Abstract

Mutually pumped phase conjugators with picosecond pulse trains are experimentally demonstrated in rhodium-doped barium titanate. Stable phase-conjugate reflectivities are obtained when the counterpropagating pulses do not meet in the crystal. In contrast, when the pulses do meet in the crystal the reflectivities become unstable and unequal in value in two directions. This behavior is caused by the interference between two counterpropagating pulses. In addition, the reflectivities for the picosecond pulses are found to be half of those for continuous waves. The reasons for the small reflectivities of the pulses are discussed.

[Optical Society of America ]

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  1. M. Cronin-Golomb , B. Fisher , J. O. While , and A. Yariv , Theory and application of four-wave mixing in photorefractive media , IEEE J. Quantum Electron. IEJQA7 QE-20 , 12 ( 1984
    [CrossRef]
  2. S. Weiss , M. Segev , S. Sternklar , and B. Fischer , Photorefractive dynamic optical interconnets , Appl. Opt. APOPAI 27 , 3422 ( 1988
    [CrossRef] [PubMed]
  3. B. Fischer , S. Weiss , and S. Sternklar , Spatial light modulation and filtering effects in photorefractive wave mixing , Appl. Phys. Lett. APPLAB 50 , 483 ( 1987
    [CrossRef]
  4. T. Shimura , M. Tamura , and K. Kuroda , Injection locking and mode switching of a diode laser with a double phase-conjugate mirror , Opt. Lett. OPLEDP 18 , 1645 ( 1993
    [CrossRef] [PubMed]
  5. J. A. Giordmaine , P. M. Rentzepis , S. L. Shapiro , and K. W. Wecht , Two-photon excitation of fluorescence by picosecond light pulses , Appl. Phys. Lett. APPLAB 11 , 216 ( 1967
    [CrossRef]
  6. P. E. Ha nninen , S. W. Hell , J. Salo , E. Soini , and C. Cremer , Two-photon excitation 4Pi confocal microscope: enhanced axial resolution microscope for biological research , Appl. Phys. Lett. APPLAB 66 , 1698 ( 1995
    [CrossRef]
  7. T. Shimura , S. A. Boothroyd , J. Chrostowski , and P. Myslinski , Investigation of grating dynamics using a phase conjugate mirror , Opt. Commun. OPCOB8 101 , 124 ( 1993
    [CrossRef]
  8. G. C. Valley , Short-pulse grating formation in photorefractive materials , IEEE J. Quantum Electron. IEJQA7 QE-19 , 1637 ( 1983
    [CrossRef]
  9. X. S. Yao , V. Dominic , and J. Feinberg , Theory of beam coupling and pulse shaping of mode-locked laser pulses in a photorefractive crystal , J. Opt. Soc. Am. B JOBPDE 7 , 2347 ( 1990
    [CrossRef]
  10. N. Barry , L. Duffault , R. Troth , T. Tamos-Garcia , and M. J. Damzen , Comparison between continuous-wave and pulsed photorefraction in barium titanate , J. Opt. Soc. Am. B JOBPDE 11 , 1758 ( 1994
    [CrossRef]
  11. H. Ishii and Y. Tomita , Dynamics of space-charge fields created in photorefractive barium titanate by single picosecond pulses: a computer simulation , Opt. Commun. OPCOB8 126 , 95 ( 1996
    [CrossRef]
  12. H. Okamura , K. Takeuchi , T. Tanaka , and K. Kuroda , Grating formation with very short pulses in photorefractive materials: weak excitation limit , J. Opt. Soc. Am. B JOBPDE 14 , 2650 ( 1997
    [CrossRef]
  13. A. A. Zozulya , Fanning and photorefractive self-pumped four-wave mixing geometries , IEEE J. Quantum Electron. IEJQA7 29 , 538 ( 1993
    [CrossRef]
  14. B. Monson , G. J. Salamo , A. G. Mott , M. J. Miller , E. J. Sharp , W. W. Clark III , G. L. Wood , and R. R. Neurgaonkar , Self-pumped phase conjugation with nanosecond pulses in strontium barium niobate , Opt. Lett. OPLEDP 15 , 12 ( 1990
    [CrossRef] [PubMed]
  15. M. J. Damzen , N. P. Barry , and M. Buttinger , High-intensity effects in self-pumped photorefractive phase conjugation using nanosecond pulses , J. Mod. Opt. JMOPEW 42 , 2051 ( 1995
    [CrossRef]
  16. M. Cronin-Golomb , J. Paslaski , and A. Yariv , Vibration resistance, short coherence length operation, and mode-locked pumping in passive phase conjugate mirrors , Appl. Phys. Lett. APPLAB 47 , 1131 ( 1985
    [CrossRef]
  17. R. K. Jain and K. Stenersen , Picosecond pulse operation of a dye laser containing a phase-conjugate mirror , Opt. Lett. OPLEDP 9 , 546 ( 1984
    [CrossRef] [PubMed]
  18. H. F. Yau , P. J. Wang , E. Y. Pan , J. Chen , and J. Y. Chang , Self-pumped phase conjugation with picosecond and femtosecond pulses using BaTiO 3 , Opt. Commun. OPCOB8 135 , 331 ( 1997
    [CrossRef]
  19. J. Feinberg , Self-pumped, continuous-wave phase conjugator using internal reflection , Opt. Lett. OPLEDP 7 , 486 ( 1982
    [CrossRef] [PubMed]
  20. T. Y. Chang , Spatial-mode cleanup of a pulsed laser beam through mutually pumped phase conjugation with a cw reference , Opt. Lett. OPLEDP 45 , 1342 ( 1990
    [CrossRef]
  21. H. Wang , N. Yoshikawa , S. Yoshikado , and T. Aruga , Mutually pumped phase conjugator with a rainbow configuration in BaTiO 3 :Ce crystal using nanosecond pulses , Opt. Lett. OPLEDP 21 , 561 ( 1996
    [CrossRef] [PubMed]
  22. L. H. Acioli , M. Ulman , E. P. Ippen , J. G. Fujimoto , H. Kong , B. S. Chen , and M. Cronin-Golomb , Femtosecond temporal encoding in barium titanate , Opt. Lett. OPLEDP 16 , 1984 ( 1991
    [CrossRef] [PubMed]
  23. E. J. Sharp , W. W. Clark III , M. J. Miller , G. L. Wood , B. Monson , G. J. Salamo , and R. Neurgaonkar , Double phase conjugation in tungsten bronze crystals , Appl. Opt. APOPAI 29 , 743 ( 1990
    [CrossRef] [PubMed]
  24. M. D. Ewbank , Mechanism for photorefractive phase conjugation using incoherent beams , Opt. Lett. OPLEDP 13 , 47 ( 1988
    [CrossRef] [PubMed]
  25. A. Nakamura , T. Shimura , and K. Kuroda , Stabilization of an externally-pumped phase conjugator by the control of mean phases of incident beams , Opt. Commun. OPCOB8 135 , 337 ( 1997
    [CrossRef]
  26. S.-C. De La Cruz , S. MacCormack , J. Feinberg , Q. B. He , H.-K. Liu , and P. Yeh , Effect of beam coherence on mutually pumped phase conjugators , J. Opt. Soc. Am. B JOBPDE 12 , 1363 ( 1995
    [CrossRef]
  27. M. V. R. K. Murty , Modification of a Michelson interferometer using only one cube-corner prism , J. Opt. Soc. Am. JOSAAH 50 , 83 ( 1960
    [CrossRef]
  28. T. Omatsu , K. Kuroda , T. Shimura , K. Chihara , M. Itoh , and I. Ogura , Measurement of spatial coherence of a copper vapour laser beam using a reversal shear interferometer , Opt. Quantum Electron. OQELDI 23 , S477 ( 1991
    [CrossRef]

