Propagation characteristics of a focused laser beam in a strontium barium niobate photorefractive crystal under reverse external electric field Q. L. Guo,1 B. L. Liang,1,* Y. Wang,1 G. Y. Deng,1 Y. H. Jiang,1 S. H. Zhang,1 G. S. Fu,1 and P. J. Simmonds2 1
College of Physics Science & Technology, Hebei University, Baoding 071002, China
2
California NanoSystem Institute, University of California, Los Angeles, California 90095, USA *Corresponding author: [email protected] Received 1 May 2014; accepted 15 August 2014; posted 26 August 2014 (Doc. ID 211171); published 24 September 2014
The propagation characteristics of a focused laser beam in a SBN:75 photorefractive crystal strongly depend on the signal-to-background intensity ratio (R Is ∕I b ) under reverse external electric field. In the range 20 > R > 0.05, the laser beam shows enhanced self-defocusing behavior with increasing external electric field, while it shows self-focusing in the range 0.03 > R > 0.01. Spatial solitons are observed under a suitable reverse external electric field for R 0.025. A theoretical model is proposed to explain the experimental observations, which suggest a new type of soliton formation due to “enhancement” not “screening” of the external electrical field. © 2014 Optical Society of America OCIS codes: (190.6135) Spatial solitons; (190.5330) Photorefractive optics; (160.5320) Photorefractive materials; (140.3300) Laser beam shaping; (230.7370) Waveguides. http://dx.doi.org/10.1364/AO.53.006422
1. Introduction
A spatial soliton or a self-trapped beam is an optical beam that propagates without diffraction, that is, the beam shape and diameter remain invariant during propagation. The spatial soliton in a photorefractive medium was first theoretically predicted by Segev et al. in 1992 and experimentally observed by Duree et al. in 1993 [1,2]. Photorefractive spatial solitons have numerous intriguing features including short response time, low laser power, and erasable and rewritable characteristics [3–7]. As a result, these solitons have many potential applications, such as optical information processing, optical storage, optical interconnects, and optical computing [8–13]. So far, reported photorefractive spatial solitons can be classified into three types: quasi-steady-state solitons [4,14,15], screening solitons [16–18], and
photovoltaic solitons [19–21]. Quasi-steady-state solitons occur when diffraction of a laser beam is completely compensated for by the nonlinearity caused by the “screening process” of an external electric field applied to the photorefractive crystal. Such quasi-steady-state solitons have been well studied in strontium barium niobate (SBN) crystals under a positive external electric field, that is, the external field is parallel to the c axis of the crystal. Recently, our group investigated the (2 1) quasi-steady-state solitons and their temporal behavior in a SBN:75 crystal with appropriate positive external field [22]. In this study, we take a step further to investigate the formation of quasi-steady-state spatial solitons in a SBN:75 crystal under reverse external electric field, that is, the external field antiparallel to the c axis of the photorefractive crystal. 2. Experiments
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The experiments are carried out using the setup shown in Fig. 1(a). A laser beam from a single
frequency solid laser with wavelength 532 nm is separated into a signal beam I s and a background beam I b . A chopper with transparent blades is used to make these two beams incoherent with each other. The signal beam is focused by a convex lens (f 12.5 cm) onto the input surface of the photorefractive crystal and the background beam covers the whole input surface of crystal. The photorefractive crystal is a 5 mm × 5 mm × 5 mm SBN:75. The signal beam spots at the input and output surface of the crystal are imaged onto a laser beam analyzer for observation and analysis. The c axis of the SBN crystal is horizontal and perpendicular to the propagation direction of the signal beam. We set the signal beam as extraordinarily polarized, the background beam as ordinarily polarized, and apply a reverse electric field to the crystal in order to obtain a larger nonlinearity. Figure 1(b) shows the relative configuration of the c axis of the SBN crystal, the signal beam polarization, and the applied electric field. 3. Results and Discussion
The evolution characteristics after the focused laser beam propagates through the SBN crystal are investigated with respect to input signal-tobackground intensity ratio R I s ∕I b . In the range 20 > R > 0.05, the output laser beam spot becomes increasingly diffracted as the external voltage is raised. Figure 2(a) shows the output laser spot as a function of the external voltage for R 15. With zero external voltage, the full width at half-maximum (FWHM) of output laser spot is 8.1 μm, which is larger than that of the input laser spot FWHM 6.5 μm due to normal diffraction effects. Then the FWHM in both the x and y directions increases almost linearly with the external voltage [Figs. 1(b) and 1(c)]. At 1000 V, the FWHM reaches ∼20 μm, more than twice that caused by normal diffraction effects alone. The laser beam shows enhanced selfdefocusing behavior with increasing external electric field in this range of values for R. When the signal-to-background intensity ratio is set in the range 0.03 > R > 0.01, the output laser spots show a different response. For R 0.025, the output laser spot exhibits self-focusing behavior (Fig. 3). Under a reverse electric field, the FWHM
Fig. 1. (a) Experimental setup, and (b) relative configuration of the c axis of SBN crystal, the signal beam polarization, and the applied electric field.
