Abstract

The performance of four different mutually pumped phase conjugators in barium titanate depends on the mutual coherence of the two input beams. In three of the conjugators the use of fully mutually coherent input beams enhances the overall phase-conjugate reflectivity. We find that backscattering and transmission gratings in the photorefractive crystal both contribute to the phase-conjugate signal and that their relative strength depends on the relative coherence of the two input beams. We numerically solve coupled-wave equations that include all gratings and find reasonable agreement between our theory and our experimental data.

© 1995 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. Weiss, S. Sternklar, and B. Fischer, "Double phaseconjugate mirror: analysis, demonstration, and applications," Opt. Lett. 12, 114 (1987). Note that the orientation of the c axis of our DPCM differs from that shown in Fig. 1 of this reference.
    [CrossRef] [PubMed]
  2. S. Sternklar, S. Weiss, M. Segev, and B. Fischer, "Beam coupling and locking of lasers using photorefractive fourwave mixing," Opt. Lett. 11, 528 (1986).
    [CrossRef] [PubMed]
  3. M. W. Wright and J. G. McInerney, "Injection locking semiconductor lasers with phase conjugate feedback," Opt. Commun. 110, 689 (1994).
    [CrossRef]
  4. S. MacCormack, J. Feinberg, and M. H. Garrett, "Injection locking a laser-diode array with a phase-conjugate beam," Opt. Lett. 19, 120 (1994).
    [CrossRef] [PubMed]
  5. M. D. Ewbank, "Mechanism for photorefractive phase conjugation using incoherent beams," Opt. Lett. 13, 47 (1988).
    [CrossRef] [PubMed]
  6. P. Yeh, "Coupled-mode theory of hologram sharing in mutually pumped phase conjugators," Appl. Opt. 28, 1961 (1989).
    [CrossRef] [PubMed]
  7. M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, "Theory and applications of four-wave mixing in photorefractive media," IEEE J. Quantum Electron. QE-20, 12 (1984).
    [CrossRef]
  8. D. Wang, Z. Zhang, Y. Zhu, S. Zhang, and P. Ye, "Observations on the coupling channel of two mutually incoherent beams without internal reflections in BaTiO3," Opt. Commun. 73, 495 (1989).
    [CrossRef]
  9. A. M. C. Smout and R. W. Eason, "Analysis of mutually incoherent beam coupling in BaTiO3," Opt. Lett. 12, 498 (1987).
    [CrossRef] [PubMed]
  10. M. T. Gruneisen, E. D. Seeberger, J. F. Mileski, and K. Koch, "Effects of laser coherence on coupling efficiency for the double phase-conjugate mirror," Opt. Lett. 16, 596 (1991).
    [CrossRef] [PubMed]
  11. Q. B. He and P. Yeh, "Photorefractive mutually-pumped phase conjugation with partially coherent beams," Appl. Phys. B 60, 47 (1994).
    [CrossRef]
  12. R. S. Cudney, R. M. Pierce, G. D. Bacher, and J. Feinberg, "Absorption gratings in photorefractive crystals with multiple levels," J. Opt. Am. B 8, 1326 (1991).
    [CrossRef]
  13. These mounts were provided by New Focus, Inc., 1275 Reamwood Avenue, Sunnyvale, Calif. 94089-2256.
  14. D. Statman and B. Liby, "Two-beam cross coupling from mutually incoherent lasers," J. Opt. Soc. Am. B 6, 1884 (1989).
    [CrossRef]
  15. K. R. MacDonald, J. Feinberg, M. Z. Zha, and P. Günter, "Asymmetric transmission through a photorefractive crystal of barium titanate," Opt. Commun. 50, 146 (1984).
    [CrossRef]
  16. M. Zgonik, P. Bernasconi, M. Duelli, P. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, "Dielectric, elastic, piezoelectric, electro-optic and elasto-optic, tensors of BaTiO3 crystals," Phys. Rev. B 50, 5941 (1994).
    [CrossRef]
  17. See, e.g., M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), Chap. 10. Note that the symbol for mutual coherence is often γ.
  18. Q. C. He, "Theory of photorefractive phase conjugators with mutually incoherent beams," IEEE J. Quantum Electron. 24, 2507 (1988).
    [CrossRef]

1994 (4)

M. W. Wright and J. G. McInerney, "Injection locking semiconductor lasers with phase conjugate feedback," Opt. Commun. 110, 689 (1994).
[CrossRef]

Q. B. He and P. Yeh, "Photorefractive mutually-pumped phase conjugation with partially coherent beams," Appl. Phys. B 60, 47 (1994).
[CrossRef]

M. Zgonik, P. Bernasconi, M. Duelli, P. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, "Dielectric, elastic, piezoelectric, electro-optic and elasto-optic, tensors of BaTiO3 crystals," Phys. Rev. B 50, 5941 (1994).
[CrossRef]

S. MacCormack, J. Feinberg, and M. H. Garrett, "Injection locking a laser-diode array with a phase-conjugate beam," Opt. Lett. 19, 120 (1994).
[CrossRef] [PubMed]

1991 (2)

M. T. Gruneisen, E. D. Seeberger, J. F. Mileski, and K. Koch, "Effects of laser coherence on coupling efficiency for the double phase-conjugate mirror," Opt. Lett. 16, 596 (1991).
[CrossRef] [PubMed]

R. S. Cudney, R. M. Pierce, G. D. Bacher, and J. Feinberg, "Absorption gratings in photorefractive crystals with multiple levels," J. Opt. Am. B 8, 1326 (1991).
[CrossRef]

1989 (3)

D. Statman and B. Liby, "Two-beam cross coupling from mutually incoherent lasers," J. Opt. Soc. Am. B 6, 1884 (1989).
[CrossRef]

P. Yeh, "Coupled-mode theory of hologram sharing in mutually pumped phase conjugators," Appl. Opt. 28, 1961 (1989).
[CrossRef] [PubMed]

D. Wang, Z. Zhang, Y. Zhu, S. Zhang, and P. Ye, "Observations on the coupling channel of two mutually incoherent beams without internal reflections in BaTiO3," Opt. Commun. 73, 495 (1989).
[CrossRef]

1988 (2)

M. D. Ewbank, "Mechanism for photorefractive phase conjugation using incoherent beams," Opt. Lett. 13, 47 (1988).
[CrossRef] [PubMed]

Q. C. He, "Theory of photorefractive phase conjugators with mutually incoherent beams," IEEE J. Quantum Electron. 24, 2507 (1988).
[CrossRef]

1987 (2)

1986 (1)

1984 (2)

K. R. MacDonald, J. Feinberg, M. Z. Zha, and P. Günter, "Asymmetric transmission through a photorefractive crystal of barium titanate," Opt. Commun. 50, 146 (1984).
[CrossRef]

M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, "Theory and applications of four-wave mixing in photorefractive media," IEEE J. Quantum Electron. QE-20, 12 (1984).
[CrossRef]

Bacher, G. D.

R. S. Cudney, R. M. Pierce, G. D. Bacher, and J. Feinberg, "Absorption gratings in photorefractive crystals with multiple levels," J. Opt. Am. B 8, 1326 (1991).
[CrossRef]

Bernasconi, P.

M. Zgonik, P. Bernasconi, M. Duelli, P. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, "Dielectric, elastic, piezoelectric, electro-optic and elasto-optic, tensors of BaTiO3 crystals," Phys. Rev. B 50, 5941 (1994).
[CrossRef]

Born, M.

See, e.g., M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), Chap. 10. Note that the symbol for mutual coherence is often γ.

Cronin-Golomb, M.

M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, "Theory and applications of four-wave mixing in photorefractive media," IEEE J. Quantum Electron. QE-20, 12 (1984).
[CrossRef]

Cudney, R. S.

R. S. Cudney, R. M. Pierce, G. D. Bacher, and J. Feinberg, "Absorption gratings in photorefractive crystals with multiple levels," J. Opt. Am. B 8, 1326 (1991).
[CrossRef]

Duelli, M.

M. Zgonik, P. Bernasconi, M. Duelli, P. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, "Dielectric, elastic, piezoelectric, electro-optic and elasto-optic, tensors of BaTiO3 crystals," Phys. Rev. B 50, 5941 (1994).
[CrossRef]

Eason, R. W.

Ewbank, M. D.

Feinberg, J.

S. MacCormack, J. Feinberg, and M. H. Garrett, "Injection locking a laser-diode array with a phase-conjugate beam," Opt. Lett. 19, 120 (1994).
[CrossRef] [PubMed]

R. S. Cudney, R. M. Pierce, G. D. Bacher, and J. Feinberg, "Absorption gratings in photorefractive crystals with multiple levels," J. Opt. Am. B 8, 1326 (1991).
[CrossRef]

K. R. MacDonald, J. Feinberg, M. Z. Zha, and P. Günter, "Asymmetric transmission through a photorefractive crystal of barium titanate," Opt. Commun. 50, 146 (1984).
[CrossRef]

Fischer, B.

