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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 16 — Aug. 3, 2009
  • pp: 14150–14155
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Surface waves in photorefractive polymer films

Takashi Fujihara, Takafumi Sassa, Tsuyoshi Muto, Shinsuke Umegaki, and Tatsuo Wada  »View Author Affiliations


Optics Express, Vol. 17, Issue 16, pp. 14150-14155 (2009)
http://dx.doi.org/10.1364/OE.17.014150


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Abstract

We observed the temporal development of surface waves and investigated their power propagation loss in typical photorefractive polymer films sandwiched between ITO glass substrates. We found that amplified scattered waves generated in a pumped region started to develop into surface waves from a point where they reached the substrate through the self-bending effect. The surface waves propagated over a distance of 1.7 mm, thereby confining the power to a region at a distance of 30 microns from the substrate. Considerable propagation power loss of the surface waves was observed at a low pumping power of the beam; however, the power loss decreased considerably when the beam had high power.

© 2009 OSA

1. Introduction

In several photorefractive (PR) crystals, a laser beam injected close to the crystal surface can develop into surface waves [1–3

1. M. C-Golomb, “Photorefractive surface wave solitons,” Opt. Lett. 20(20), 2075–2077 (1995). [CrossRef]

]. A surface wave propagates along the crystal surface, thereby confining power to a narrow region. Since surface waves can maintain high optical intensity over a relatively long distance, they can be used to increase optical pumping efficiency upon charge generation or space-charge field formation. Moreover, since they are formed in a self-organized manner, they can be used to achieve efficient optical wave coupling or phase matching. For example, speedup of PR wave coupling [2

2. A. A. Kamshilin, E. Raita, V. V. Prokofiev, and T. Jaaskelainen, “Nonlinear self-channeling of a laser beam at the surface of a photorefractive fiber,” Appl. Phys. Lett. 67(22), 3242–3244 (1995). [CrossRef]

,4

4. E. Raita, A. A. Kamshilin, and T. Jaaskelainen, “Fast mutually pumped phase conjugation induced by a transient photorefractive surface wave,” J. Opt. Soc. Am. B 15(7), 2023–2031 (1998). [CrossRef]

] and enhancement of second harmonic generation (SHG) [5

5. I. I. Smolyaninov, C. H. Lee, and C. C. Davis, “Giant enhancement of surface second harmonic generation in BaTiO3 due to photorefractive surface wave excitation,” Phys. Rev. Lett. 83(12), 2429–2432 (1999). [CrossRef]

,6

6. T. H. Zhang, J. Yang, H. Z. Kang, L. Feng, J. J. Xu, C. P. Zhang, X. K. Ren, B. H. Wang, Y. Z. Lu, F. Jia, and W. W. Shao, “Surface second-harmonic generation in Sr0.6Ba0.4NbO3 with a nonlinear diffusion mechanism,” Phys. Rev. B 73(15), 153402 (2006). [CrossRef]

] using surface waves have been successfully demonstrated.

It has been shown that surface waves require both self-bending propagation and total reflective interfaces [7

7. V. Aleshkevich, V. Vysloukh, and Y. Kartashov, “Localized surface waves at the interface between the linear dielectric and photorefractive medium with drift and diffusion nonlinearity,” Opt. Quantum Electron. 33(12), 1205–1221 (2001). [CrossRef]

]. They propagate by repeated total reflection at the interface and by self-bending, because of which they return to the interface. For efficient self-bending, large two-beam coupling coefficients (Γ’s) [8

8. O. V. Lyubomudrov and V. V. Shkunov, “Self-bending specklons in photorefractive crystals,” J. Opt. Soc. Am. B 11(8), 1403–1408(1994). [CrossRef]

] and amplified scattering or the generation of a fanned beam [1

1. M. C-Golomb, “Photorefractive surface wave solitons,” Opt. Lett. 20(20), 2075–2077 (1995). [CrossRef]

,9

9. P. Xie, J.-H. Dai, P.-Y. Wang, H.-J. Zhang, and P.-Y. Wang, “A two-dimensional theory and propagation of beam fanning in photorefractive crystals,” J. Appl. Phys. 75(4), 1891–1894 (1994). [CrossRef]

,10

10. A. A. Kamshilin, E. Raita, and A. V. Khomenko, “Intensity redistribution in a thin photorefractive crystal caused by strong fanning effect and internal reflections,” J. Opt. Soc. Am. B 13(11), 2536–2543 (1996). [CrossRef]

] are necessary.