Fig. 2. (a) Evolution of the output signal beam spots with the signal-to-background intensity ratio of R Is ∕I b 15; (b) and (c) FWHM of the output spots varies as a function of the applied voltage along x direction and y direction. The x direction and y direction are indicated in Fig. 1(b).
of the output laser spot in the x-axis direction is smaller than the normal diffraction spot (0 V). However, it diffuses more along the y axis with increasing voltage, and by 200 V the beam has split into two spots. These two spots have almost equal intensity and FWHM. The center-to-center distance between the two spots is 9.3 μm, and this separation increases as external voltage is raised. At 400 V, the FWHMs of the two spots are almost equal to that of the input spot, meaning that two spatial solitons have formed simultaneously for R 0.025. At 600 V, the bottom spot appears to split again into two new spots. The top spot almost has no change during the increasing of external voltage to 1000 V. As we decrease the voltage and monitor the output laser beam we can study the stability of spatial solitons in this system. As shown in Fig. 4, we observe three soliton-like spots at 1100 V. Lowering the voltage from 1100 to 700 V results in the spots merging into one big spot, with FWHM 8.1 μm. Additional reductions in voltage lead to the spot size decreasing, until at 400 V, the FWHM 6.5 μm (i.e., the same as the FWHM of the input spot), indicating that a spatial soliton has formed. The FWHM of the spot then 1 October 2014 / Vol. 53, No. 28 / APPLIED OPTICS
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Fig. 3. Evolution of the output spots from the SBN crystal for R 0.025 while the external voltage is increased from 0 to 1000 V.
Fig. 4. Evolution of the output spot from the SBN crystal for R 0.025, as the external voltage is reduced from 1100 to 0 V.