Garrett, M. H.

M. Zgonik, P. Bernasconi, M. Duelli, P. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, "Dielectric, elastic, piezoelectric, electro-optic and elasto-optic, tensors of BaTiO3 crystals," Phys. Rev. B 50, 5941 (1994).
[CrossRef]

S. MacCormack, J. Feinberg, and M. H. Garrett, "Injection locking a laser-diode array with a phase-conjugate beam," Opt. Lett. 19, 120 (1994).
[CrossRef] [PubMed]

Gruneisen, M. T.

Günter, P.

M. Zgonik, P. Bernasconi, M. Duelli, P. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, "Dielectric, elastic, piezoelectric, electro-optic and elasto-optic, tensors of BaTiO3 crystals," Phys. Rev. B 50, 5941 (1994).
[CrossRef]

K. R. MacDonald, J. Feinberg, M. Z. Zha, and P. Günter, "Asymmetric transmission through a photorefractive crystal of barium titanate," Opt. Commun. 50, 146 (1984).
[CrossRef]

He, Q. B.

Q. B. He and P. Yeh, "Photorefractive mutually-pumped phase conjugation with partially coherent beams," Appl. Phys. B 60, 47 (1994).
[CrossRef]

He, Q. C.

Q. C. He, "Theory of photorefractive phase conjugators with mutually incoherent beams," IEEE J. Quantum Electron. 24, 2507 (1988).
[CrossRef]

Koch, K.

Liby, B.

MacCormack, S.

MacDonald, K. R.

K. R. MacDonald, J. Feinberg, M. Z. Zha, and P. Günter, "Asymmetric transmission through a photorefractive crystal of barium titanate," Opt. Commun. 50, 146 (1984).
[CrossRef]

McInerney, J. G.

M. W. Wright and J. G. McInerney, "Injection locking semiconductor lasers with phase conjugate feedback," Opt. Commun. 110, 689 (1994).
[CrossRef]

Mileski, J. F.

Pierce, R. M.

R. S. Cudney, R. M. Pierce, G. D. Bacher, and J. Feinberg, "Absorption gratings in photorefractive crystals with multiple levels," J. Opt. Am. B 8, 1326 (1991).
[CrossRef]

Rytz, D.

M. Zgonik, P. Bernasconi, M. Duelli, P. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, "Dielectric, elastic, piezoelectric, electro-optic and elasto-optic, tensors of BaTiO3 crystals," Phys. Rev. B 50, 5941 (1994).
[CrossRef]

Schlesser, P.

M. Zgonik, P. Bernasconi, M. Duelli, P. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, "Dielectric, elastic, piezoelectric, electro-optic and elasto-optic, tensors of BaTiO3 crystals," Phys. Rev. B 50, 5941 (1994).
[CrossRef]

Seeberger, E. D.

Segev, M.

Smout, A. M. C.

Statman, D.

Sternklar, S.

Wang, D.

D. Wang, Z. Zhang, Y. Zhu, S. Zhang, and P. Ye, "Observations on the coupling channel of two mutually incoherent beams without internal reflections in BaTiO3," Opt. Commun. 73, 495 (1989).
[CrossRef]

Weiss, S.

White, J. O.

M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, "Theory and applications of four-wave mixing in photorefractive media," IEEE J. Quantum Electron. QE-20, 12 (1984).
[CrossRef]

Wolf, E.

See, e.g., M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), Chap. 10. Note that the symbol for mutual coherence is often γ.

Wright, M. W.

M. W. Wright and J. G. McInerney, "Injection locking semiconductor lasers with phase conjugate feedback," Opt. Commun. 110, 689 (1994).
[CrossRef]

Wu, X.

M. Zgonik, P. Bernasconi, M. Duelli, P. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, "Dielectric, elastic, piezoelectric, electro-optic and elasto-optic, tensors of BaTiO3 crystals," Phys. Rev. B 50, 5941 (1994).
[CrossRef]

Yariv, A.

M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, "Theory and applications of four-wave mixing in photorefractive media," IEEE J. Quantum Electron. QE-20, 12 (1984).
[CrossRef]

Ye, P.