Organic amorphous PR materials can show large Γ with efficient amplified scattering. Therefore, surface waves are expected to become a critical key to improve the light-induced performances as in the crystals case. Further, amorphous PR materials can exhibit large optical wave coupling and high SHG activity [11

11. O. Ostroverkhova and W. E. Moerner, “Organic photorefractives: mechanisms, materials, and applications,” Chem. Rev. 104(7), 3267–3314 (2004). [CrossRef] [PubMed]

]. In addition, they can form a large variety of compounds, whose films have high shock resistance and can be prepared easily at low cost. Organic amorphous PR materials can be considered as valued alternatives to PR crystals. However, only a few studies have been conducted to investigate surface wave generation in such materials [12

12. K. Meerholz, R. Bittner, and Y. D. Nardin, “Field asymmetry of the dynamic gain coefficient in organic photorefractive devices,” Opt. Commun. 150(1–6), 205–209 (1998). [CrossRef]

]. In this study, we experimentally demonstrate the formation of surface waves in PR polymer films. Moreover, we estimate the propagation loss of the surface waves and also propose a method for reducing the loss.

2. Experimental

Fig. 1. Schematic illustration of experimental setup. The inset (left) shows pictures captured by CCD #1 to measure the propagation distance L. The two dashed lines show edges of the thin rectanguar-cut substrate having a width of 5 mm. The other inset (right) shows top- and side-view images of the sample cell as well as the direction of the applied electric field. The pumped area was 0.7 × 0.2 mm.

The sample cell was mounted on a prism beam coupler. The pumping beam was injected into the polymer layer via the prism, which can yield large angle of incidence in the polymer [15

15. T. Sassa, T. Muto, and T. Wada, “Enhanced photorefractive two-beam coupling in low-Tg polymeric materials with a new device structure,” J. Opt. Soc. Am. B 21(6), 1255–1261 (2004). [CrossRef]

] and achieve efficient formation of surface waves [7

7. V. Aleshkevich, V. Vysloukh, and Y. Kartashov, “Localized surface waves at the interface between the linear dielectric and photorefractive medium with drift and diffusion nonlinearity,” Opt. Quantum Electron. 33(12), 1205–1221 (2001). [CrossRef]

]. The prism had the same refractive index as the bottom substrate; then, a maximum incidence angle of 54° was obtained for the pump beam. In this configuration, upon the application of an electric field in the + x direction, amplified scattered waves generated in the pumped region could propagate along the bottom substrate in the + z direction [14

14. T. Sassa, T. Muto, T. Wada, Y. Takeda, T. Fujihara, and S. Umegaki, “Strongly electric-field-dependent spatial properties of fanning beam in polymeric medium,” Appl. Phys. Lett. 86(8), 84103 (2005). [CrossRef]

] and develop into surface waves. It should be noted that an incidence angle for the pump beam achieved in this work was smaller than those previously realized to observe surface waves [1

1. M. C-Golomb, “Photorefractive surface wave solitons,” Opt. Lett. 20(20), 2075–2077 (1995). [CrossRef]

,2

2. A. A. Kamshilin, E. Raita, V. V. Prokofiev, and T. Jaaskelainen, “Nonlinear self-channeling of a laser beam at the surface of a photorefractive fiber,” Appl. Phys. Lett. 67(22), 3242–3244 (1995). [CrossRef]

,4–6

4. E. Raita, A. A. Kamshilin, and T. Jaaskelainen, “Fast mutually pumped phase conjugation induced by a transient photorefractive surface wave,” J. Opt. Soc. Am. B 15(7), 2023–2031 (1998). [CrossRef]

].

In spite of the low C60 concentration, amplified scattering could be observed on the screen with naked eyes above an external field of 30 V/μm at the minimum pumping power (70 μW, measured before the prism) used in the experiments. The scattering intensity was strengthened as the field strength increased. Since an electric field of 45 V/μm yielded an emission that was sufficiently strong for carrying out recording, all the measurements were performed at this field strength.