remains unchanged at 6.5 μm as the voltage is decreased to 0 V. Even without any external electric field applied to the crystal, it takes several hours before the soliton beam decays to the beam’s normal diffraction size FWHM ∼ 8.1 μm, which demonstrates the temporal stability of the soliton state. These experiments show that the evolution of the laser beam is strongly dependent on the signal-tobackground intensity ratio, R. As R ≫ 1, for example R ≅ 10, the propagation characteristics of a focused signal laser beam in a SBN photorefractive crystal under positive external electric field have been well studied [14,17,22,23]. In the region illuminated by the focused signal laser beam, as indicated in Fig. 5(a), a space charge field generated by optically excited carriers locally screens the external field. According to photorefractive theory, the change of refractive index caused by the linear electro-optic effect can be written as Δn −n30 reff E0 − Esc ∕2, where no is the refractive index of the SBN crystal in the absence of an electric field, reff is the effective linear electro-optic coefficient, E0 is the applied external field, and Esc is the space-charge field. So a graded-index waveguide is created that, in the case of negative index perturbation, has larger index in the bright region and leads to a self-focusing effect. A spatial soliton forms when the diffraction of the laser beam is exactly balanced by the self-focusing effect. The weak background light is generally used to speed up this process and help the focused signal laser beam to create an “index waveguide” that guides itself [14,17]. However, under the same signal-to-background intensity ratio R ≅ 10, a reverse external electric field has the opposite effect. A graded index is created with smaller index in the bright region as indicated by Fig. 5(b), eliminating the “index waveguide” effect. In this case, diffraction of the output laser spot increases as the external voltage is raised, that is, it is self-defocusing, confirming our experimental observations in Fig. 2. The mechanism changes once again when R ≪ 1 with a reverse external electric field. As indicated by Fig. 5(c), the photon-generated carriers are not mainly excited in the focused signal laser beam region any more, but generated by the strong
Fig. 5. Illustration of the self-focusing and self-defocusing effect of a focused laser beam under different external electric fields and signalto-background intensity ratios. 6424
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background in the whole crystal. The optically excited conduction carriers are then driven to move in the boundary region of the focused signal laser beam. Now, the space-charge field generated by optically excited carriers in the focused signal laser beam region is in the same direction of the external field. The space-charge field does not locally “screen” the external field any more, which is very interesting. In other words, the electric field in the focused signal laser beam region is not screened but is enhanced. The combination of the space charge field and the external field gives a positive index profile to create an “index waveguide” in the region illuminated by the focused signal laser beam to guide the signal laser beam, thereby eliminating diffraction and resulting in the self-focusing effect we observed in Fig. 3. In this case, a soliton waveguide can be formed under a suitable reverse electric field. Clearly, the formation of the soliton waveguide when R ≪ 1 with a reverse external electric field is not due to “screening” of external electric field by space-charge field any more, but due to the “enhancement” of the electric field by the space charge field. It is a never reported type of soliton waveguide, different from the wellstudied spatial solitons in SBN crystal under positive external electric field as R ≫ 1. It is also worth noting that when R ≪ 1 and the two beams are in orthogonal polarization states, a photovoltaic current perpendicular to the c axis of the crystal is likely to be generated, subsequently changing the distribution of the spatial charge field, as well as refractive index [6,24,25]. We speculate that such a photovoltaic effect works together with the “enhancement” process in the SBN crystal to create more than one waveguide structure. The incident signal beam can then form multiple discrete diffraction spots, as we observed in experiments. If the nonlinear self-focusing caused by these waveguides balances the diffraction of the beam, discrete solitons will arise. Indeed, the FWHMs of the two output spots are almost equal to that of the input signal beam after splitting at 400 V in Fig. 3. 4. Conclusion