Buttinger, M

M. J. Damzen , N. P. Barry , and M. Buttinger , High-intensity effects in self-pumped photorefractive phase conjugation using nanosecond pulses , J. Mod. Opt. JMOPEW 42 , 2051 ( 1995
[CrossRef]

Chihara, K

T. Omatsu , K. Kuroda , T. Shimura , K. Chihara , M. Itoh , and I. Ogura , Measurement of spatial coherence of a copper vapour laser beam using a reversal shear interferometer , Opt. Quantum Electron. OQELDI 23 , S477 ( 1991
[CrossRef]

De La Cruz, S.-C

Pan, E. Y

H. F. Yau , P. J. Wang , E. Y. Pan , J. Chen , and J. Y. Chang , Self-pumped phase conjugation with picosecond and femtosecond pulses using BaTiO 3 , Opt. Commun. OPCOB8 135 , 331 ( 1997
[CrossRef]

Tamos-Garcia, T

Wang, P. J

H. F. Yau , P. J. Wang , E. Y. Pan , J. Chen , and J. Y. Chang , Self-pumped phase conjugation with picosecond and femtosecond pulses using BaTiO 3 , Opt. Commun. OPCOB8 135 , 331 ( 1997
[CrossRef]

While, J. O

M. Cronin-Golomb , B. Fisher , J. O. While , and A. Yariv , Theory and application of four-wave mixing in photorefractive media , IEEE J. Quantum Electron. IEJQA7 QE-20 , 12 ( 1984
[CrossRef]