3. Results and discussion

For L ≥ 0.3 mm, we observed typical intensity profiles for surface waves in the polymer layer. Figures 2(a) and (b) show typical results. The shapes of the intensity profiles in the polymer layer, which were broad in the early temporal stage, changed gradually to steep peaks positioned near the edge of the bottom substrate [1

1. M. C-Golomb, “Photorefractive surface wave solitons,” Opt. Lett. 20(20), 2075–2077 (1995). [CrossRef]

,2

2. A. A. Kamshilin, E. Raita, V. V. Prokofiev, and T. Jaaskelainen, “Nonlinear self-channeling of a laser beam at the surface of a photorefractive fiber,” Appl. Phys. Lett. 67(22), 3242–3244 (1995). [CrossRef]

]. The peak strength increased with time and stabilized after pumping for approximately 70 s. The positions of the peak maximum were almost the same (x ~305) for all L values. On the other hand, for L = 0 mm, the shape of the profile did not change; however, the peak strength increased (Fig. 2(c)). This indicated that self-bending propagation was not dominant for the amplified scattered wave propagating in the pumped region. Due to a relatively small incidence angle of the pump beam, the amplified scattered wave should obtain sufficiently low power compared to that of the pump beam, resulting in the negligible self-bending [9

9. P. Xie, J.-H. Dai, P.-Y. Wang, H.-J. Zhang, and P.-Y. Wang, “A two-dimensional theory and propagation of beam fanning in photorefractive crystals,” J. Appl. Phys. 75(4), 1891–1894 (1994). [CrossRef]

,14

14. T. Sassa, T. Muto, T. Wada, Y. Takeda, T. Fujihara, and S. Umegaki, “Strongly electric-field-dependent spatial properties of fanning beam in polymeric medium,” Appl. Phys. Lett. 86(8), 84103 (2005). [CrossRef]

]. Additionally, for L = 0.3 mm in the top substrate region, we observed the peaks (indicated by A) to first increase with time, then to decrease with time, and finally to almost disappear (Figs. 2(a) and (b)). Moreover, for L = 1.1 mm, other peaks (indicated by B) were observed to first increase with time and then stabilize (Fig. 2(b)). Light in the top substrate region corresponded to the amplified scattered light which reflected at the bottom-substrate interface after the self-bending propagation. It was reported such reflected amplified scattered light exhibited periodical light intensity distribution [16

16. A. V. Khomenko, E. Nippolainen, A. A. Kamshilin, A. Z. Segundo, and T. Jaaskelainen, “Leaky photorefractive surface waves in Bi12TiO29 and Bi12SiO20 crystals,” Opt. Commun. 150(1–6), 175–179 (1998). [CrossRef]

] and we regarded the peaks A and B as part of it. If the reflected light bended again to the bottom substrate, then it could propagate as surface waves. Temporal change of peak A, therefore, suggested that sufficient self-bending at the reflected amplified scattered waves occurred; this behavior suggests the formation of surface waves at L ≥ 0.3 mm. In contrast, temporal change of peak B indicated insufficient bending of the reflected components, suggesting the formation of leaky surface waves [16

16. A. V. Khomenko, E. Nippolainen, A. A. Kamshilin, A. Z. Segundo, and T. Jaaskelainen, “Leaky photorefractive surface waves in Bi12TiO29 and Bi12SiO20 crystals,” Opt. Commun. 150(1–6), 175–179 (1998). [CrossRef]

] at L ≥ 1.1 mm. Later, we present a detailed estimation of the propagation loss.

Here, we show results of the temporal evolution of the width of the peak profiles (Fig. 3). For L ≥ 0.3 mm, narrowing of the peak profiles with time due to surface wave formation was clearly observed, and all the widths were found to approach a value of approximately 30 μm in approximately 30 s after pumping. The final width was attained first at L = 0.7 mm and then at 1.1, 1.5, 2.0, and 0.3 mm. This indicated that amplified scattered waves generated from the pumped region (z = z p) first concentrated the power at a distance of 0.7 mm and then started to develop into surface waves toward the polymer layer edge (z = z 0), concentrating the power in nearly the same area. The starting point of surface wave formation was considered to be the point where all the amplified scattered components propagated to the bottom substrate due to the self-bending and generated reflection waves. Such a point did act as an initiating site for surface wave formation [7

7. V. Aleshkevich, V. Vysloukh, and Y. Kartashov, “Localized surface waves at the interface between the linear dielectric and photorefractive medium with drift and diffusion nonlinearity,” Opt. Quantum Electron. 33(12), 1205–1221 (2001). [CrossRef]

,16

16. A. V. Khomenko, E. Nippolainen, A. A. Kamshilin, A. Z. Segundo, and T. Jaaskelainen, “Leaky photorefractive surface waves in Bi12TiO29 and Bi12SiO20 crystals,” Opt. Commun. 150(1–6), 175–179 (1998). [CrossRef]

]. The temporal development of surface waves toward the polymer edge was also confirmed by the temporal evolution of a streak line observed by CCD #1, as shown in Media 1 in Fig. 3, where the pump beam was injected at a time of 10 s using a stopwatch.

Fig. 2. Temporal changes of intensity profiles of amplified scattered waves for (a) L = 0.7 mm, (b) L = 1.1 mm, and (c) L = 0 mm. The dotted line shows the intensity profile of an end-face image of the sample cell, showing the position of the polymer layer from x = 302 to x = 332. Regions of (I), (II) and (III) correspond to the bottom substrate, polymer layer and top substrate, respectively. Image resolution through CCD #2 was 3 μm/pixel.
Fig. 3. Temporal changes of peak width (FWHM) of intensity profile in polymer region and a streak line (Media 1, 2X playback speed).
Fig. 4. Propagation distance dependence of optical power inside polymer after pumping for 70s.

Since the surface wave formation for L = 0.3 - 2.0 mm can be regarded as the channel waveguide formation [2

2. A. A. Kamshilin, E. Raita, V. V. Prokofiev, and T. Jaaskelainen, “Nonlinear self-channeling of a laser beam at the surface of a photorefractive fiber,” Appl. Phys. Lett. 67(22), 3242–3244 (1995). [CrossRef]

], the propagation loss can be evaluated from the change in optical power inside the polymer with the propagation distance (Fig. 4). The power was evaluated from the intensity profile area corresponding to the polymer region obtained after pumping for 70 s. The power was found to decrease abruptly above L= 0.7 mm, and the loss was evaluated to be 7 cm-1, which is considerably larger than that of the material. On the other hand, the loss for L = 0.3 - 0.7 mm was relatively small. This trend agreed well with the above result, in which leaky propagation was observed for L ≥ 1.1 mm. From the viewpoint of optical applications, propagation loss should be small. To reduce the loss in this system, self-bending of the beam for L ≥ 0.7 mm should be enhanced. One possible approach to achieve this is to enhance amplified scattering, which in turn can be achieved by increasing pumping power [17

17. L. Solymar, D. J. Webb, and A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Oxford, New York, 1996), Chap. 10, pp. 320–322.

]. Figure 5 shows the dependence of the power inside the polymer evaluated at L = 2.0 mm on the pumping power. The power inside the polymer was found to increase superlinearly. Additionally, intensity profiles in the top substrate region (shown by an arrow in the inset of Fig. 5), which correspond to the peak B described above, revealed a decrease in the amplitude with pumping power, indicating suppression of the leaky loss. It is noteworthy that the profile almost disappeared at a pump power of 560 μW. Propagation loss of the surface waves was successfully reduced by increasing the pumping power. Finally we note that considerable increase of a response speed for the output power change was also found with an increase of the pumping power; roughly ten times higher speed for a pump power of 560 μW compared to that for 70 μW.

Fig. 5. Pumping power dependence of optical power inside polymer (L = 2.0 mm). The inset shows the intensity profiles in the polymer and the top substrate regions.

4. Conclusion

We observed the temporal change of amplified scattered waves to surface waves by using typical PR polymer films. The surface waves started to grow from a point where the amplified scattered waves reached a substrate due to self-bending, and the surface waves proceeded in the propagation direction, confining the power to a constant area. We also observed that propagation loss of the surface waves effectively decreased with an increase in pumping power. Consequently, we used organic amorphous PR materials and experimentally demonstrated the formation of surface waves with low propagation loss over millimeter scale distances.

References and links

1.

M. C-Golomb, “Photorefractive surface wave solitons,” Opt. Lett. 20(20), 2075–2077 (1995). [CrossRef]

2.

A. A. Kamshilin, E. Raita, V. V. Prokofiev, and T. Jaaskelainen, “Nonlinear self-channeling of a laser beam at the surface of a photorefractive fiber,” Appl. Phys. Lett. 67(22), 3242–3244 (1995). [CrossRef]

3.

J. J. Sanchez-Mondragon, S. Stepanov, S. Stepanov, and G. S. Quirino, “Nonlinear surface optical waves in photorefractive crystals with a diffusion mechanism of nonlinearity,” Phys. Rev. A 51(2), 1571–1577 (1995). [CrossRef] [PubMed]

4.