In conclusion, we have investigated the propagation characteristics of a focused laser beam in a SBN crystal under reverse applied electric field. The evolution of the output laser beam from the crystal is strongly dependent on the input signal-to-background intensity ratio R I s ∕I b . In the range 20 > R > 0.05, the laser beam shows enhanced self-defocusing behavior as the external voltage increases. Conversely, in the range 0.03 > R > 0.01, the laser beam shows selffocusing behavior as the external voltage is increased. Spatial solitons are observed under a suitable negative voltage for R 0.025. We have proposed a model to explain the spatial soliton formation in the SBN crystal under a reverse external electric field by the “enhancement” of the external field. This work provides an additional experimental method by which to form spatial solitons
and enriches the current understanding of photorefractive spatial solitons. This project is supported by Foundations from Hebei Province (Grant Nos. E2013100013 and F2009000222) and the Natural Science Foundation of China (Grant No. 11204062). The authors acknowledge the support and useful discussion with Prof. Greg Salamo. References 1. M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926 (1992). 2. G. Duree, J. L. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. 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). 3. G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. D. Porto, E. Sharp, and A. Yariv, “Dark photorefractive spatial solitons and photorefractive vortex solitons,” Phys. Rev. Lett. 74, 1978–1981 (1995). 4. M. Morin, G. Duree, G. J. Salamo, and M. Segev, “Waveguides formed by quasi-steady-state photorefractive spatial solitons,” Opt. Lett. 20, 2066–2068 (1995). 5. H. S. Eisenberg, R. Morandotti, and Y. Silberg, “Optical discrete solitons in waveguide arrays. I. Soliton formation,” J. Opt. Soc. Am. B 19, 2938–2944 (2002). 6. M. Chauvet, “Temporal analysis of open-circuit dark photovoltaic spatial solitons,” J. Opt. Soc. Am. B 20, 2515–2522 (2003). 7. M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, “Selfdeflection of steady-state bright spatial solitons in biased photorefractive crystals,” Opt. Commun. 120, 311–315 (1995). 8. D. N. Christodoulides, F. Lederer, and Y. Siberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003). 9. R. Guo, Z. F. Ling, X. H. Chen, G. Q. Zhang, X. Z. Zhang, H. D. Wen, Y. Jiang, and S. M. Liu, “Saturable nonlinearity in photovoltaic-photorefractive crystals under open-circuit condition,” Chin. Phys. Lett. 17, 804–805 (2000). 10. K. Q. Lu, M. Z. Zhang, W. Zhao, Y. L. Yang, Y. Yang, Y. H. Zhang, X. M. Liu, Y. P. Zhang, and J. P. Song, “Waveguides induced by screening-photovoltaic solitons in biased photorefractive–photovoltaic crystals,” Chin. Phys. Lett. 23, 2770– 2773 (2006). 11. B. L. Liang, Q. L. Guo, Y. H. Jiang, Y. Wang, S. H. Zhang, and G. S. Fu, “Energy transfer through photorefractive spatial soliton interaction,” Appl. Phys. Express 6, 062201 (2013). 12. T. T. Shi and S. Chi, “Nonlinear photonic switching by using the spatial soliton collision,” Opt. Lett. 15, 1123–1125 (1990). 13. M. Shalaby and A. Barthelemy, “Experimental spatial soliton trapping and switching,” Opt. Lett. 16, 1472–1474 (1991). 14. M. Segev, B. Crosignani, P. DiPorto, A. Yariv, G. Duree, G. J. Salamo, and E. Sharp, “Stability of photorefractive spatial solitons,” Opt. Lett. 19, 1296–1298 (1994). 15. N. Fressengeas, J. Maufoy, and G. Kugel, “Temporal behavior of bidimensional photorefractive bright spatial solitons,” Phys. Rev. E 54, 6866–6875 (1996). 16. D. N. Christostoulides and M. I. Carvalho, “Bright, dark, and gray spatial soliton states in photorefractive media,” J. Opt. Soc. Am. B 12, 1628–1633 (1995). 17. M. Shih, M. Segev, G. C. Valley, G. J. Salamo, B. Crosignani, and P. DiPorto, “Observation of two-dimensional steady state photorefractive screening-solitons,” Electron. Lett. 31, 826– 827 (1995). 18. M. Shih, P. Leach, M. Segev, M. H. Garrett, G. Salamo, and G. C. Valley, “Two-dimensional steady-state photorefractive screening solitons,” Opt. Lett. 21, 324–326 (1996). 19. G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. C. Bashaw, “Dark and bright photovoltaic spatial solitons,” Phys. Rev. A 50, R4457–R4460 (1994). 1 October 2014 / Vol. 53, No. 28 / APPLIED OPTICS
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20. M. Taya, M. C. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, “Observation of dark photovoltaic spatial solitons,” Phys. Rev. A 52, 3095–3100 (1995). 21. Z. Chen, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Maker, “Self-trapping of an optical vortex by use of the bulk photovoltaic effect,” Phys. Rev. Lett. 78, 2948–2951 (1997). 22. Q. L. Guo, G. Y. Deng, B. L. Liang, P. L. Li, Y. Li, and X. Li, “Solitons with periodic behavior in an SBN:75 photorefractive crystal,” Chin. Phys. Lett. 27, 084204 (2010).
