OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 15, Iss. 10 — Oct. 1, 1998
  • pp: 2552–2559

Optimum orientation of volume phase gratings in sillenite crystals: is it always [111]?

E. Shamonina, V. P. Kamenov, K. H. Ringhofer, G. Cedilnik, A. Kiessling, and R. Kowarschik  »View Author Affiliations

JOSA B, Vol. 15, Issue 10, pp. 2552-2559 (1998)

View Full Text Article

Enhanced HTML    Acrobat PDF (317 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We study the simultaneous influence of optical activity, piezoelectric effect, and elasto-optic effect on two-wave mixing (TWM) under diffusion recording in photorefractive Bi12TiO20 and Bi12SiO20 crystals and find numerically the maximum of the TWM gain as a function of the orientation of the grating vector. Contrary to widespread belief, the grating orientation K[111] is the optimum orientation only if optical activity is negligibly small. Nonzero optical activity results in a strong dependence of the optimum grating orientation on the crystal thickness. The strongest deviation of the optimum from the [111] direction is achieved for ϱd=180°, where ϱ is the rotatory power and d is the crystal thickness. Our theory explains well prior results for crystals of moderate thickness and predicts new effects for thick (e.g., fiberlike) crystals.

© 1998 Optical Society of America

OCIS Codes
(090.7330) Holography : Volume gratings
(190.4400) Nonlinear optics : Nonlinear optics, materials
(190.5330) Nonlinear optics : Photorefractive optics
(190.7070) Nonlinear optics : Two-wave mixing