Yau, H. F

H. F. Yau , P. J. Wang , E. Y. Pan , J. Chen , and J. Y. Chang , Self-pumped phase conjugation with picosecond and femtosecond pulses using BaTiO 3 , Opt. Commun. OPCOB8 135 , 331 ( 1997
[CrossRef]

Yoshikado, S

Yoshikawa, N

Other (28)

M. Cronin-Golomb , B. Fisher , J. O. While , and A. Yariv , Theory and application of four-wave mixing in photorefractive media , IEEE J. Quantum Electron. IEJQA7 QE-20 , 12 ( 1984
[CrossRef]

S. Weiss , M. Segev , S. Sternklar , and B. Fischer , Photorefractive dynamic optical interconnets , Appl. Opt. APOPAI 27 , 3422 ( 1988
[CrossRef] [PubMed]

B. Fischer , S. Weiss , and S. Sternklar , Spatial light modulation and filtering effects in photorefractive wave mixing , Appl. Phys. Lett. APPLAB 50 , 483 ( 1987
[CrossRef]

T. Shimura , M. Tamura , and K. Kuroda , Injection locking and mode switching of a diode laser with a double phase-conjugate mirror , Opt. Lett. OPLEDP 18 , 1645 ( 1993
[CrossRef] [PubMed]

J. A. Giordmaine , P. M. Rentzepis , S. L. Shapiro , and K. W. Wecht , Two-photon excitation of fluorescence by picosecond light pulses , Appl. Phys. Lett. APPLAB 11 , 216 ( 1967
[CrossRef]

P. E. Ha nninen , S. W. Hell , J. Salo , E. Soini , and C. Cremer , Two-photon excitation 4Pi confocal microscope: enhanced axial resolution microscope for biological research , Appl. Phys. Lett. APPLAB 66 , 1698 ( 1995
[CrossRef]

T. Shimura , S. A. Boothroyd , J. Chrostowski , and P. Myslinski , Investigation of grating dynamics using a phase conjugate mirror , Opt. Commun. OPCOB8 101 , 124 ( 1993
[CrossRef]

G. C. Valley , Short-pulse grating formation in photorefractive materials , IEEE J. Quantum Electron. IEJQA7 QE-19 , 1637 ( 1983
[CrossRef]

X. S. Yao , V. Dominic , and J. Feinberg , Theory of beam coupling and pulse shaping of mode-locked laser pulses in a photorefractive crystal , J. Opt. Soc. Am. B JOBPDE 7 , 2347 ( 1990
[CrossRef]

N. Barry , L. Duffault , R. Troth , T. Tamos-Garcia , and M. J. Damzen , Comparison between continuous-wave and pulsed photorefraction in barium titanate , J. Opt. Soc. Am. B JOBPDE 11 , 1758 ( 1994
[CrossRef]

H. Ishii and Y. Tomita , Dynamics of space-charge fields created in photorefractive barium titanate by single picosecond pulses: a computer simulation , Opt. Commun. OPCOB8 126 , 95 ( 1996
[CrossRef]

H. Okamura , K. Takeuchi , T. Tanaka , and K. Kuroda , Grating formation with very short pulses in photorefractive materials: weak excitation limit , J. Opt. Soc. Am. B JOBPDE 14 , 2650 ( 1997
[CrossRef]

A. A. Zozulya , Fanning and photorefractive self-pumped four-wave mixing geometries , IEEE J. Quantum Electron. IEJQA7 29 , 538 ( 1993
[CrossRef]

B. Monson , G. J. Salamo , A. G. Mott , M. J. Miller , E. J. Sharp , W. W. Clark III , G. L. Wood , and R. R. Neurgaonkar , Self-pumped phase conjugation with nanosecond pulses in strontium barium niobate , Opt. Lett. OPLEDP 15 , 12 ( 1990
[CrossRef] [PubMed]

M. J. Damzen , N. P. Barry , and M. Buttinger , High-intensity effects in self-pumped photorefractive phase conjugation using nanosecond pulses , J. Mod. Opt. JMOPEW 42 , 2051 ( 1995
[CrossRef]

M. Cronin-Golomb , J. Paslaski , and A. Yariv , Vibration resistance, short coherence length operation, and mode-locked pumping in passive phase conjugate mirrors , Appl. Phys. Lett. APPLAB 47 , 1131 ( 1985
[CrossRef]

R. K. Jain and K. Stenersen , Picosecond pulse operation of a dye laser containing a phase-conjugate mirror , Opt. Lett. OPLEDP 9 , 546 ( 1984
[CrossRef] [PubMed]