E. Raita, A. A. Kamshilin, and T. Jaaskelainen, “Fast mutually pumped phase conjugation induced by a transient photorefractive surface wave,” J. Opt. Soc. Am. B 15(7), 2023–2031 (1998). [CrossRef]

5.

I. I. Smolyaninov, C. H. Lee, and C. C. Davis, “Giant enhancement of surface second harmonic generation in BaTiO3 due to photorefractive surface wave excitation,” Phys. Rev. Lett. 83(12), 2429–2432 (1999). [CrossRef]

6.

T. H. Zhang, J. Yang, H. Z. Kang, L. Feng, J. J. Xu, C. P. Zhang, X. K. Ren, B. H. Wang, Y. Z. Lu, F. Jia, and W. W. Shao, “Surface second-harmonic generation in Sr0.6Ba0.4NbO3 with a nonlinear diffusion mechanism,” Phys. Rev. B 73(15), 153402 (2006). [CrossRef]

7.

V. Aleshkevich, V. Vysloukh, and Y. Kartashov, “Localized surface waves at the interface between the linear dielectric and photorefractive medium with drift and diffusion nonlinearity,” Opt. Quantum Electron. 33(12), 1205–1221 (2001). [CrossRef]

8.

O. V. Lyubomudrov and V. V. Shkunov, “Self-bending specklons in photorefractive crystals,” J. Opt. Soc. Am. B 11(8), 1403–1408(1994). [CrossRef]

9.

P. Xie, J.-H. Dai, P.-Y. Wang, H.-J. Zhang, and P.-Y. Wang, “A two-dimensional theory and propagation of beam fanning in photorefractive crystals,” J. Appl. Phys. 75(4), 1891–1894 (1994). [CrossRef]

10.

A. A. Kamshilin, E. Raita, and A. V. Khomenko, “Intensity redistribution in a thin photorefractive crystal caused by strong fanning effect and internal reflections,” J. Opt. Soc. Am. B 13(11), 2536–2543 (1996). [CrossRef]

11.

O. Ostroverkhova and W. E. Moerner, “Organic photorefractives: mechanisms, materials, and applications,” Chem. Rev. 104(7), 3267–3314 (2004). [CrossRef] [PubMed]

12.

K. Meerholz, R. Bittner, and Y. D. Nardin, “Field asymmetry of the dynamic gain coefficient in organic photorefractive devices,” Opt. Commun. 150(1–6), 205–209 (1998). [CrossRef]

13.

A. G-Jepsen, C. L. Thompson, R. J. Twieg, and W. E. Moerner, “Amplified scattering in a high-gain photorefractive polymer,” J. Opt. Soc. Am. B 15, 901–904 (1998). [CrossRef]

14.

T. Sassa, T. Muto, T. Wada, Y. Takeda, T. Fujihara, and S. Umegaki, “Strongly electric-field-dependent spatial properties of fanning beam in polymeric medium,” Appl. Phys. Lett. 86(8), 84103 (2005). [CrossRef]

15.

T. Sassa, T. Muto, and T. Wada, “Enhanced photorefractive two-beam coupling in low-Tg polymeric materials with a new device structure,” J. Opt. Soc. Am. B 21(6), 1255–1261 (2004). [CrossRef]

16.

A. V. Khomenko, E. Nippolainen, A. A. Kamshilin, A. Z. Segundo, and T. Jaaskelainen, “Leaky photorefractive surface waves in Bi12TiO29 and Bi12SiO20 crystals,” Opt. Commun. 150(1–6), 175–179 (1998). [CrossRef]

17.

L. Solymar, D. J. Webb, and A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Oxford, New York, 1996), Chap. 10, pp. 320–322.

OCIS Codes
(160.5320) Materials : Photorefractive materials
(190.4710) Nonlinear optics : Optical nonlinearities in organic materials
(190.5940) Nonlinear optics : Self-action effects
(190.7070) Nonlinear optics : Two-wave mixing

ToC Category:
Nonlinear Optics

History
Original Manuscript: May 18, 2009
Revised Manuscript: July 17, 2009
Manuscript Accepted: July 20, 2009
Published: August 3, 2009

Citation
Takashi Fujihara, Takafumi Sassa, Tsuyoshi Muto, Shinsuke Umegaki, and Tatsuo Wada, "Surface waves in photorefractive polymer films," Opt. Express 17, 14150-14155 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-16-14150