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23. A. Guo, M. Henry, and G. J. Salamo, “Fixing multiple waveguides induced by photorefractive solitons: directional couplers and beam splitters,” Opt. Lett. 26, 1274–1276 (2001). 24. M. Simon, S. Wevering, K. Buse, and E. Kratzig, “The bulk photovoltaic effect of photorefractive LiNbO3:Fe crystals at high light intensities,” J. Phys. D 30, 144–149 (1997). 25. M. Simon, K. Buse, R. Pankrath, E. Kratzig, and A. A. Freschi, “Photoconductivity of photorefractive Sr0.61Ba0.39Nb2O6:Ce crystals at high light intensities,” J. Appl. Phys. 80, 2221– 2224 (1996).
College of Physics Science & Technology, Hebei University, Baoding 071002, China
2
California NanoSystem Institute, University of California, Los Angeles, California 90095, USA *Corresponding author: [email protected] Received 1 May 2014; accepted 15 August 2014; posted 26 August 2014 (Doc. ID 211171); published 24 September 2014
The propagation characteristics of a focused laser beam in a SBN:75 photorefractive crystal strongly depend on the signal-to-background intensity ratio (R Is ∕I b ) under reverse external electric field. In the range 20 > R > 0.05, the laser beam shows enhanced self-defocusing behavior with increasing external electric field, while it shows self-focusing in the range 0.03 > R > 0.01. Spatial solitons are observed under a suitable reverse external electric field for R 0.025. A theoretical model is proposed to explain the experimental observations, which suggest a new type of soliton formation due to “enhancement” not “screening” of the external electrical field. © 2014 Optical Society of America OCIS codes: (190.6135) Spatial solitons; (190.5330) Photorefractive optics; (160.5320) Photorefractive materials; (140.3300) Laser beam shaping; (230.7370) Waveguides. http://dx.doi.org/10.1364/AO.53.006422
1. Introduction
A spatial soliton or a self-trapped beam is an optical beam that propagates without diffraction, that is, the beam shape and diameter remain invariant during propagation. The spatial soliton in a photorefractive medium was first theoretically predicted by Segev et al. in 1992 and experimentally observed by Duree et al. in 1993 [1,2]. Photorefractive spatial solitons have numerous intriguing features including short response time, low laser power, and erasable and rewritable characteristics [3–7]. As a result, these solitons have many potential applications, such as optical information processing, optical storage, optical interconnects, and optical computing [8–13]. So far, reported photorefractive spatial solitons can be classified into three types: quasi-steady-state solitons [4,14,15], screening solitons [16–18], and
photovoltaic solitons [19–21]. Quasi-steady-state solitons occur when diffraction of a laser beam is completely compensated for by the nonlinearity caused by the “screening process” of an external electric field applied to the photorefractive crystal. Such quasi-steady-state solitons have been well studied in strontium barium niobate (SBN) crystals under a positive external electric field, that is, the external field is parallel to the c axis of the crystal. Recently, our group investigated the (2 1) quasi-steady-state solitons and their temporal behavior in a SBN:75 crystal with appropriate positive external field [22]. In this study, we take a step further to investigate the formation of quasi-steady-state spatial solitons in a SBN:75 crystal under reverse external electric field, that is, the external field antiparallel to the c axis of the photorefractive crystal. 2. Experiments
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The experiments are carried out using the setup shown in Fig. 1(a). A laser beam from a single