E. Shamonina, V. P. Kamenov, K. H. Ringhofer, G. Cedilnik, A. Kiessling, and R. Kowarschik, "Optimum orientation of volume phase gratings in sillenite crystals: is it always [111]?," J. Opt. Soc. Am. B 15, 2552-2559 (1998)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. A. A. Izvanov, A. E. Mandel, N. D. Khatkov, and S. M. Shandarov, “Influence of the piezoelectric effect on hologram writing and reconstruction in photorefractive crystals,” Optoelectronics 2, 80–84 (1986).
  2. S. Stepanov, S. M. Shandarov, and N. D. Khat’kov, “Photoelastic contribution to the photorefractive effect in cubic crystals,” Sov. Phys. Solid State 29, 1754–1756 (1987).
  3. A. E. Mandel, S. M. Shandarov, and V. V. Shepelevich, “Influence of piezoelectric effect and gyrotropy on light diffraction in cubic photorefractive crystals,” Opt. Spectrosc. 67, 481–484 (1989).
  4. V. V. Shepelevich, S. M. Shandarov, and A. E. Mandel, “Light diffraction by holographic gratings in optically active photorefractive piezocrystals,” Ferroelectrics 110, 235–249 (1990). [CrossRef]
  5. S. M. Shandarov, V. V. Shepelevich, and N. D. Khatkov, “Variation of the permittivity tensor in cubic photorefractive piezoelectric crystals under the influence of the electric field of a holographic grating,” Opt. Spectrosc. 70, 627–630 (1991).
  6. V. V. Shepelevich and N. N. Egorov, “Light diffraction on holographic gratings in gyrotropic cubic photorefractive crystals,” Opt. Spectrosc. 71, 600–603 (1991).
  7. N. V. Kukhtarev, T. I. Semenec, and P. Hribek, “The influence of photoelasticity on the self-diffraction of light in cubic photorefractive crystals,” Ferroelectr. Lett. Sect. 13, 29–35 (1991). [CrossRef]
  8. G. Pauliat, P. Mathey, and G. Roosen, “Influence of piezoelectricity on the photorefractive effect,” J. Opt. Soc. Am. B 8, 1942–1946 (1991). [CrossRef]
  9. S. M. Shandarov, “Influence of piezoelectric effect on photorefractive gratings in electro-optic crystals,” Appl. Phys. A 55, 91–96 (1992). [CrossRef]
  10. E. Anastassakis, “Photorefractive effects in cubic crystals: explicit treatment of the piezoelectric contribution,” IEEE J. Quantum Electron. 29, 2239–2244 (1993). [CrossRef]
  11. V. V. Shepelevich, “Optimization of the energy transfer in cubic photorefractive piezocrystals,” in Technical Digest on Topical Meeting on Photorefractive Materials, Effects, and Devices (Ukrainian Academy of Sciences, Theophania, Kiev, Ukraine, 1993), pp. 128–131.
  12. V. V. Shepelevich, N. N. Egorov, and V. Shepelevich, “Orientation and polarization effects of two-beam coupling in a cubic optically active photorefractive piezoelectric BSO crystal,” J. Opt. Soc. Am. B 11, 1394–1402 (1994). [CrossRef]
  13. R. Litvinov and S. Shandarov, “Influence of piezoelectric and photoelastic effects on pulse hologram recording in photorefractive crystals,” J. Opt. Soc. Am. B 11, 1204–1210 (1994). [CrossRef]
  14. H. C. Ellin and L. Solymar, “Light scattering in bismuth silicate: matching of experimental results,” Opt. Commun. 130, 85–88 (1996). [CrossRef]
  15. S. M. Shandarov, A. Emelyanov, O. Kobozev, A. Reshet’ko, V. V. Volkov, and Yu. F. Kargin, “Photorefractive properties of doped sillenite crystals,” in Nonlinear Optics of Low-Dimensional Structures and New Materials, V. I. Emelýanov and V. Y. Panchenko, eds., Proc. SPIE 2801, 221–230 (1996). [CrossRef]
  16. V. V. Shepelevich, N. N. Egorov, P. I. Ropot, and P. P. Khomutovskiy, “Extremal conditions of diffraction and two-wave mixing in cubic gyrotropic photorefractive piezocrystals,” in Optical Organic and Semiconductor Inorganic Materials, E. A. Siliush, A. Medvids, A. R. Lusis, and A. O. Ozols, eds., Proc. SPIE 2968, 301–306 (1997). [CrossRef]
  17. V. V. Shepelevich, N. N. Egorov, G. von Bally, S. G. Odoulov, and P. P. Khomutovskiy, “Optimization of energy exchange of light waves in crystal BTO by selection of grating vector orientation and thickness of crystal,” in Proceedings of Topical Meeting on Photorefractive Materials, Effects, and Devices (Optical Society of Japan, Tokyo, Japan, 1997), pp. 319–321.
  18. V. V. Shepelevich, “Diffraction and two-wave coupling in cubic gyrotropic piezoelectric crystals of an arbitrary cut: general relations,” Opt. Spectrosc. 83, 161–165 (1997).
  19. H. J. Eichler, Y. Ding, and B. Smandek, “Photorefractive two-wave mixing in semiconductors of the 4¯3m space group in general spatial orientation,” Phys. Rev. A 52, 2411–2418 (1995). [CrossRef] [PubMed]
  20. P. Günter and M. Zgonik, “Clamped–unclamped electro-optic coefficient dilemma in photorefractive phenomena,” Opt. Lett. 16, 1826–1828 (1991). [CrossRef]
  21. M. Zgonik, K. Nakagawa, and P. Günter, “Electro-optic and dielectric properties of photorefractive BaTiO3 and KNbO3,” J. Opt. Soc. Am. B 12, 1416–1421 (1995). [CrossRef]
  22. G. Montemezzani, A. A. Zozulya, L. Czaia, D. Z. Anderson, M. Zgonik, and P. Günter, “Origin of the lobe structure in photorefractive beam fanning,” Phys. Rev. A 52, 1791–1794 (1995). [CrossRef] [PubMed]
  23. P. Mathey, “Photorefractive-gain dependence on piezoelectric and photoelastic effects in barium titanate,” Phys. Rev. E 55, 7782–7784 (1997). [CrossRef]
  24. A. Mandel, N. Khatkov, and S. Shandarov, “Light diffraction in holographic arrays—different mechanisms of photorefractive effect in ferroelectrics,” Ferroelectrics 83, 215–220 (1988). [CrossRef]
  25. A. Kiessling and L. Wenke, “Real-time holographic interferometry using degenerated four-wave mixing in Bi12TiO20,” Int. J. Optoelectron. 8, 617–627 (1993).
  26. S. I. Stepanov, “Applications of photorefractive crystals,” Rep. Prog. Phys. 57, 39–116 (1994), and references cited therein. [CrossRef]
  27. D. Dirksen, F. Matthes, S. Riehemann, and G. von Bally, “Phase shifting holographic double expose interferometry with fast photorefractive crystals,” Opt. Commun. 134, 310 (1997). [CrossRef]
  28. M. P. Georges and P. C. Lemaire, “Real-time holographic interferometry with sillenite crystals: a breadboard system for industrial applications, I and II,” in Proceedings of Topical Meeting on Photorefractive Materials, Effects, and Devices (Optical Society of Japan, Tokyo, Japan, 1997), pp. 495–498 and 637–640 and references cited therein.
  29. M. P. Petrov, S. I. Stepanov, and A. V. Khomenko, Photorefractive Crystals in Coherent Optical Systems, Vol. 59 of Springer Series in Optical Sciences (Springer-Verlag, Heidelberg, Germany, 1991), pp. 233–239.
  30. L. Solymar, D. J. Webb, and A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Clarendon, Oxford, 1996).
  31. P. V. Lenzo, E. G. Spencer, and A. A. Ballman, “Optical activity and electrooptic effect in bismuth germanium oxide (Bi12GeO20),” Appl. Opt. 5, 1688–1689 (1966). [CrossRef] [PubMed]
  32. A. J. Fox and T. M. Bruton, “Electro-optic effects in the optically active compounds Bi12TiO20 and Bi40Ga2O63,” Appl. Phys. Lett. 27, 360–362 (1975). [CrossRef]
  33. A. Marrakchi, R. V. Johnson, and A. R. Tanguay, Jr., “Polarization properties of photorefractive diffraction in electrooptic and optically active sillenite crystals (Bragg regime),” J. Opt. Soc. Am. B 3, 321–336 (1986). [CrossRef]
  34. F. Vachss and L. Hesselink, “Measurements of the electrogyratory and electro-optic effects in BSO and BGO,” Opt. Commun. 62, 159–165 (1987). [CrossRef]
  35. C. Stace, A. K. Powell, K. Walsh, and T. J. Hall, “Coupling modulation in photorefractive materials by applying ac electric fields,” Opt. Commun. 70, 509–514 (1989). [CrossRef]
  36. A. Yariv and P. Yeh, Optical Waves in Crystals, Wiley Series in Pure and Applied Optics (Wiley, New York, 1984), pp. 223–237.
  37. E. Shamonina, G. Cedilnik, M. Mann, A. Kiessling, D. J. Webb, R. Kowarschik, and K. H. Ringhofer, “Investigation of two-wave mixing in arbitrary oriented sillenite crystals,” Appl. Phys. B 64, 49–56 (1997). [CrossRef]
  38. A. A. Kamshilin, V. Prokofiev, and T. Jaaskelainen, “Beam fanning and double phase conjugation in a fiber-like photorefractive sample,” IEEE J. Quantum Electron. 31, 1642–1647 (1995). [CrossRef]
  39. 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, 2536–2543 (1996). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1 Fig. 2 Fig. 3
Fig. 4 Fig. 5

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited