxation behaviour arising from a simple empirical decay function,” Trans. Faraday. Soc 66, 80–85 (1970). [CrossRef]

].

Table 2. Parameters obtained from fitting Eq. (1) to the experimental data depicted in Fig. 1 and of Eq. (6) to the data in Fig. 2.

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Fig. 2 Normalized intensity of the first order diffracted beam I(1st)/I0 at t = 1μs as a function of pump intensity Ip for (a) Kc-axis (s-polarization) and (b) K || c-axis (p-polarization) using the same recording and probing condition as in Fig. 1. The solid line corresponds to a fit of a saturation function Eq. (6) while the dashed line represents a fit of a quadratic intensity dependence to the data.

4. Discussion

Our results highlight the prominent features of polaron-based holograms in the visible spectrum in thermally reduced lithium niobate. For the field of applications, the striking features are the diffraction efficiency of η = (0.108 ± 0.01) by means of single 8 ns-laser pulse recording (Ip = 380GW/m2) and the hologram self-decay within a few miliseconds at room temperature. Taking into account the crystal thickness of d = 1.23 mm this corresponds to a photosensitivity [19

19. 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]

] of:
S|ns488nm=δηδt1Ipd8.4cm/J,
(2)
i.e. a value that is by one order of magnitude larger compared with holograms recorded via the photorefractive effect [19

19. 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]

, 20

20. K. Buse, “Light-induced charge transport processes in photorefractive crystals II: Materials,” Appl. Phys. B 64, 391–407 (1997). [CrossRef]

].

From the point of view of small polarons, there are two outstanding findings associated with the visible spectrum:
  • The amplitude of the diffraction efficiency at 488 nm is reduced by a factor of two in comparison with probing at 785 nm, i.e. an abnormal dispersion behavior is found.
  • The intensity dependence of the diffraction efficiency is qualitatively different for the recording geometries Kc and K || c. We will discuss these two findings below along the expectations for polaron-based hologram recording in the visible.

The further properties have already been reported for the near-infrared spectral range [1

1. M. Imlau, H. Brüning, B. Schoke, R.-S. Hardt, D. Conradi, and C. Merschjann, “Hologram recording via spatial density modulation of NbLi4+/5+ antisites in lithium niobate,” Opt. Express 19, 15322–15338 (2011). [CrossRef] [PubMed]

] and give strong evidence for the polaronic origin of the hologram recording and read-out process:
  • ⊳ a stretched-exponential decay of the diffraction efficiency,
  • ⊳ a hologram lifetime in the ms-range,
  • ⊳ a thermally activated hologram decay,
  • ⊳ an activation energy of the latter that corresponds to the activation energy of the small bound NbLi4+ polaron and
  • ⊳ a pronounced dependence of the diffraction efficiency on the recording geometry.

We should like to note the assumptions made in the following discussion: First, the action of extrinsic defect centers, that foster hologram recording via the photorefractive effect, is not considered [21

21. M. Imlau, “Defects and photorefraction: A relation with mutual benefit,” Phys. Status Solidi A 204, 642–652 (2007). [CrossRef]

]. This is justified because the number density of extrinsic photorefractive/transition metal centers, such as Fe, is far below 5 ppm in our nominally undoped LiNbO3 samples [14

14. 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]

]. Furthermore, the thermal reduction pre-treatment results in a considerable transfer of the valence state from acceptor to donor levels. For instance, the number density of Fe3+ is considerably damped c(Fe3+) ≪ 1, but it is decisive for the photorefractive response as the amplitude of the index change is linearly dependent on c(Fe3+) [22

22. J. Imbrock, S. Wevering, K. Buse, and E. Krätzig, “Nonvolatile holographic storage in photorefractive lithium tantalate crystals with laser pulses,” J. Opt. Soc. Am. B 16, 1392–1397 (1999). [CrossRef]

]. Second, the role of small free NbNb4+ electron polaron densities is neglected because of their sub-μs-lifetime [23

23. 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, 284–286 (2008). [CrossRef]

] and the chosen limitation of the temporal dynamics to the time range t ≥ 1μs.