frequency solid laser with wavelength 532 nm is separated into a signal beam I s and a background beam I b . A chopper with transparent blades is used to make these two beams incoherent with each other. The signal beam is focused by a convex lens (f 12.5 cm) onto the input surface of the photorefractive crystal and the background beam covers the whole input surface of crystal. The photorefractive crystal is a 5 mm × 5 mm × 5 mm SBN:75. The signal beam spots at the input and output surface of the crystal are imaged onto a laser beam analyzer for observation and analysis. The c axis of the SBN crystal is horizontal and perpendicular to the propagation direction of the signal beam. We set the signal beam as extraordinarily polarized, the background beam as ordinarily polarized, and apply a reverse electric field to the crystal in order to obtain a larger nonlinearity. Figure 1(b) shows the relative configuration of the c axis of the SBN crystal, the signal beam polarization, and the applied electric field. 3. Results and Discussion
The evolution characteristics after the focused laser beam propagates through the SBN crystal are investigated with respect to input signal-tobackground intensity ratio R I s ∕I b . In the range 20 > R > 0.05, the output laser beam spot becomes increasingly diffracted as the external voltage is raised. Figure 2(a) shows the output laser spot as a function of the external voltage for R 15. With zero external voltage, the full width at half-maximum (FWHM) of output laser spot is 8.1 μm, which is larger than that of the input laser spot FWHM 6.5 μm due to normal diffraction effects. Then the FWHM in both the x and y directions increases almost linearly with the external voltage [Figs. 1(b) and 1(c)]. At 1000 V, the FWHM reaches ∼20 μm, more than twice that caused by normal diffraction effects alone. The laser beam shows enhanced selfdefocusing behavior with increasing external electric field in this range of values for R. When the signal-to-background intensity ratio is set in the range 0.03 > R > 0.01, the output laser spots show a different response. For R 0.025, the output laser spot exhibits self-focusing behavior (Fig. 3). Under a reverse electric field, the FWHM
Fig. 1. (a) Experimental setup, and (b) relative configuration of the c axis of SBN crystal, the signal beam polarization, and the applied electric field.
Fig. 2. (a) Evolution of the output signal beam spots with the signal-to-background intensity ratio of R Is ∕I b 15; (b) and (c) FWHM of the output spots varies as a function of the applied voltage along x direction and y direction. The x direction and y direction are indicated in Fig. 1(b).
of the output laser spot in the x-axis direction is smaller than the normal diffraction spot (0 V). However, it diffuses more along the y axis with increasing voltage, and by 200 V the beam has split into two spots. These two spots have almost equal intensity and FWHM. The center-to-center distance between the two spots is 9.3 μm, and this separation increases as external voltage is raised. At 400 V, the FWHMs of the two spots are almost equal to that of the input spot, meaning that two spatial solitons have formed simultaneously for R 0.025. At 600 V, the bottom spot appears to split again into two new spots. The top spot almost has no change during the increasing of external voltage to 1000 V. As we decrease the voltage and monitor the output laser beam we can study the stability of spatial solitons in this system. As shown in Fig. 4, we observe three soliton-like spots at 1100 V. Lowering the voltage from 1100 to 700 V results in the spots merging into one big spot, with FWHM 8.1 μm. Additional reductions in voltage lead to the spot size decreasing, until at 400 V, the FWHM 6.5 μm (i.e., the same as the FWHM of the input spot), indicating that a spatial soliton has formed. The FWHM of the spot then 1 October 2014 / Vol. 53, No. 28 / APPLIED OPTICS
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Fig. 3. Evolution of the output spots from the SBN crystal for R 0.025 while the external voltage is increased from 0 to 1000 V.
Fig. 4. Evolution of the output spot from the SBN crystal for R 0.025, as the external voltage is reduced from 1100 to 0 V.