D. Wang, Z. Zhang, Y. Zhu, S. Zhang, and P. Ye, "Observations on the coupling channel of two mutually incoherent beams without internal reflections in BaTiO3," Opt. Commun. 73, 495 (1989).
[CrossRef]

Yeh, P.

Q. B. He and P. Yeh, "Photorefractive mutually-pumped phase conjugation with partially coherent beams," Appl. Phys. B 60, 47 (1994).
[CrossRef]

P. Yeh, "Coupled-mode theory of hologram sharing in mutually pumped phase conjugators," Appl. Opt. 28, 1961 (1989).
[CrossRef] [PubMed]

Zgonik, M.

M. Zgonik, P. Bernasconi, M. Duelli, P. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, "Dielectric, elastic, piezoelectric, electro-optic and elasto-optic, tensors of BaTiO3 crystals," Phys. Rev. B 50, 5941 (1994).
[CrossRef]

Zha, M. Z.

K. R. MacDonald, J. Feinberg, M. Z. Zha, and P. Günter, "Asymmetric transmission through a photorefractive crystal of barium titanate," Opt. Commun. 50, 146 (1984).
[CrossRef]

Zhang, S.

D. Wang, Z. Zhang, Y. Zhu, S. Zhang, and P. Ye, "Observations on the coupling channel of two mutually incoherent beams without internal reflections in BaTiO3," Opt. Commun. 73, 495 (1989).
[CrossRef]

Zhang, Z.

D. Wang, Z. Zhang, Y. Zhu, S. Zhang, and P. Ye, "Observations on the coupling channel of two mutually incoherent beams without internal reflections in BaTiO3," Opt. Commun. 73, 495 (1989).
[CrossRef]

Zhu, Y.

M. Zgonik, P. Bernasconi, M. Duelli, P. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, "Dielectric, elastic, piezoelectric, electro-optic and elasto-optic, tensors of BaTiO3 crystals," Phys. Rev. B 50, 5941 (1994).
[CrossRef]

D. Wang, Z. Zhang, Y. Zhu, S. Zhang, and P. Ye, "Observations on the coupling channel of two mutually incoherent beams without internal reflections in BaTiO3," Opt. Commun. 73, 495 (1989).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

Q. B. He and P. Yeh, "Photorefractive mutually-pumped phase conjugation with partially coherent beams," Appl. Phys. B 60, 47 (1994).
[CrossRef]

IEEE J. Quantum Electron. (2)

M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, "Theory and applications of four-wave mixing in photorefractive media," IEEE J. Quantum Electron. QE-20, 12 (1984).
[CrossRef]

Q. C. He, "Theory of photorefractive phase conjugators with mutually incoherent beams," IEEE J. Quantum Electron. 24, 2507 (1988).
[CrossRef]

J. Opt. Am. B (1)

R. S. Cudney, R. M. Pierce, G. D. Bacher, and J. Feinberg, "Absorption gratings in photorefractive crystals with multiple levels," J. Opt. Am. B 8, 1326 (1991).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Commun. (3)

D. Wang, Z. Zhang, Y. Zhu, S. Zhang, and P. Ye, "Observations on the coupling channel of two mutually incoherent beams without internal reflections in BaTiO3," Opt. Commun. 73, 495 (1989).
[CrossRef]

M. W. Wright and J. G. McInerney, "Injection locking semiconductor lasers with phase conjugate feedback," Opt. Commun. 110, 689 (1994).
[CrossRef]

K. R. MacDonald, J. Feinberg, M. Z. Zha, and P. Günter, "Asymmetric transmission through a photorefractive crystal of barium titanate," Opt. Commun. 50, 146 (1984).
[CrossRef]

Opt. Lett. (6)

Phys. Rev. B (1)

M. Zgonik, P. Bernasconi, M. Duelli, P. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, "Dielectric, elastic, piezoelectric, electro-optic and elasto-optic, tensors of BaTiO3 crystals," Phys. Rev. B 50, 5941 (1994).
[CrossRef]

Other (2)

See, e.g., M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), Chap. 10. Note that the symbol for mutual coherence is often γ.

These mounts were provided by New Focus, Inc., 1275 Reamwood Avenue, Sunnyvale, Calif. 94089-2256.

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.


Figures (10)

Fig. 1
Fig. 1

Four different mutually pumped phase conjugators. The British and the bird-wing conjugators use internal reflections to guide the beams.