4.1. Hologram recording by spatially modulated polaron densities

Exposure to a spatially modulated intensity pattern I(x) = Ip[1 + cos(|K|x)] results in the appearance of spatially modulated polaron densities. Densities NGP,HP of small bound electron and small hole polarons are increased in the bright region of the fringe pattern while the bipolaron density NBP is diminished in the same regions. In the dark regions there are no changes of polaron densities. The formation time of the small polaron density is limited by a sequence of processes starting from the optical excitation of a charge-carrier by absorption and ending with self-localization at a NbLi5+-site via electron-phonon coupling. The period in-between is characterized by coherent electron transport in the conduction band. Because of its coherence in the presence of electron-lattice coupling this intermediate state can be regarded as a large polaron. The formation time of small free polarons at room temperature has been reported for Mg-doped LiNbO3 to ≈ 110 fs [6

6. 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, 232–235 (2005). [CrossRef]

] while small bound polarons appear within 400 fs [24

24. O. Beyer, D. Maxein, T. Woike, and K. Buse, “Generation of small bound polarons in lithium niobate crystals on the subpicosecond time scale,” Appl. Phys. B 83, 527–530 (2006). [CrossRef]

] after the optical pulse. If the duration of illumination exceeds the polaron formation time, a repetitive excitation of charge carriers from localized states becomes possible. Thereby, the distance of the small polaron with respect to the initial polaron site can be increased significantly. This may affect the appearance of polaron-based photovoltaic currents (cf. section (4.4)), or the dynamics of the hologram recording process.

Fig. 3 (a) Spatial modulation of the absorption coefficient α(x) with amplitude α1 and average value of α0 +α1. The overall absorption change in the maximum of the fringe pattern αli is assembled from absorption changes of the individual polaron types: αGP,HP,BP. All absorption contributions are related to λ = 488 nm and extraordinary light polarization. (b) Sinusoidal intensity pattern I(x) applied for exposure with average intensity Ip = IR + IS and modulation depth unity resulting in a modulated density of polarons and, therefore, a modulated change of absorption α(x). This modulated absorption change is linked to a modulated change of the index of refraction n(x) via the Kramers-Kronig relation as shown in figure 7 in Ref. [1].

4.2. Dispersion of diffraction efficiency

Fig. 4 (a) Dispersion of the diffraction efficiency ηest.(λ) (solid line) that has been estimated according to Eq. (3) and the parameters published in Ref. [1]. The grey area denotes the error for ηest.(λ). The experimentally determined efficiencies at a probing wavelength of 488 nm (△, this work) and 785 nm (□, Ref. [1]) have been added for comparison. (b) Dispersion of the ratio of the diffraction efficiency for a pure absorption grating and a pure index grating. A predominant contribution of the absorption grating is found at 785 nm while amplitude and index grating likewise contribute to the overall efficiency at 488 nm.

4.3. Intensity dependence of diffraction efficiency

The key in understanding the saturation behavior of the diffraction efficiency at 488 nm as a function of pump beam intensity (Fig. 2(a)) is the intensity dependence of the small polaron densities involved in the hologram recording process, i.e., of bipolarons and bound polarons. According to our model, the bipolaron density is reduced via optical gating processes in the bright regions of the fringe pattern and yields an increase of the number density of small bound polarons by Nli,GP with
Nli,GP=2Nli,BP.
(4)
Here, Nli,BP denotes the number density of optically gated bipolarons. Because of the limited number density of bipolarons NBP in the groundstate, a saturation behavior according to
Nli,BP=NBP[1exp(IpIc)]
(5)
is to be expected and has been experimentally verified by means of the intensity dependence of the light-induced, transient absorption at 488 nm in Ref. [12

12. 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]

]. Because of the relation given by Eq. (4), the intensity dependence of small bound polarons shows saturation with the same characteristic intensity Ic, but an amplitude by a factor of two larger compared with Eq. (5). Furthermore, the absorption amplitude and the increase of polaron number density are directly linked via the absorption cross section. Hence, saturation as a function of pump beam intensity also appears for the amplitudes α1,BP,GP,HP and, taking into account Kramers-Kronig relation, for n1,GP,BP,HP. The latter enter equation Eq. (3), so that the diffraction efficiency inevitably shows saturation, as well. For small amplitudes α1, n1 and α1α0, we can approximate
η(Ip)(c1n1(Ip))2+(c2α1(Ip))2=ηsat.[1exp(IpIc)]2.
(6)
The function is determined by only two fitting parameters: the saturation value ηsat., and the characteristic intensity Ic. Obviously, the fit can be applied to describe the intensity behavior within the error bars as depicted by the solid line in Fig. 2. The resulting fitting parameters are summarized in Table 2, the characteristic intensity Ic is of the same order of magnitude as the characteristic intensity of the light-induced absorption as reported in Ref. [12

12. 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]

].