remains unchanged at 6.5 μm as the voltage is decreased to 0 V. Even without any external electric field applied to the crystal, it takes several hours before the soliton beam decays to the beam’s normal diffraction size FWHM ∼ 8.1 μm, which demonstrates the temporal stability of the soliton state. These experiments show that the evolution of the laser beam is strongly dependent on the signal-tobackground intensity ratio, R. As R ≫ 1, for example R ≅ 10, the propagation characteristics of a focused signal laser beam in a SBN photorefractive crystal under positive external electric field have been well studied [14,17,22,23]. In the region illuminated by the focused signal laser beam, as indicated in Fig. 5(a), a space charge field generated by optically excited carriers locally screens the external field. According to photorefractive theory, the change of refractive index caused by the linear electro-optic effect can be written as Δn −n30 reff E0 − Esc ∕2, where no is the refractive index of the SBN crystal in the absence of an electric field, reff is the effective linear electro-optic coefficient, E0 is the applied external field, and Esc is the space-charge field. So a graded-index waveguide is created that, in the case of negative index perturbation, has larger index in the bright region and leads to a self-focusing effect. A spatial soliton forms when the diffraction of the laser beam is exactly balanced by the self-focusing effect. The weak background light is generally used to speed up this process and help the focused signal laser beam to create an “index waveguide” that guides itself [14,17]. However, under the same signal-to-background intensity ratio R ≅ 10, a reverse external electric field has the opposite effect. A graded index is created with smaller index in the bright region as indicated by Fig. 5(b), eliminating the “index waveguide” effect. In this case, diffraction of the output laser spot increases as the external voltage is raised, that is, it is self-defocusing, confirming our experimental observations in Fig. 2. The mechanism changes once again when R ≪ 1 with a reverse external electric field. As indicated by Fig. 5(c), the photon-generated carriers are not mainly excited in the focused signal laser beam region any more, but generated by the strong
Fig. 5. Illustration of the self-focusing and self-defocusing effect of a focused laser beam under different external electric fields and signalto-background intensity ratios. 6424
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background in the whole crystal. The optically excited conduction carriers are then driven to move in the boundary region of the focused signal laser beam. Now, the space-charge field generated by optically excited carriers in the focused signal laser beam region is in the same direction of the external field. The space-charge field does not locally “screen” the external field any more, which is very interesting. In other words, the electric field in the focused signal laser beam region is not screened but is enhanced. The combination of the space charge field and the external field gives a positive index profile to create an “index waveguide” in the region illuminated by the focused signal laser beam to guide the signal laser beam, thereby eliminating diffraction and resulting in the self-focusing effect we observed in Fig. 3. In this case, a soliton waveguide can be formed under a suitable reverse electric field. Clearly, the formation of the soliton waveguide when R ≪ 1 with a reverse external electric field is not due to “screening” of external electric field by space-charge field any more, but due to the “enhancement” of the electric field by the space charge field. It is a never reported type of soliton waveguide, different from the wellstudied spatial solitons in SBN crystal under positive external electric field as R ≫ 1. It is also worth noting that when R ≪ 1 and the two beams are in orthogonal polarization states, a photovoltaic current perpendicular to the c axis of the crystal is likely to be generated, subsequently changing the distribution of the spatial charge field, as well as refractive index [6,24,25]. We speculate that such a photovoltaic effect works together with the “enhancement” process in the SBN crystal to create more than one waveguide structure. The incident signal beam can then form multiple discrete diffraction spots, as we observed in experiments. If the nonlinear self-focusing caused by these waveguides balances the diffraction of the beam, discrete solitons will arise. Indeed, the FWHMs of the two output spots are almost equal to that of the input signal beam after splitting at 400 V in Fig. 3. 4. Conclusion
In conclusion, we have investigated the propagation characteristics of a focused laser beam in a SBN crystal under reverse applied electric field. The evolution of the output laser beam from the crystal is strongly dependent on the input signal-to-background intensity ratio R I s ∕I b . In the range 20 > R > 0.05, the laser beam shows enhanced self-defocusing behavior as the external voltage increases. Conversely, in the range 0.03 > R > 0.01, the laser beam shows selffocusing behavior as the external voltage is increased. Spatial solitons are observed under a suitable negative voltage for R 0.025. We have proposed a model to explain the spatial soliton formation in the SBN crystal under a reverse external electric field by the “enhancement” of the external field. This work provides an additional experimental method by which to form spatial solitons
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