Fig. 2
Fig. 2

Two contributions to the phase-conjugate signal: the shared transmission grating deflects each input beam into the conjugate of the other beam, whereas the backscattering gratings deflect each input beam into its own phase conjugate. Backscattering gratings form only if the two input beams are at least partially mutually coherent.

Fig. 3
Fig. 3

Experimental setup. The piezoelectric pusher imparts a phase jitter to cause input beams 2 and 4 to be partially mutually incoherent, as measured by the linear photodiode array. The half-wave plate and the polarizer form a variable attenuator to equalize the powers of the two input beams at the crystal.

Fig. 4
Fig. 4

Measurement of the mutual coherence ν of the two input beams. (a) Interference fringes produced by two partially mutually coherent beams with a background offset subtracted. (b) No fringes produced by two completely incoherent beams, with the same offset subtracted. Division of trace (a) by trace (b) produces the sinusoidal fringe pattern (c), which in this case has a measured visibility ν = 0.54.

Fig. 5
Fig. 5

Behavior of the DPCM mutually pumped phase conjugator as we alter the mutual coherence of the input beams from mutually incoherent (ν = 0) to mutually coherent (ν = 1). The reflectivity data include contributions from both transmission and backscattering gratings, whereas the transmission data come only from the transmission grating. The solid curves are our theoretical fits to the two total reflectivities. The horizontal and the vertical bars on a few representative data points show the uncertainty in the measured coherence values and the fluctuations in the measured signals. Note that the DPCM conjugator turns off when the input beams become too coherent with each other.

Fig. 6
Fig. 6

Bird-wing conjugator. The symmetry of the beam paths inside the crystal ensures similar data for the two input beams. The fits are to the reflectivity data.

Fig. 7
Fig. 7

Bridge conjugator. The asymmetry shown in the reflectivities of the bridge conjugator is caused by the difference in the sign of the backscattering coupling strength for the two input beams. The fits are to the reflectivity data.

Fig. 8
Fig. 8

British I conjugator has a small loop in the crystal. The fits are to the reflectivity data.

Fig. 9
Fig. 9

British II conjugator has a larger loop in the crystal. The large signal fluctuations shown in these data were caused by a less stable optical setup. When we switched to a more stable setup the British conjugator was the least noisy of the four types of conjugator investigated. The fits are to the reflectivity data.

Fig. 10
Fig. 10

Amplitude two-beam coupling efficient γb for a beam and its counterpropagating beam as a function of the internal angle between the beam and the BaTiO3 crystal’s c axis. A positive coupling coefficient means that the beam is gaining energy from its counterpropagating beam. For example, a beam propagating between 6.7° and 90° to the +c axis is depleted by its counterpropagating beam. This calculation uses recent values for the electro-optic coefficients12 and assumes an effective charge-carrier density of N = 5 × 1016 cm−3 and e-polarized rays at λ = 514.5 nm.

Tables (2)

Tables Icon

Table 1 Ease-of-Use and Signal Fluctuations of the Mutually Pumped Phase Conjugators

Tables Icon

Table 2 Values of the Fitting Parametersa

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

backscatter reflectivity = ( total reflectivity ± transmission ) 2 ,
d A 1 d z = γ t A 1 A 4 * + A 2 * A 3 I 0 A 4 + γ r β 13 A 1 A 3 * + β 24 A 2 * A 4 I 0 A 3 + γ b β 12 A 1 A 2 * I 0 A 2 - α A 1 , d A 2 * d z = γ t A 1 A 4 * + A 2 * A 3 I 0 A 3 * + γ r β 13 A 1 A 3 * + β 24 A 2 * A 4 I 0 A 4 * + γ b β 12 A 1 A 2 * I 0 A 1 * + α A 2 * , d A 3 d z = γ t A 1 A 4 * + A 2 2 A 3 I 0 A 2 + γ r β 13 A 1 * A 3 + β 24 A 2 A 4 * I 0 A 1 - γ b β 34 A 3 A 4 * I 0 A 4 + α A 3 , d A 4 * d z = - γ t A 1 A 4 * + A 2 * A 3 I 0 A 1 * + γ r β 13 A 1 * A 3 + β 24 A 2 A 4 * I 0 A 2 * - γ b β 34 A 3 A 4 * I 0 A 3 - α A 4 * .
A 1 ( 0 ) = A 3 ( L ) = 0 , A 4 ( 0 ) 2 A 2 ( L ) 2 = q ,

Metrics