4.4. Dependence on the recording configuration

Understanding the dependence of the diffraction efficiency on the recording configuration Kc-axis and K || c-axis remains a challenging task. While the situation for Kc-axis is completely explained in the model of a spatially modulated polaron density, further physical processes need to be taken into account to model the results for K || c-axis. It is reasonable to assign the pronounced increase of the diffraction efficiency to the action of the linear electro-optic effect because r331 = 0, r223 ≠ 0, and r333 ≠ 0. Moreover, a predominant contribution of the index grating over the absorption grating is inferred from the efficiency exceeding the theoretical limit 3.7% of pure lossy gratings. As a consequence, the build-up of an electric field with light exposure is required. At the same time, the stretched-exponential grating decay and its temperature dependence with an activation energy of EA = (0.57±0.07) eV unambiguously assign the temporal behavior of the diffraction signal to the decay of a spatially modulated density of small bound NbLi4+ polarons. Thus, a relation between the small polaron density and the electric field, both spatially modulated along the direction of K, must be postulated. The electric field strength that modulates the index with amplitude n1 = (−2.0 ± 0.5) · 10−4 can be estimated via E=2n1/(ne3r333) (cf. Ref. [1

1. M. Imlau, H. Brüning, B. Schoke, R.-S. Hardt, D. Conradi, and C. Merschjann, “Hologram recording via spatial density modulation of NbLi4+/5+ antisites in lithium niobate,” Opt. Express 19, 15322–15338 (2011). [CrossRef] [PubMed]

]). With ne(488nm) = (2.2556 ± 0.0005) [27

27. D. S. Smith, H. D. Riccius, and R. P. Edwin, “Refractive indices of lithium niobate,” Opt. Commun. 17, 332–335 (1976). [CrossRef]

] and r333(488nm) = 34.4 pm/V [28

28. T. Fujiwara, M. Takahasi, M. Ohama, A. J. Ikushima, Y. Furukawa, and K. Kitamura, “Comparison of electro-optic effect between stoichiometric and congruent LiNbO3,” Electron. Lett. 35, 499–501 (1999). [CrossRef]

] we get E ≈ 10 kV/cm that is much larger than the saturation field for diffusion transport mechanisms Ediff = (kBT/e)(2π/Λ) ≈ 0.67 kV/cm. Hence, a photovoltaic transport mechanism can be concluded, similar to the small polaron based model approach that explains the bulk photovoltaic effect in Fe-doped LiNbO3 [10

10. 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]

].

We finally note that nonlinearities of the diffraction efficiency are reported in photorefractive-recording of holograms with ns-laser pulses in transition-metal doped LiNbO3, as well [29

29. C.-T. Chen, D. M. Kim, and D. von der Linde, “Efficient hologram recording in LiNbO3:Fe using optical pulses,” Appl. Phys. Lett. 34, 321–324 (1979). [CrossRef]

]. Contrary to solely polaron-based hologram recording, the simultaneous interplay of carriers excited from intrinsic and extrinsic defect centers needs to be considered. Thereby, an intensity limit of the nonlinearity results that represents a striking difference to our findings.

5. Conclusion

From the materials’ point of view, nominally undoped LiNbO3 becomes more attractive as hologram material for modern holographic applications, including real-time holographic displays. It can be expected that equivalent recording mechanisms are present for a variety of other oxide crystals, as well. For instance, pronounced small polaron densities can also be generated by single laser pulses in KNbO3 and BaTiO3 [11

11. 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]

].

