Abstract

We report on the first observation, to our knowledge, of self-focusing without an external electric field in barium titanate crystals under cw laser beam irradiance. This effect we observed at an intensity of 0.2W/cm2 on the 633nm wavelength regime in the case of ordinarily as well as extraordinarily polarized light.

© 2006 Optical Society of America

1. Introduction

Photorefractive, nonlinear optical crystals, such as BaTiO3, are currently used for a wide range of applications in electronics, optics and optoelectronics. So it is very desirable to know how this material acts under laser irradiance, and what interactions between material and light appear. One of the nonlinear optical effects mostly discussed in the last decade is self-focusing. In balance with diffraction this effect can cause soliton formation. Usually an external electric field is applied to change the refractive index of the material by the electro-optic effect, and so to generate self-focusing. This excites in balance with self-diffraction screening solitons [1, 2]. In BaTiO3 a strong self-focusing effect occurred using external fields in the range of 2.8kV/cm [3, 4].

But it is also known that photorefractive self-focusing can appear without an external electric field, only due to intrinsic fields and the anisotropic properties of the material [5, 6, 7]. Here, also a balance between self-focusing and diffraction can be achieved, which leads to so called photovoltaic solitons [8, 9]. Until now photovoltaic solitons were observed only in LiNbO 3 crystals [10, 11]. Another way to obtain self-focusing without external field is the use of high laser intensities, which leads to thermal focusing effects. In barium titanate as well as in SBN this effect is observed with short laser pulses in the range of 102…103W/mm2 [11, 12].

In this letter we present experimental data, which show that self-focusing without external field occurs also in BaTiO3, using only an intensity of 0.2W/cm2. It is demonstrated that the effect depends on the crystal doping and cut, and on the polarization direction of the laser beam as well.

2. Experimental Set-Up

The experiments on investigations of the optical induced changes of the diameter of a laser beam were performed at room temperature. Poled single crystals of ferroelectric BaTiO 3 that belong to the point group 4mm were used. BaTiO3 possesses large linear electro-optic coefficients [13] and a large spontaneous polarization. The samples lay clamp free on a board. The source of light was a He-Ne-laser with λ=633nm, whose beam first passed an intensity filter IF and a Glan-Thompson-polarizer P like it is shown in Fig. 1. The light was focused on the front face of the crystal K by a micro-objective O with a focus diameter of about 4µm. The beam at the rear face of the crystal was imaged by a telescope system L on a CCD-camera C with a reproduction scale of M=2.

An intensity of 0.2Wcm-2 was used. During the whole measurement the intensity of the laser beam behind the crystal was proofed to be constant.

 

Fig. 1. Experimental set-up: La: He-Ne-laser, I: intensity filter, P: Glan-Thompson-polarizer, O: micro-objective, K: crystal, L: telescope system, C: CCD-matrix.

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3. Experimental Results

The samples of BaTiO3, used in the experiments (see table 1), were nominal pure or doped with Rh or Co. The typical run of transmission of these three types of doping in dependence on the wavelength is shown in Fig. 2.

Studying the effect of self-focusing it is remarkable that the undoped crystals showed a much stronger focusing effect than rhodium or cobalt doped crystals under the above described conditions (Fig. 3).

Tables Icon

Table 1. Samples (1–19) of the barium titanate crystals with edge lengths a/b/c, color, absorption coefficients α at 633nm, doping and cut

 

Fig. 2. Dependence of the crystals transmission on the wavelength.

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Another important parameter is the cut of the crystals. We analyzed two 45°cut samples and six 0°cut samples of undoped barium titanate. Although self-focusing of the laser beam in 0°cut samples could be observed, the effect was stronger in the 45°cut samples, like it is shown in Fig. 4.

 

Fig. 3. Comparison of self-focusing in nominal pure, Rh and Co doped crystals. The beam diameter w at the rear face of the crystal is normalized at the output diameter w at the beginning of the measurement.

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Fig. 4. Comparison of self-focusing in 0° and 45°cut crystals of undoped barium titanate. The beam diameter w at the rear face of the crystal is normalized at the output diameter w at the beginning of the measurement.

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Therefore, to investigate the dependence of the self-focusing effect on the polarization direction of the beam a undoped 45°cut BaTiO3 crystal (number 19 in the table above) was used. The crystals size, the direction of the optical axis and the two used polarization directions are shown in Fig. 5.

Using ordinarily polarized light, the beam diameter related to I=Imaxe2 at the rear face of the crystal scaled down about 15%within 17 minutes (Fig. 6). The reduction was of the same value parallel to the x-axis as parallel to the y-axis. By contrast, if an extraordinarily polarized beam was applied its diameter parallel to the x-axis scaled down about 22%, but the beam diameter in y-direction only ran through a transient focus. This temporal development is shown in Fig. 6, too, in comparison with the diameter of ordinarily polarized light.

 

Fig. 5. Direction of polarizations of the laser beam and edge length of the crystal that was used in experiment.

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Fig. 6. Beam diameter at

I=Imaxe2

in dependence on time in the case of ordinarily and extraorinarily polarized light. The beam diameter w at the rear face of the crystal is normalized at the output diameter w at the beginning of the measurement.

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In the case of ordinarily polarized light, there was an external white light source, as background illumination, necessary to achieve a self-focusing effect. Using extraordinarily polarized light, no dependence on this white light illumination could be observed.

After reaching the stable focussed state, the beam diameter didn’t change within 10 hours. As expected, the wave-guiding canal in the crystal remained stable for month if the crystal isn’t illuminated and not heated [14]. To avoid the influence of previously written refraction index changes, before starting the investigation, the crystal had to be illuminated homogeneously with light, for instance by a white light emitting diode. Thus, the charge distribution became homogenized, older stored changes of the refractive index were erased. With a diode current of 28mA, it took about 30 minutes to get the crystal in its original state.

4. Conclusion

It could be shown that in BaTiO3 a self-focusing effect appears at a laser beam intensity of 0.2W/cm2 without applying an external electric field. This effect can be observed by use of ordinarily polarized light as well as extraordinarily polarized light. The greatest focusing we achieved in undoped crystals with 45°cut and using extraordinarily polarized light. The focused state remains stable in darkness about 10 hours.

Acknowledgments

We would like to thank the Deutsche Forschungsgemeinschaft for financial support within the Forschergruppe “Nichtlineare raum-zeitliche Dynamik in dissipativen und diskreten optischen Systemen”.

References and links

1. M. Segev, B. Crosignani, A. Yariv, and B. Fisher, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926 (1992). [CrossRef]   [PubMed]  

2. G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993). [CrossRef]   [PubMed]  

3. E. DelRe, M. Tamburrini, and G. Egidi, Bright photorefractive spatial solitons in tilted BaTiO3, presented at the Eleventh Annual Meeting of the [IEEE Lasers and Electro-Optics Society] (LEOS 98), Orlando, Fla., 3–4 December 1998.

4. J. Andrade-Lucio, M. Iturbe-Castillo, P. Marquez-Aguilar, and R. Ramos-Garcia, “Self-focusing in photorefractive BaTiO3 crystal under external DC electric field,” Opt. Quantum Electron. 30, 829–834 (1998). [CrossRef]  

5. P. Guenter and J. Huignard, Photorefractive Materials and Their Applications 1 - Fundamental Phenomena (Springer, Berlin, 1988). [CrossRef]  

6. W. Kaenzig, “Space charge layer near the surface of a ferroelectric,” Phys. Rev. 98, 549–550 (1955). [CrossRef]  

7. V. Matusevich, A. Krasnoberski, D. Khmelnitski, A. Kiessling, and R. Kowarschik, “Some aspects of fanning, self-focusing and self-defocusing in a photorefractive Ba0.77Ca0.23TiO3 crystal,” J. Opt. A: Pure Appl. Opt. 6, 507–513 (2003). [CrossRef]  

8. G. Valley, M. Segev, B. Crosignani, A. Yariv, and M. B. Fejer, “Dark and Bright Photovoltaic Spatial Solitons,” Phys. Rev. A 50, R4457–R4460 (1994). [CrossRef]   [PubMed]  

9. J. Liu, “Existence and stability of rigid photovoltaic solitons in an open-circuit amplifying or absorbing photo-voltaic medium,” Phys. Rev. E 68, 0266071–0266077 (2003). [CrossRef]  

10. F. Chen, “Optically induced change of refractive indices in LiNbO3,” J. App. Phys. 40, 3389–3396 (1969). [CrossRef]  

11. L. Palfalv, J. Hebling, G. Almasi, A. Peter, and K. Polgar, “Refractive index changes in Mg-doped LiNbO3 caused by photorefraction and thermal effects,” J. Opt. A 5, S280–S283 (2003). [CrossRef]  

12. M. Horowitz, R. Daisy, O. Werner, and B. Fischer, “Large thermal nonlinearities and spatial self-phase modulation in SrxBa1-xNb2O6 and BaTiO3 crystals,” J. Appl. Phys. 17, 475–477 (1992).

