OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 5, Iss. 5 — May. 1, 1988
  • pp: 690–701

Nonlinear photorefractive response at high modulation depths

Frederick Vachss and Lambertus Hesselink  »View Author Affiliations


JOSA A, Vol. 5, Issue 5, pp. 690-701 (1988)
http://dx.doi.org/10.1364/JOSAA.5.000690


View Full Text Article

Enhanced HTML    Acrobat PDF (1460 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The response of photorefractive materials to sinusoidal intensity patterns of high modulation depths is considered. It is shown that the induced refractive-index response in this regime is highly nonlinear. Concise analytic expressions for the various nonlinear harmonics of the photorefractive response field are developed and compared with exact numerical solutions of the underlying charge-transport equations as well as with the results of previous theoretical models over a broad range of physical parameters. We show that the nonlinear response characteristics are strongly dependent on both the magnitude of applied electric fields and the relative concentrations of charge donor and acceptor sites in the material. For drift dominated recording, in particular, we determine analytically that in the limit of a minimal acceptor/donor ratio, the amplitudes of higher spatial harmonics of the response reach a maximum and eventually decay as functions of increasing applied field, whereas these amplitudes reach a nonzero limit in the case of a near-unity acceptor/donor ratio. Finally, we generalize our results to account for diffusion effects in an appended derivation.

© 1988 Optical Society of America

History
Original Manuscript: February 10, 1987
Manuscript Accepted: December 21, 1987
Published: May 1, 1988

Citation
Frederick Vachss and Lambertus Hesselink, "Nonlinear photorefractive response at high modulation depths," J. Opt. Soc. Am. A 5, 690-701 (1988)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-5-5-690


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. D. M. Kim, R. R. Shah, T. A. Rabson, F. K. Tittel, “Nonlinear dynamic theory for photorefractive phase hologram formation,” Appl. Phys. Lett. 28, 338–340 (1976). [CrossRef]
  2. G. A. Alphonse, R. C. Alig, D. L. Staebler, W. Phillips, “Time-dependent characteristics of photo-induced space-charge field and phase holograms in lithium niobate and other photorefractive media,” RCA Rev. 36, 213–228 (1975).
  3. J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hell-warth, “Photorefractive effects and light-induced charge migration in barium titanate,” J. Appl. Phys. 51, 1297–1305 (1980). [CrossRef]
  4. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22,949–960 (1979). [CrossRef]
  5. M. Peltier, F. Micheron, “Volume hologram recording and charge transfer process in Bi12SiO20 and Bi12GeO20,” J. Appl. Phys. 48, 3683–3690 (1977). [CrossRef]
  6. M. G. Moharam, T. K. Gaylord, R. Magnusson, L. Young, “Holographic grating formation in photorefractive crystals with arbitrary electron transport lengths,” J. Appl. Phys. 50, 5642–5651 (1979). [CrossRef]
  7. T. J. Hall, R. Jaura, L. M. Connors, P. D. Foote, “The photorefractive effect—a review,” Prog. Quantum Electron. 10, 77–146 (1985). [CrossRef]
  8. M. P. Petrov, S. V. Miridonov, S. I. Stepanov, V. V. Kulikov, “Light diffraction and non-linear image processing in electro-optic Bi12SiO20crystals,” Opt. Commun. 31, 301–305 (1979). [CrossRef]
  9. T. Y. Chang, P. Yeh, “Observation of harmonic phase conjugation in a photorefractive medium,” J. Opt. Soc. Am. A 3(13), P33 (1986).
  10. J. P. Huignard, B. Ledu, “Collinear Bragg diffraction in photorefractive Bi12SiO20,” Opt. Lett. 7, 310–312 (1982). [CrossRef] [PubMed]
  11. E. Ochoa, F. Vachss, L. Hesselink, “Higher-order analysis of the photorefrctive effect for large modulation depths,” J. Opt. Soc. Am. A 3, 181–187 (1986). [CrossRef]
  12. P. Refregier, L. Solymar, H. Rajbenbach, J. P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–47 (1985). [CrossRef]
  13. G. C. Valley, “Simultaneous electron/hole transport in photorefractive materials,” J. Appl. Phys. 59, 3363–3366 (1986). [CrossRef]
  14. F. P. Strohkendl, J. M. C. Jonathan, R. W. Hellwarth, “Hole–electron competition in photorefractive gratings,” Opt. Lett. 11, 312–314 (1986). [CrossRef] [PubMed]
  15. M. B. Klein, G. C. Valley, “Beam coupling in BaTiO3at 442 nm,” J. Appl. Phys. 57, 4901–4905 (1985). [CrossRef]
  16. R. A. Mullen, R. W. Hellwarth, “Optical measurement of the photorefractive parameters of Bi12SiO20,” J. Appl. Phys. 58, 40–44 (1985). [CrossRef]
  17. P. Gunter, “Holography, coherent light amplification and optical phase conjugation with photorefractive materials,” doctoral dissertation (Swiss Federal Institute of Technology, Zurich, Switzerland, 1981).
  18. G. C. Valley, “Erase rates in photorefractive materials with two photoactive species,” Appl. Opt. 22, 3160–3164 (1983). [CrossRef] [PubMed]
  19. E. Ochoa, “Real-time intensity inversion using four-wave mixing in photorefractive crystals,” doctoral dissertation (Stanford University, Stanford, Calif., 1985).
  20. G. C. Valley, M. B. Klein, “Optical properties of photorefractive materials for optical data processing,” Opt. Eng. 22, 704–711 (1983). [CrossRef]
  21. G. C. Valley, “Competition between forward- and backward-stimulated photorefractive scattering in BaTiO3,” J. Opt. Soc. Am: B 4, 14–19 (1987). [CrossRef]
  22. M. Carrascosa, F. Agullo-Lopez, “Kinetics for optical erasure of sinusoidal holographic gratings in photorefractive materials,” IEEE J. Quantum Electron. QE-22, 1369–1375 (1986).Note that although the charge-transport equations given in this reference have somewhat different nomenclature, they are formally equivalent to those given by Kukhtarev et al.4 [CrossRef]
  23. M. Abramowitz, I. A. Stegun, eds., Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables (Dover, New York, 1965), p. 256.
  24. P. M. Woodward, A. M. Woodward, R. Hensman, H. H. Davies, N. Gamble, “Four-figure tables of the airy functions in the complex plane,” Philos. Mag. 37, 236–261 (1946).Data are given only in the region 0 < Re(z) < 2.54, −2.54 < Im(z) < 2.54. In this region the magnitude of the difference between our approximate form and Ai(z) is less than 0.05 |Ai(z)|.

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.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited