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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 12, Iss. 12 — Dec. 1, 1995
  • pp: 2453–2462

Nonlinear combinations of gratings in drift-dominated recording in Bi12SiO20

P. E. Andersen, P. M. Petersen, and P. Buchhave  »View Author Affiliations

JOSA B, Vol. 12, Issue 12, pp. 2453-2462 (1995)

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Multiwave mixing in Bi12SiO20 causes the formation of multiple grating because of the photorefractive effect. These primary gratings interact and cause the formation of additional gratings at frequencies that are combinations of the primary grating frequencies. The nonlinear combinations of gratings stem from the nonlinear response of the space-charge field to the incident optical interference pattern through the generation of electrons into the conduction band. We investigate drift-dominated recording. The effects of nonlinear combinations of gratings are investigated quantitatively in a three-wave mixing configuration, in which one reference beam and two closely situated object beams induce three primary gratings. Using a sinusoidal phase modulation on one of the object beams provides absolute control of the primary grating strengths. Specifically, two of the primary gratings may be completely erased, and the nonlinear effect may be obtained as the relative change in the diffraction efficiency from the remaining grating. For drift-dominated recording an expression for the total space-charge field is derived, including multiple spatial frequencies. The derivation is based on the band-transport model. A numerical model is presented in which the relative change in diffraction efficiency is calculated from the corresponding change in the grating strengths. The grating strengths are found from the corresponding frequency components of the total space-charge field. The model is valid in the limit of low diffraction efficiencies and small coupling constants. The investigation is carried out with different values of the intensity ratio between the reference beam and the sum of the two object beams, the applied field to the crystal, and the separation angle between the two object beams. It is shown that relative changes of 200% in the diffraction efficiency occur. Thus the magnitude of the additional grating strengths may be substantial and even comparable with those of the primary grating. Comparing the predictions of the numerical model with the experimental data shows excellent agreement.

© 1995 Optical Society of America

P. E. Andersen, P. M. Petersen, and P. Buchhave, "Nonlinear combinations of gratings in drift-dominated recording in Bi12SiO20," J. Opt. Soc. Am. B 12, 2453-2462 (1995)

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  1. A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, "Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3," Appl. Phys. Lett. 9, 72–74 (1966).
  2. F. S. Chen, "Optically induced change of refractive indices in LiNbO3 and LiTaO3," J. Appl. Phys. 40, 3389–3396 (1969).
  3. J. W. Goodman, F. J. Leonberger, S.-Y. Kung, and R. A. Athale, "Optical interconnections for VLSI systems," Proc. IEEE 72, 850–866 (1984).
  4. P. B. Berra, A. Ghafoor, M. Guizani, S. J. Marcinkowski, and P. A. Mitkas, "Optics and supercomputing," Proc. IEEE 77, 1798–1815 (1989).
  5. S. I. Stepanov, "Applications of photorefractive crystals," Rep. Prog. Phys. 57, 36–116 (1994).
  6. F. Vachss and L. Hesselink, "Nonlinear photorefractive response at high modulation depths," J. Opt. Soc. Am. A 5, 690–701 (1988).
  7. L. B. Au and L. Solymar, "Higher harmonic gratings in photorefractive materials at large modulation with moving fringes," J. Opt. Soc. Am. A 7, 1554–1561 (1990).
  8. J. P. Huignard and B. Ledu, "Collinear Bragg diffraction in photorefractive Bi12SiO20," Opt. Lett. 7, 310–312 (1982).
  9. S. Fries, S. Bauschulte, E. Krátzig, K. Ringhofer, and Y. Yacoby, "Spatial frequency mixing in lithium niobate," Opt. Commun. 84, 251–257 (1991).
  10. P. Buchhave, P. E. Andersen, P. M. Petersen, and M. V. Vasnetsov, "Nonlinear grating interaction in photorefractive Bi12SiO20," Appl. Phys. Lett. 66, 792–794 (1995).
  11. P. E. Andersen, P. Buchhave, P. M. Petersen, and M. Vasnetsov, "Nonlinear combinations of gratings in Bi12SiO20: theory and experiments," J. Opt. Soc. Am. B 12, 1422–1433 (1995).
  12. L. B. Au and L. Solymar, "Higher diffraction orders in photorefractive materials," IEEE J. Quantum Electron. 24, 162–168 (1988).
  13. A. Marrakchi, J. P. Huignard, and P. Gülnter, "Diffraction efficiency and energy transfer in two-wave mixing experiments with Bi12SiO20 crystals," Appl. Phys. 24, 131–138 (1981).
  14. P. E. Andersen, P. M. Petersen, and P. Buchhave, "Crosstalk in dynamic optical interconnects in photorefractive crystals," Appl. Phys. Lett. 65, 271–273 (1994).
  15. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, "Holographic storage in electrooptic crystals. I. Steady state," Ferroelectrics 22, 949–960 (1979).
  16. H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909–2947 (1969).
  17. P. M. Johansen, "Enhanced four-wave mixing in photorefractive BSO produced by temporal phase shifts," J. Phys. D 22, 247–253 (1989).
  18. A. Marrakchi, W. M. Hubbard, S. F. Habiby, and J. S. Patel, "Dynamic holographic interconnects with analog weights in photorefractive crystals," Opt. Eng. 29, 215–225 (1990).
  19. 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).
  20. P. Refrégier, L. Solymar, H. Rajbenbach, and J. P. Huignard, "Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments," J. Appl. Phys. 58, 45–57 (1985).
  21. C. H. Kwak, S. Y. Park, J. S. Jeong, H. H. Suh, and E. Lee, "An analytical solution for large modulation effects in photorefractive two-wave couplings," Opt. Commun. 105, 353–358 (1994).
  22. B. Edvold, P. E. Andersen, P. Buchhave, and P. M. Petersen, "Polarization properties of a photorefractive Bi12SiO20 crystal and their application in an optical correlator," IEEE J. Quantum Electron. 30, 1075–1089 (1994).
  23. P. D. Foote and T. J. Hall, "Influence of optical activity on two beam coupling constants in photorefractive Bi12SiO20," Opt. Commun. 57, 201–206 (1986).

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