13. D. Nolte, Photorefractive effects and materials (Kluwer Acad. Publ., Boston, 1995).

14. G. Bacher, M. Chiao, G. Dunning, M. Klein, C. Nelson, and B. Wechsler, “Ultralong dark decay measurements in BaTiO3,” Opt. Lett. 21, 18–20 (1996). [CrossRef]   [PubMed]  

References

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  1. M. Segev, B. Crosignani, A. Yariv and B. Fisher, "Spatial solitons in photorefractive media," Phys. Rev. Lett. 68,923-926 (1992).
    [CrossRef] [PubMed]
  2. G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, E. J. Sharp and R. R. Neurgaonkar, "Observation of self-trapping of an optical beam due to the photorefractive effect," Phys. Rev. Lett. 71,533-536 (1993).
    [CrossRef] [PubMed]
  3. E. DelRe, M. Tamburrini, and G. Egidi, Bright photorefractive spatial solitons in tilted BaTiO3, presented at the Eleventh Annual Meeting of the [IEEE Lasers and Electro-Optics Society] (LEOS 98), Orlando, Fla., 3 - 4 December 1998.
  4. J. Andrade-Lucio, M. Iturbe-Castillo, P. Marquez-Aguilar and R. Ramos-Garcia, "Self-focusing in photorefractive BaTiO3 crystal under external DC electric field," Opt. Quantum Electron. 30,829-834 (1998).
    [CrossRef]
  5. P. Guenter and J. Huignard, Photorefractive Materials and Their Applications 1 - Fundamental Phenomena (Springer, Berlin, 1988).
    [CrossRef]
  6. W. Kaenzig, "Space charge layer near the surface of a ferroelectric," Phys. Rev. 98,549-550 (1955).
    [CrossRef]
  7. V. Matusevich, A. Krasnoberski, D. Khmelnitski, A. Kiessling and R. Kowarschik, "Some aspects of fanning, self-focusing and self-defocusing in a photorefractive Ba0.77Ca0.23TiO3 crystal," J. Opt. A: Pure Appl. Opt. 6,507-513 (2003).
    [CrossRef]
  8. G. Valley, M. Segev, B. Crosignani, A. Yariv and M. B. Fejer, "Dark and bright photovoltaic spatial solitons," Phys. Rev. A 50,R4457-R4460 (1994).
    [CrossRef] [PubMed]
  9. J. Liu, "Existence and stability of rigid photovoltaic solitons in an open-circuit amplifying or absorbing photovoltaic medium," Phys. Rev. E 68,0266071-0266077 (2003).
    [CrossRef]
  10. F. Chen, "Optically induced change of refractive indices in LiNbO3," J. Appl. Phys. 40,3389-3396 (1969).
    [CrossRef]
  11. L. Palfalv, J. Hebling, G. Almasi, A. Peter and K. Polgar, "Refractive index changes in Mg-doped LiNbO3 caused by photorefraction and thermal effects," J. Opt. A 5,S280-S283 (2003).
    [CrossRef]
  12. M. Horowitz, R. Daisy, O. Werner and B. Fischer, "Large thermal nonlinearities and spatial self-phase modulation in SrxBa1−xNb2O6 and BaTiO3 crystals," J. Appl. Phys. 17,475-477 (1992).
  13. D. Nolte, Photorefractive effects and materials (Kluwers Academic Publishers, Boston, 1995).
  14. G. Bacher, M. Chiao, G. Dunning, M. Klein, C. Nelson and B. Wechsler, "Ultralong dark decay measurements in BaTiO3," Opt. Lett. 21,18-20 (1996).
    [CrossRef] [PubMed]

2003

V. Matusevich, A. Krasnoberski, D. Khmelnitski, A. Kiessling and R. Kowarschik, "Some aspects of fanning, self-focusing and self-defocusing in a photorefractive Ba0.77Ca0.23TiO3 crystal," J. Opt. A: Pure Appl. Opt. 6,507-513 (2003).
[CrossRef]

J. Liu, "Existence and stability of rigid photovoltaic solitons in an open-circuit amplifying or absorbing photovoltaic medium," Phys. Rev. E 68,0266071-0266077 (2003).
[CrossRef]

L. Palfalv, J. Hebling, G. Almasi, A. Peter and K. Polgar, "Refractive index changes in Mg-doped LiNbO3 caused by photorefraction and thermal effects," J. Opt. A 5,S280-S283 (2003).
[CrossRef]

1998

J. Andrade-Lucio, M. Iturbe-Castillo, P. Marquez-Aguilar and R. Ramos-Garcia, "Self-focusing in photorefractive BaTiO3 crystal under external DC electric field," Opt. Quantum Electron. 30,829-834 (1998).
[CrossRef]

1996

1994

G. Valley, M. Segev, B. Crosignani, A. Yariv and M. B. Fejer, "Dark and bright photovoltaic spatial solitons," Phys. Rev. A 50,R4457-R4460 (1994).
[CrossRef] [PubMed]

1993

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, E. J. Sharp and R. R. Neurgaonkar, "Observation of self-trapping of an optical beam due to the photorefractive effect," Phys. Rev. Lett. 71,533-536 (1993).
[CrossRef] [PubMed]

1992

M. Segev, B. Crosignani, A. Yariv and B. Fisher, "Spatial solitons in photorefractive media," Phys. Rev. Lett. 68,923-926 (1992).
[CrossRef] [PubMed]

M. Horowitz, R. Daisy, O. Werner and B. Fischer, "Large thermal nonlinearities and spatial self-phase modulation in SrxBa1−xNb2O6 and BaTiO3 crystals," J. Appl. Phys. 17,475-477 (1992).

1969

F. Chen, "Optically induced change of refractive indices in LiNbO3," J. Appl. Phys. 40,3389-3396 (1969).
[CrossRef]

1955

W. Kaenzig, "Space charge layer near the surface of a ferroelectric," Phys. Rev. 98,549-550 (1955).
[CrossRef]

Almasi, G.

L. Palfalv, J. Hebling, G. Almasi, A. Peter and K. Polgar, "Refractive index changes in Mg-doped LiNbO3 caused by photorefraction and thermal effects," J. Opt. A 5,S280-S283 (2003).
[CrossRef]

Andrade-Lucio, J.

J. Andrade-Lucio, M. Iturbe-Castillo, P. Marquez-Aguilar and R. Ramos-Garcia, "Self-focusing in photorefractive BaTiO3 crystal under external DC electric field," Opt. Quantum Electron. 30,829-834 (1998).
[CrossRef]

Bacher, G.

Chen, F.

F. Chen, "Optically induced change of refractive indices in LiNbO3," J. Appl. Phys. 40,3389-3396 (1969).
[CrossRef]

Chiao, M.

Crosignani, B.

G. Valley, M. Segev, B. Crosignani, A. Yariv and M. B. Fejer, "Dark and bright photovoltaic spatial solitons," Phys. Rev. A 50,R4457-R4460 (1994).
[CrossRef] [PubMed]

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, E. J. Sharp and R. R. Neurgaonkar, "Observation of self-trapping of an optical beam due to the photorefractive effect," Phys. Rev. Lett. 71,533-536 (1993).
[CrossRef] [PubMed]

M. Segev, B. Crosignani, A. Yariv and B. Fisher, "Spatial solitons in photorefractive media," Phys. Rev. Lett. 68,923-926 (1992).
[CrossRef] [PubMed]

Daisy, R.

M. Horowitz, R. Daisy, O. Werner and B. Fischer, "Large thermal nonlinearities and spatial self-phase modulation in SrxBa1−xNb2O6 and BaTiO3 crystals," J. Appl. Phys. 17,475-477 (1992).

Dunning, G.

Duree, G. C.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, E. J. Sharp and R. R. Neurgaonkar, "Observation of self-trapping of an optical beam due to the photorefractive effect," Phys. Rev. Lett. 71,533-536 (1993).
[CrossRef] [PubMed]

Fejer, M. B.

G. Valley, M. Segev, B. Crosignani, A. Yariv and M. B. Fejer, "Dark and bright photovoltaic spatial solitons," Phys. Rev. A 50,R4457-R4460 (1994).
[CrossRef] [PubMed]

Fischer, B.

M. Horowitz, R. Daisy, O. Werner and B. Fischer, "Large thermal nonlinearities and spatial self-phase modulation in SrxBa1−xNb2O6 and BaTiO3 crystals," J. Appl. Phys. 17,475-477 (1992).

Fisher, B.