Acknowledgment

The authors thank Gerda Cornelsen and Werner Geisler for sample preparation and the Deutsche Forschungsgemeinschaft (projects IM37/5, INST 190/137-1) and the Deutscher Akademischer Austausch Dienst in cooperation with the Hungarian Scholarship Board Office (projects 50445542, 54377942 and P-MB/840 and 29696) for financial support.

References and links

1.

M. Imlau, H. Brüning, B. Schoke, R.-S. Hardt, D. Conradi, and C. Merschjann, “Hologram recording via spatial density modulation of NbLi4+/5+ antisites in lithium niobate,” Opt. Express 19, 15322–15338 (2011). [CrossRef] [PubMed]

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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, 232–235 (2005). [CrossRef]

7.

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]

8.

O. F. Schirmer, “O Bound small polarons in oxide materials,” J. Phys.: Condens. Matter 18, R667–R704 (2006). [CrossRef]

9.

S. Tay, P.-A. Blanche, R. Voorakaranam, A. V. Tunc, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451, 694–698 (2008). [CrossRef] [PubMed]

10.

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]

11.

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]

12.

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]

13.

J. Koppitz, O. F. Schirmer, and A. I. Kuznetsov, “Thermal dissociation of bipolarons in reduced undoped LiNbO3,” Europhys. Lett. 4, 1055–1059 (1987). [CrossRef]

14.

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]

15.

F. Jermann and K. Buse, “Light-induced thermal gratings in LiNbO3:Fe,” Appl. Phys. B 59, 437–443 (1994). [CrossRef]

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18.

O. F. Schirmer, H.-J. Reyher, and M. Woehlecke, “Characterization of point defects in photorefractive oxide crystals by paramagnetic resonance methods” in Insulting Materials for Optoelectronics: New Developments, (World Scientific Publishing, Singapore, 1995), 93–124. [CrossRef]

19.

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]

20.

K. Buse, “Light-induced charge transport processes in photorefractive crystals II: Materials,” Appl. Phys. B 64, 391–407 (1997). [CrossRef]

21.

M. Imlau, “Defects and photorefraction: A relation with mutual benefit,” Phys. Status Solidi A 204, 642–652 (2007). [CrossRef]

22.

J. Imbrock, S. Wevering, K. Buse, and E. Krätzig, “Nonvolatile holographic storage in photorefractive lithium tantalate crystals with laser pulses,” J. Opt. Soc. Am. B 16, 1392–1397 (1999). [CrossRef]

23.

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, 284–286 (2008). [CrossRef]

24.

O. Beyer, D. Maxein, T. Woike, and K. Buse, “Generation of small bound polarons in lithium niobate crystals on the subpicosecond time scale,” Appl. Phys. B 83, 527–530 (2006). [CrossRef]

25.

V. Lucarini, J. J. Saarinen, K.-E. Peiponen, and E. M. Vartiainen eds., Kramers-Kronig Relations in Optical Materials Research (Springer Verlag, 2005).

26.

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

27.

D. S. Smith, H. D. Riccius, and R. P. Edwin, “Refractive indices of lithium niobate,” Opt. Commun. 17, 332–335 (1976). [CrossRef]

28.

T. Fujiwara, M. Takahasi, M. Ohama, A. J. Ikushima, Y. Furukawa, and K. Kitamura, “Comparison of electro-optic effect between stoichiometric and congruent LiNbO3,” Electron. Lett. 35, 499–501 (1999). [CrossRef]

29.

C.-T. Chen, D. M. Kim, and D. von der Linde, “Efficient hologram recording in LiNbO3:Fe using optical pulses,” Appl. Phys. Lett. 34, 321–324 (1979). [CrossRef]

30.

D. Maxein, J. Bückers, D. Haertle, and K. Buse, “Photorefraction in LiNbO3:Fe crystals with femtosecond pulses at 532 nm,” Appl. Phys. B 95, 399–405 (2009) [CrossRef]

31.

C. Nölleke, J. Imbrock, and C. Denz, “Two-step holographic recording in photorefractive lithium niobate crystals using ultrashort laser pulses,” Appl. Phys. B 95, 391–397 (2009). [CrossRef]

32.

M. Simon, F. Jermann, and E. Krätzig, “Photorefractive effects in LiNbO3:Fe, me at high light intensities,” Opt. Mat. 4, 286 – 289 (1995). [CrossRef]

33.