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References

  1. M. C-Golomb, “Photorefractive surface wave solitons,” Opt. Lett. 20(20), 2075–2077 (1995). [CrossRef]
  2. A. A. Kamshilin, E. Raita, V. V. Prokofiev, and T. Jaaskelainen, “Nonlinear self-channeling of a laser beam at the surface of a photorefractive fiber,” Appl. Phys. Lett. 67(22), 3242–3244 (1995). [CrossRef]
  3. J. J. Sanchez-Mondragon, S. Stepanov, S. Stepanov, and G. S. Quirino, “Nonlinear surface optical waves in photorefractive crystals with a diffusion mechanism of nonlinearity,” Phys. Rev. A 51(2), 1571–1577 (1995). [CrossRef] [PubMed]
  4. E. Raita, A. A. Kamshilin, and T. Jaaskelainen, “Fast mutually pumped phase conjugation induced by a transient photorefractive surface wave,” J. Opt. Soc. Am. B 15(7), 2023–2031 (1998). [CrossRef]
  5. I. I. Smolyaninov, C. H. Lee, and C. C. Davis, “Giant enhancement of surface second harmonic generation in BaTiO3 due to photorefractive surface wave excitation,” Phys. Rev. Lett. 83(12), 2429–2432 (1999). [CrossRef]
  6. T. H. Zhang, J. Yang, H. Z. Kang, L. Feng, J. J. Xu, C. P. Zhang, X. K. Ren, B. H. Wang, Y. Z. Lu, F. Jia, and W. W. Shao, “Surface second-harmonic generation in Sr0.6Ba0.4NbO3 with a nonlinear diffusion mechanism,” Phys. Rev. B 73(15), 153402 (2006). [CrossRef]
  7. V. Aleshkevich, V. Vysloukh, and Y. Kartashov, “Localized surface waves at the interface between the linear dielectric and photorefractive medium with drift and diffusion nonlinearity,” Opt. Quantum Electron. 33(12), 1205–1221 (2001). [CrossRef]
  8. O. V. Lyubomudrov and V. V. Shkunov, “Self-bending specklons in photorefractive crystals,” J. Opt. Soc. Am. B 11(8), 1403–1408 (1994). [CrossRef]
  9. P. Xie, J.-H. Dai, P.-Y. Wang, H.-J. Zhang, and P.-Y. Wang, “A two-dimensional theory and propagation of beam fanning in photorefractive crystals,” J. Appl. Phys. 75(4), 1891–1894 (1994). [CrossRef]
  10. A. A. Kamshilin, E. Raita, and A. V. Khomenko, “Intensity redistribution in a thin photorefractive crystal caused by strong fanning effect and internal reflections,” J. Opt. Soc. Am. B 13(11), 2536–2543 (1996). [CrossRef]
  11. O. Ostroverkhova and W. E. Moerner, “Organic photorefractives: mechanisms, materials, and applications,” Chem. Rev. 104(7), 3267–3314 (2004). [CrossRef] [PubMed]
  12. K. Meerholz, R. Bittner, and Y. D. Nardin, “Field asymmetry of the dynamic gain coefficient in organic photorefractive devices,” Opt. Commun. 150(1-6), 205–209 (1998). [CrossRef]
  13. A. G-Jepsen, “C. L. Thompson, R. J. Twieg, and W. E. Moerner, “Amplified scattering in a high-gain photorefractive polymer,” J. Opt. Soc. Am. B 15, 901–904 (1998). [CrossRef]
  14. T. Sassa, T. Muto, T. Wada, Y. Takeda, T. Fujihara, and S. Umegaki, “Strongly electric-field-dependent spatial properties of fanning beam in polymeric medium,” Appl. Phys. Lett. 86(8), 84103 (2005). [CrossRef]
  15. T. Sassa, T. Muto, and T. Wada, “Enhanced photorefractive two-beam coupling in low-Tg polymeric materials with a new device structure,” J. Opt. Soc. Am. B 21(6), 1255–1261 (2004). [CrossRef]
  16. A. V. Khomenko, E. Nippolainen, A. A. Kamshilin, A. Z. Segundo, and T. Jaaskelainen, “Leaky photorefractive surface waves in Bi12TiO29 and Bi12SiO20 crystals,” Opt. Commun. 150(1-6), 175–179 (1998). [CrossRef]
  17. L. Solymar, D. J. Webb, and A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Oxford, New York, 1996), Chap. 10, pp. 320–322.

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