H. F. Yau , P. J. Wang , E. Y. Pan , J. Chen , and J. Y. Chang , Self-pumped phase conjugation with picosecond and femtosecond pulses using BaTiO 3 , Opt. Commun. OPCOB8 135 , 331 ( 1997
[CrossRef]

J. Feinberg , Self-pumped, continuous-wave phase conjugator using internal reflection , Opt. Lett. OPLEDP 7 , 486 ( 1982
[CrossRef] [PubMed]

T. Y. Chang , Spatial-mode cleanup of a pulsed laser beam through mutually pumped phase conjugation with a cw reference , Opt. Lett. OPLEDP 45 , 1342 ( 1990
[CrossRef]

H. Wang , N. Yoshikawa , S. Yoshikado , and T. Aruga , Mutually pumped phase conjugator with a rainbow configuration in BaTiO 3 :Ce crystal using nanosecond pulses , Opt. Lett. OPLEDP 21 , 561 ( 1996
[CrossRef] [PubMed]

L. H. Acioli , M. Ulman , E. P. Ippen , J. G. Fujimoto , H. Kong , B. S. Chen , and M. Cronin-Golomb , Femtosecond temporal encoding in barium titanate , Opt. Lett. OPLEDP 16 , 1984 ( 1991
[CrossRef] [PubMed]

E. J. Sharp , W. W. Clark III , M. J. Miller , G. L. Wood , B. Monson , G. J. Salamo , and R. Neurgaonkar , Double phase conjugation in tungsten bronze crystals , Appl. Opt. APOPAI 29 , 743 ( 1990
[CrossRef] [PubMed]

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

A. Nakamura , T. Shimura , and K. Kuroda , Stabilization of an externally-pumped phase conjugator by the control of mean phases of incident beams , Opt. Commun. OPCOB8 135 , 337 ( 1997
[CrossRef]

S.-C. De La Cruz , S. MacCormack , J. Feinberg , Q. B. He , H.-K. Liu , and P. Yeh , Effect of beam coherence on mutually pumped phase conjugators , J. Opt. Soc. Am. B JOBPDE 12 , 1363 ( 1995
[CrossRef]

M. V. R. K. Murty , Modification of a Michelson interferometer using only one cube-corner prism , J. Opt. Soc. Am. JOSAAH 50 , 83 ( 1960
[CrossRef]

T. Omatsu , K. Kuroda , T. Shimura , K. Chihara , M. Itoh , and I. Ogura , Measurement of spatial coherence of a copper vapour laser beam using a reversal shear interferometer , Opt. Quantum Electron. OQELDI 23 , S477 ( 1991
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Experimental setups of (a) the bridge phase conjugator and (b) the bird-wing phase conjugator: BS, beam splitter; M’s, mirrors; D’s, photodetectors; HWP, half-wave plate; RS, resettable stage; PZT, piezoelectric transducer; NDF, neutral-density filter; other abbreviations defined in text. (c) Top-view photograph of the typical beam path in the bridge conjugator for pulse operation.

Fig. 2
Fig. 2

Measured reflectivity versus path-length difference between two input pulses (a) in the bridge conjugator and (b) in the bird-wing conjugator: reflectivities, R1=I1*/I1 and R2=I2*/I2. The path-length difference corresponds to the delay of input pulse 2 from input pulse 1.

Fig. 3
Fig. 3

Measured reflectivity versus path-length difference plotted in a small range near zero (a) in the bridge conjugator and (b) in the bird-wing conjugator.

Fig. 4
Fig. 4

Measured reflectivity versus path-length difference when the two input pulses are mutually incoherent (a) in the bridge conjugator and (b) in the bird-wing conjugator.

Fig. 5
Fig. 5

Gratings that contribute to the phase-conjugate signals (a) in the bridge conjugator and (b) in the bird-wing conjugator. The shared transmission grating diffracts each input beam into the phase conjugate wave of the other beam, whereas the 2k grating diffracts each input beam into its own phase-conjugate wave. 2k gratings are formed only where the counterpropagating pulses meet.

Fig. 6
Fig. 6

Measured reflectivity versus input power in the bridge conjugator (a) for pulse operation and (b) for cw operation.

Fig. 7
Fig. 7

Photographs of the projected patterns of the fanning beams when a single beam is input (a) for pulse operation and (b) for cw operation. (c) Arrangement of the input beam, the crystal, and the projected screen.

Fig. 8
Fig. 8

Simple model illustrating how the temporal coherence affects beam fanning and the phase-conjugate reflectivities: θ, propagating direction of the diffracted beam; w, beam diameter; lc, temporal coherence; L, interaction length of the diffracted light. If the temporal coherence of the beam is low, the grating modulation will be low and L will be short.

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