M. Segev, B. Crosignani, A. Yariv and B. Fisher, "Spatial solitons in photorefractive media," Phys. Rev. Lett. 68,923-926 (1992).
[CrossRef] [PubMed]

Hebling, J.

L. Palfalv, J. Hebling, G. Almasi, A. Peter and K. Polgar, "Refractive index changes in Mg-doped LiNbO3 caused by photorefraction and thermal effects," J. Opt. A 5,S280-S283 (2003).
[CrossRef]

Horowitz, M.

M. Horowitz, R. Daisy, O. Werner and B. Fischer, "Large thermal nonlinearities and spatial self-phase modulation in SrxBa1−xNb2O6 and BaTiO3 crystals," J. Appl. Phys. 17,475-477 (1992).

Iturbe-Castillo, M.

J. Andrade-Lucio, M. Iturbe-Castillo, P. Marquez-Aguilar and R. Ramos-Garcia, "Self-focusing in photorefractive BaTiO3 crystal under external DC electric field," Opt. Quantum Electron. 30,829-834 (1998).
[CrossRef]

Kaenzig, W.

W. Kaenzig, "Space charge layer near the surface of a ferroelectric," Phys. Rev. 98,549-550 (1955).
[CrossRef]

Khmelnitski, D.

V. Matusevich, A. Krasnoberski, D. Khmelnitski, A. Kiessling and R. Kowarschik, "Some aspects of fanning, self-focusing and self-defocusing in a photorefractive Ba0.77Ca0.23TiO3 crystal," J. Opt. A: Pure Appl. Opt. 6,507-513 (2003).
[CrossRef]

Kiessling, A.

V. Matusevich, A. Krasnoberski, D. Khmelnitski, A. Kiessling and R. Kowarschik, "Some aspects of fanning, self-focusing and self-defocusing in a photorefractive Ba0.77Ca0.23TiO3 crystal," J. Opt. A: Pure Appl. Opt. 6,507-513 (2003).
[CrossRef]

Klein, M.

Kowarschik, R.

V. Matusevich, A. Krasnoberski, D. Khmelnitski, A. Kiessling and R. Kowarschik, "Some aspects of fanning, self-focusing and self-defocusing in a photorefractive Ba0.77Ca0.23TiO3 crystal," J. Opt. A: Pure Appl. Opt. 6,507-513 (2003).
[CrossRef]

Krasnoberski, A.

V. Matusevich, A. Krasnoberski, D. Khmelnitski, A. Kiessling and R. Kowarschik, "Some aspects of fanning, self-focusing and self-defocusing in a photorefractive Ba0.77Ca0.23TiO3 crystal," J. Opt. A: Pure Appl. Opt. 6,507-513 (2003).
[CrossRef]

Liu, J.

J. Liu, "Existence and stability of rigid photovoltaic solitons in an open-circuit amplifying or absorbing photovoltaic medium," Phys. Rev. E 68,0266071-0266077 (2003).
[CrossRef]

Marquez-Aguilar, P.

J. Andrade-Lucio, M. Iturbe-Castillo, P. Marquez-Aguilar and R. Ramos-Garcia, "Self-focusing in photorefractive BaTiO3 crystal under external DC electric field," Opt. Quantum Electron. 30,829-834 (1998).
[CrossRef]

Matusevich, V.

V. Matusevich, A. Krasnoberski, D. Khmelnitski, A. Kiessling and R. Kowarschik, "Some aspects of fanning, self-focusing and self-defocusing in a photorefractive Ba0.77Ca0.23TiO3 crystal," J. Opt. A: Pure Appl. Opt. 6,507-513 (2003).
[CrossRef]

Nelson, C.

Neurgaonkar, R. R.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, E. J. Sharp and R. R. Neurgaonkar, "Observation of self-trapping of an optical beam due to the photorefractive effect," Phys. Rev. Lett. 71,533-536 (1993).
[CrossRef] [PubMed]

Palfalv, L.

L. Palfalv, J. Hebling, G. Almasi, A. Peter and K. Polgar, "Refractive index changes in Mg-doped LiNbO3 caused by photorefraction and thermal effects," J. Opt. A 5,S280-S283 (2003).
[CrossRef]

Peter, A.

L. Palfalv, J. Hebling, G. Almasi, A. Peter and K. Polgar, "Refractive index changes in Mg-doped LiNbO3 caused by photorefraction and thermal effects," J. Opt. A 5,S280-S283 (2003).
[CrossRef]

Polgar, K.

L. Palfalv, J. Hebling, G. Almasi, A. Peter and K. Polgar, "Refractive index changes in Mg-doped LiNbO3 caused by photorefraction and thermal effects," J. Opt. A 5,S280-S283 (2003).
[CrossRef]

Porto, P. D.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, E. J. Sharp and R. R. Neurgaonkar, "Observation of self-trapping of an optical beam due to the photorefractive effect," Phys. Rev. Lett. 71,533-536 (1993).
[CrossRef] [PubMed]

Ramos-Garcia, R.

J. Andrade-Lucio, M. Iturbe-Castillo, P. Marquez-Aguilar and R. Ramos-Garcia, "Self-focusing in photorefractive BaTiO3 crystal under external DC electric field," Opt. Quantum Electron. 30,829-834 (1998).
[CrossRef]

Salamo, G. J.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, E. J. Sharp and R. R. Neurgaonkar, "Observation of self-trapping of an optical beam due to the photorefractive effect," Phys. Rev. Lett. 71,533-536 (1993).
[CrossRef] [PubMed]

Segev, M.

G. Valley, M. Segev, B. Crosignani, A. Yariv and M. B. Fejer, "Dark and bright photovoltaic spatial solitons," Phys. Rev. A 50,R4457-R4460 (1994).
[CrossRef] [PubMed]

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, E. J. Sharp and R. R. Neurgaonkar, "Observation of self-trapping of an optical beam due to the photorefractive effect," Phys. Rev. Lett. 71,533-536 (1993).
[CrossRef] [PubMed]

M. Segev, B. Crosignani, A. Yariv and B. Fisher, "Spatial solitons in photorefractive media," Phys. Rev. Lett. 68,923-926 (1992).
[CrossRef] [PubMed]

Sharp, E. J.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, E. J. Sharp and R. R. Neurgaonkar, "Observation of self-trapping of an optical beam due to the photorefractive effect," Phys. Rev. Lett. 71,533-536 (1993).
[CrossRef] [PubMed]

Shultz, J. L.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, E. J. Sharp and R. R. Neurgaonkar, "Observation of self-trapping of an optical beam due to the photorefractive effect," Phys. Rev. Lett. 71,533-536 (1993).
[CrossRef] [PubMed]

Valley, G.

G. Valley, M. Segev, B. Crosignani, A. Yariv and M. B. Fejer, "Dark and bright photovoltaic spatial solitons," Phys. Rev. A 50,R4457-R4460 (1994).
[CrossRef] [PubMed]

Wechsler, B.

Werner, O.

M. Horowitz, R. Daisy, O. Werner and B. Fischer, "Large thermal nonlinearities and spatial self-phase modulation in SrxBa1−xNb2O6 and BaTiO3 crystals," J. Appl. Phys. 17,475-477 (1992).

Yariv, A.

G. Valley, M. Segev, B. Crosignani, A. Yariv and M. B. Fejer, "Dark and bright photovoltaic spatial solitons," Phys. Rev. A 50,R4457-R4460 (1994).
[CrossRef] [PubMed]

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, E. J. Sharp and R. R. Neurgaonkar, "Observation of self-trapping of an optical beam due to the photorefractive effect," Phys. Rev. Lett. 71,533-536 (1993).
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Figures (6)

Fig. 1.
Fig. 1.

Experimental set-up: La: He-Ne-laser, I: intensity filter, P: Glan-Thompson-polarizer, O: micro-objective, K: crystal, L: telescope system, C: CCD-matrix.

Fig. 2.
Fig. 2.

Dependence of the crystals transmission on the wavelength.

Fig. 3.
Fig. 3.

Comparison of self-focusing in nominal pure, Rh and Co doped crystals. The beam diameter w at the rear face of the crystal is normalized at the output diameter w at the beginning of the measurement.

Fig. 4.
Fig. 4.

Comparison of self-focusing in 0° and 45°cut crystals of undoped barium titanate. The beam diameter w at the rear face of the crystal is normalized at the output diameter w at the beginning of the measurement.

Fig. 5.
Fig. 5.

Direction of polarizations of the laser beam and edge length of the crystal that was used in experiment.

Fig. 6.
Fig. 6.

Beam diameter at

Tables (1)

Tables Icon

Table 1. Samples (1–19) of the barium titanate crystals with edge lengths a/b/c, color, absorption coefficients α at 633nm, doping and cut

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