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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 73, Iss. 5 — May. 1, 1983
  • pp: 548–553

Theory of a self-pumped phase conjugator with two coupled interaction regions

Kenneth R. MacDonald and Jack Feinberg  »View Author Affiliations

JOSA, Vol. 73, Issue 5, pp. 548-553 (1983)

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We present a plane-wave analysis of a recently demonstrated self-pumped phase conjugator. This device uses four-wave mixing to produce the phase-conjugate replica of an incident optical wave. All the waves are derived from the single incident wave: there are no externally supplied pumping beams. We consider the case of fourwave mixing in two interaction regions coupled by simple reflection. We calculate the phase-conjugate reflectivity as a function of coupling strength, taking into account imperfect coupling between the two interaction regions, and show that there is a threshold coupling strength below which the reflectivity is zero and above which the reflectivity is multiple valued. We also compute the coupling strength per unit length for a photorefractive crystal of barium titanate.

© 1983 Optical Society of America

Kenneth R. MacDonald and Jack Feinberg, "Theory of a self-pumped phase conjugator with two coupled interaction regions," J. Opt. Soc. Am. 73, 548-553 (1983)

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  1. A recent review of phase conjugation is featured in Opt. Electron. 21, 155–283 (1982).
  2. A. Yariv, "Four-wave nonlinear optical mixing as real-time holography," IEEE J. Quantum Electron. QE-14, 650–660 (1978).
  3. J. P. Huignard, J. P. Herriau, P. Aubourg, and E. Spitz, "Phaseconjugate wave-front generation via real-time holography in Bi12SiO20 crystals," Opt. Lett. 4, 21–23 (1979); J. Feinberg and R. W. Hellwarth, "Phase-conjugate mirror with continuous-wave gain," Opt. Lett. 5, 519–521 (1980); erratum 6, 257 (1981).
  4. S. M. Jensen and R. W. Hellwarth, "Generation of time-reversed waves by nonlinear refraction in a waveguide," Appl. Phys. Lett. 33, 404–405 (1978).
  5. J. O. White, M. Cronin-Golomb, B. Fischer, and A. Yariv, "Coherent oscillation by self-induced gratings in the photorefractive crystal BaTiO3," Appl. Phys. Lett. 40, 450–452 (1982).
  6. M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, "A passive (self-pumped) phase-conjugate mirror: a theoretical and experimental investigation," Appl. Phys. Lett. 41, 689–691 (19821).
  7. J. Feinberg, "Self-pumped, continuous-wave phase-conjugator using internal reflection," Opt. Lett. 7, 486–488 (1982).
  8. R. W. Hellwarth, "Theory of phase-conjugation by four-wave mixing in a waveguide," IEEE J. Quantum Electron. QE-15, 101–109 (1979).
  9. M. Cronin-Golomb, J. O. White, B. Fischer, and A. Yariv, "Exact solution of a nonlinear model of four-wave mixing and phase conjugation," Opt. Lett. 7, 313–315 (1982).
  10. B. Fischer, M. Cronin-Golomb, J. O. White, and A. Yariv, "Amplified reflection, transmission, and self-oscillation in real-time holography," Opt. Lett. 6, 519–521 (1981).
  11. In Ref. 10 the coupled wave equations are derived with the as- sumption that the charges involved in the photorefractive effect (and consequently the sign of the coupling parameter γ) are negative. Since these charges are positive in barium titanate,13 we consistently take γ to have the opposite sign.
  12. The coupling strength γ is generally complex; in barium titanate γ is real in the absence of any uniform dc electric field (either applied or intrinsic).13 We take γ to be real here and will consider the more-general case in a future publication.
  13. J. Feinberg, D. Heiman, A. R. Tanguay, Jr., and R. W. Hellwarth, "Photorefractive effects and light-induced charge migration in barium titanate," J. Appl. Phys. 51, 1297–1305 (1980); erratum 537 (1981).
  14. J. Feinberg, "Asymmetric self-defocusing of an optical beam from the photorefractive effect," J. Opt. Soc. Am. 72, 46–51 (1982).
  15. S. H. Wemple, D. Didomenico, Jr., and I. Camlibel, "Dielectric optical properties of melt-grown BaTiO3," J. Phys. Chem. Solids 29, 1797–1806 (1968).
  16. A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975).
  17. In addition to the threshold in the coupling strength, there is a small intensity threshold (of the order of 10-2 W/cm2). This is because the input wave intensity must be high enough that the grating-formation rate (which is proportional to the intensity) exceeds the dark leakage rate.

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