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]

34.

D. von der Linde, O. F. Schirmer, and H. Kurz, “Intrinsic photorefractive effect of LiNbO3,” Appl. Phys. A 15, 153–156 (1978).

35.

G. A. Brost, R. A. Motes, and J. R. Rotge, “Intensity-dependent absorption and photorefractive effects in barium titanate,” J. Opt. Soc. Am. B 5, 1879–1885 (1988). [CrossRef]

36.

H. Vormann and E. Krätzig, “Two step excitation in LiTaO3:Fe for optical data storage,” Solid State Communications 49, 843–847 (1984). [CrossRef]

37.

Y. S. Bai and R. Kachru, “Nonvolatile holographic storage with two-step recording in lithium niobate using cw lasers,” Phys. Rev. Lett. 78, 2944–2947 (1997). [CrossRef]

38.

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]

OCIS Codes
(090.7330) Holography : Volume gratings
(160.3730) Materials : Lithium niobate
(160.4670) Materials : Optical materials
(160.4760) Materials : Optical properties
(190.4400) Nonlinear optics : Nonlinear optics, materials
(160.5335) Materials : Photosensitive materials

ToC Category:
Holography

History
Original Manuscript: April 27, 2012
Revised Manuscript: May 23, 2012
Manuscript Accepted: May 23, 2012
Published: May 29, 2012

Citation
H. Brüning, V. Dieckmann, B. Schoke, K.-M. Voit, M. Imlau, G. Corradi, and C. Merschjann, "Small-polaron based holograms in LiNbO3 in the visible spectrum," Opt. Express 20, 13326-13336 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-12-13326


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References

  1. M. Imlau, H. Brüning, B. Schoke, R.-S. Hardt, D. Conradi, and C. Merschjann, “Hologram recording via spatial density modulation of NbLi4+/5+ antisites in lithium niobate,” Opt. Express19, 15322–15338 (2011). [CrossRef] [PubMed]
  2. D. Emin, “Polaron” in McGraw-Hill Encyclopedia of Science and Technology, (McGraw-Hill, New York, 2007) 125
  3. P.-A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W.-Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “Holographic three-dimensional telepresence using large-area photorefractive polymer,” Nature468, 80–83 (2010). [CrossRef] [PubMed]
  4. C. Gu, Fu, and J.-R. Lien, “Correlation patterns and cross-talk noise in volume holographic optical correlators,” J. Opt. Soc. Am. A12, 861–868 (1995). [CrossRef]
  5. D. Sadot and E. Boimovich, “Tunable optical filters for dense wdm networks,” IEEE Commun. Mag.36, 50 –55 (1998). [CrossRef]
  6. Y. Qiu, K. B. Ucer, and R. T. Williams, “Formation time of a small electron polaron in LiNbO3: measurements and interpretation,” Phys. Status Solidi C2, 232–235 (2005). [CrossRef]
  7. 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]
  8. O. F. Schirmer, “O− Bound small polarons in oxide materials,” J. Phys.: Condens. Matter18, R667–R704 (2006). [CrossRef]
  9. S. Tay, P.-A. Blanche, R. Voorakaranam, A. V. Tunc, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature451, 694–698 (2008). [CrossRef] [PubMed]
  10. O. F. Schirmer, M. Imlau, and C. Merschjann, “Bulk photovoltaic effect of LiNbO3:Fe and its small-polaron-based microscopic interpretation,” Phys. Rev. B83, 165106 (2011). [CrossRef]
  11. 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. B78, 125112 (2008). [CrossRef]
  12. 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. B76, 085114 (2007). [CrossRef]
  13. J. Koppitz, O. F. Schirmer, and A. I. Kuznetsov, “Thermal dissociation of bipolarons in reduced undoped LiNbO3,” Europhys. Lett.4, 1055–1059 (1987). [CrossRef]
  14. 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. Matter21, 015906 (2009). [CrossRef]
  15. F. Jermann and K. Buse, “Light-induced thermal gratings in LiNbO3:Fe,” Appl. Phys. B59, 437–443 (1994). [CrossRef]
  16. R. S. Weis and T. K. Gaylord, “Lithium niobate: summery of physical properties and crystal structure,” Appl. Phys. A37, 191–203 (1985). [CrossRef]
  17. G. Williams and D. C. Watts, “Non–symmetrical dielectric relaxation behaviour arising from a simple empirical decay function,” Trans. Faraday. Soc66, 80–85 (1970). [CrossRef]
  18. O. F. Schirmer, H.-J. Reyher, and M. Woehlecke, “Characterization of point defects in photorefractive oxide crystals by paramagnetic resonance methods” in Insulting Materials for Optoelectronics: New Developments, (World Scientific Publishing, Singapore, 1995), 93–124. [CrossRef]
  19. L. Hesselink, S. S. Orlov, A. Lie, A. Akella, D. Lande, and R. R. Neurgaonkar, “Photorefractive materials for nonvolatile volume holographic data storage,” Science282, 1089 (1998). [CrossRef] [PubMed]
  20. K. Buse, “Light-induced charge transport processes in photorefractive crystals II: Materials,” Appl. Phys. B64, 391–407 (1997). [CrossRef]
  21. M. Imlau, “Defects and photorefraction: A relation with mutual benefit,” Phys. Status Solidi A204, 642–652 (2007). [CrossRef]
  22. J. Imbrock, S. Wevering, K. Buse, and E. Krätzig, “Nonvolatile holographic storage in photorefractive lithium tantalate crystals with laser pulses,” J. Opt. Soc. Am. B16, 1392–1397 (1999). [CrossRef]
  23. 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. RRL2, 284–286 (2008). [CrossRef]
  24. O. Beyer, D. Maxein, T. Woike, and K. Buse, “Generation of small bound polarons in lithium niobate crystals on the subpicosecond time scale,” Appl. Phys. B83, 527–530 (2006). [CrossRef]
  25. V. Lucarini, J. J. Saarinen, K.-E. Peiponen, and E. M. Vartiainen eds., Kramers-Kronig Relations in Optical Materials Research (Springer Verlag, 2005).
  26. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J.48, 2909 (1969).
  27. D. S. Smith, H. D. Riccius, and R. P. Edwin, “Refractive indices of lithium niobate,” Opt. Commun.17, 332–335 (1976). [CrossRef]
  28. T. Fujiwara, M. Takahasi, M. Ohama, A. J. Ikushima, Y. Furukawa, and K. Kitamura, “Comparison of electro-optic effect between stoichiometric and congruent LiNbO3,” Electron. Lett.35, 499–501 (1999). [CrossRef]
  29. C.-T. Chen, D. M. Kim, and D. von der Linde, “Efficient hologram recording in LiNbO3:Fe using optical pulses,” Appl. Phys. Lett.34, 321–324 (1979). [CrossRef]
  30. D. Maxein, J. Bückers, D. Haertle, and K. Buse, “Photorefraction in LiNbO3:Fe crystals with femtosecond pulses at 532 nm,” Appl. Phys. B95, 399–405 (2009) [CrossRef]
  31. C. Nölleke, J. Imbrock, and C. Denz, “Two-step holographic recording in photorefractive lithium niobate crystals using ultrashort laser pulses,” Appl. Phys. B95, 391–397 (2009). [CrossRef]
  32. M. Simon, F. Jermann, and E. Krätzig, “Photorefractive effects in LiNbO3:Fe, me at high light intensities,” Opt. Mat.4, 286 – 289 (1995). [CrossRef]
  33. 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]
  34. D. von der Linde, O. F. Schirmer, and H. Kurz, “Intrinsic photorefractive effect of LiNbO3,” Appl. Phys. A15, 153–156 (1978).
  35. G. A. Brost, R. A. Motes, and J. R. Rotge, “Intensity-dependent absorption and photorefractive effects in barium titanate,” J. Opt. Soc. Am. B5, 1879–1885 (1988). [CrossRef]
  36. H. Vormann and E. Krätzig, “Two step excitation in LiTaO3:Fe for optical data storage,” Solid State Communications49, 843–847 (1984). [CrossRef]
  37. Y. S. Bai and R. Kachru, “Nonvolatile holographic storage with two-step recording in lithium niobate using cw lasers,” Phys. Rev. Lett.78, 2944–2947 (1997). [CrossRef]
  38. 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]

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