Abstract

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

PDF Article

References

  • View by:
  • |
  • |
  • |

  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.

1982

1981

1979

1978

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).

A. Yariv, "Four-wave nonlinear optical mixing as real-time holography," IEEE J. Quantum Electron. QE-14, 650–660 (1978).

1968

S. H. Wemple, D. Didomenico, Jr., and I. Camlibel, "Dielectric optical properties of melt-grown BaTiO3," J. Phys. Chem. Solids 29, 1797–1806 (1968).

Aubourg, P.

Camlibel, I.

S. H. Wemple, D. Didomenico, Jr., and I. Camlibel, "Dielectric optical properties of melt-grown BaTiO3," J. Phys. Chem. Solids 29, 1797–1806 (1968).

Cronin-Golomb, M.

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).

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).

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).

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).

Didomenico, Jr., D.

S. H. Wemple, D. Didomenico, Jr., and I. Camlibel, "Dielectric optical properties of melt-grown BaTiO3," J. Phys. Chem. Solids 29, 1797–1806 (1968).

Feinberg, J.

J. Feinberg, "Asymmetric self-defocusing of an optical beam from the photorefractive effect," J. Opt. Soc. Am. 72, 46–51 (1982).

J. Feinberg, "Self-pumped, continuous-wave phase-conjugator using internal reflection," Opt. Lett. 7, 486–488 (1982).

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).

Fischer, B.

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).

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).

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).

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).

Heiman, D.

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).

Hellwarth, R. W.

R. W. Hellwarth, "Theory of phase-conjugation by four-wave mixing in a waveguide," IEEE J. Quantum Electron. QE-15, 101–109 (1979).

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).

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).

Herriau, J. P.

Huignard, J. P.

Jensen, S. M.

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).

Spitz, E.

Tanguay, Jr., A. R.

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).

Wemple, S. H.

S. H. Wemple, D. Didomenico, Jr., and I. Camlibel, "Dielectric optical properties of melt-grown BaTiO3," J. Phys. Chem. Solids 29, 1797–1806 (1968).

White, J. O.

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).

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).

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).

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).

Yariv, A.

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).

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).

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).

A. Yariv, "Four-wave nonlinear optical mixing as real-time holography," IEEE J. Quantum Electron. QE-14, 650–660 (1978).

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).

A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975).

Appl. Phys. Lett.

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).

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).

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).

IEEE J. Quantum Electron.

R. W. Hellwarth, "Theory of phase-conjugation by four-wave mixing in a waveguide," IEEE J. Quantum Electron. QE-15, 101–109 (1979).

A. Yariv, "Four-wave nonlinear optical mixing as real-time holography," IEEE J. Quantum Electron. QE-14, 650–660 (1978).

J. Opt. Soc. Am.

J. Phys. Chem. Solids

S. H. Wemple, D. Didomenico, Jr., and I. Camlibel, "Dielectric optical properties of melt-grown BaTiO3," J. Phys. Chem. Solids 29, 1797–1806 (1968).

Opt. Lett.

Other

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.

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.

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).

A recent review of phase conjugation is featured in Opt. Electron. 21, 155–283 (1982).

A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975).

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.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.