Abstract

Mutually pumped phase conjugation with a recording time of few milliseconds is obtained in Bi12TiO20 crystals by use of transient photorefractive beam coupling under a dc external electric field. It is demonstrated that the additional acceleration of the positive-feedback-loop formation is required for successful generation of transient phase-conjugate wave fronts. This acceleration is provided by the high-intensity transient photorefractive surface wave that appears immediately after application of the external electric field as the result of coupling of the incident beam with the reflected fanning beams. To the authors’ knowledge, this is the first experimental observation of a transient photorefractive surface wave.

[Optical Society of America ]

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References

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  1. M. Cronin-Golomb , A. Yariv , and I. Ury , Coherent coupling of diode lasers by phase conjugation , Appl. Phys. Lett. APPLAB 48 , 1240 1242 ( 1986
    [CrossRef]
  2. M. D. Ewbank , Mechanism of photorefractive phase-conjugation using incoherent beams , Opt. Lett. OPLEDP 13 , 47 49 ( 1988
    [CrossRef] [PubMed]
  3. S. Sternklar , S. Weiss , M. Segev , and B. Fischer , Beam coupling and locking of lasers using photorefractive four-wave mixing , Opt. Lett. OPLEDP 11 , 528 530 ( 1986
    [CrossRef] [PubMed]
  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 1647 ( 1993
    [CrossRef] [PubMed]
  5. P. Delaye , A. Blouin , D. Drolet , and J.-P. Monchalin , Heterodyne detection of ultrasound from rough surfaces using a double phase conjugate mirror , Appl. Phys. Lett. APPLAB 67 , 3251 3253 ( 1995
    [CrossRef]
  6. V. V. Voronov , I. R. Dorosh , Y. S. Kuzminov , and N. V. Tkachenko , Photoinduced light scattering in cerium-doped barium strontium niobate crystals , Sov. J. Quantum Electron. SJQEAF 10 , 1346 1349 ( 1980
    [CrossRef]
  7. D. L. Staebler and J. J. Amodey , Coupled-wave analysis of holographic storage in LiNbO 3 , J. Appl. Phys. JAPIAU 43 , 1042 1049 ( 1972
    [CrossRef]
  8. S. I. Stepanov and M. P. Petrov , Efficient unstationary holographic recording in photorefractive crystals under an ex-ternal alternating electric field , Opt. Commun. OPCOB8 53 , 292 295 ( 1985
    [CrossRef]
  9. N. V. Kukhtarev , V. B. Markov , and S. G. Odulov , Transient energy transfer during hologram formation in LiNbO 3 in external electric field , Opt. Commun. OPCOB8 23 , 338 343 ( 1977
    [CrossRef]
  10. J. M. Heaton and L. Solymar , Transient effects during dynamic hologram formation in BSO crystals: theory and experiment , IEEE J. Quantum Electron. IEJQA7 24 , 558 567 ( 1988
    [CrossRef]
  11. E. Raita , A. A. Kamshilin , V. V. Prokofiev , and T. Jaaskelainen , Fast mutually pumped phase conjugation using transient photorefractive coupling , Appl. Phys. Lett. APPLAB 70 , 1641 1643 ( 1997
    [CrossRef]
  12. N. V. Kukhtarev , V. B. Markov , S. G. Odulov , M. S. Soskin , and V. L. Vinetskii , Holographic storage in electrooptic crystals. I. Steady state , Ferroelectrics FEROA8 22 , 949 960 ( 1979
    [CrossRef]
  13. F. Vachss , Frequency-dependent photorefractive response in the presence of applied ac electric fields , J. Opt. Soc. Am. B JOBPDE 11 , 1045 1058 ( 1994
    [CrossRef]
  14. H. Tuovinen , A. A. Kamshilin , and T. Jaaskelainen , Asymmetry of two-wave coupling in cubic photorefractive crystals , J. Opt. Soc. Am. B JOBPDE 14 , 3383 3392 ( 1997
    [CrossRef]
  15. S. I. Stepanov , S. M. Shandarov , and N. D. Hat kov , Photoelastic contribution to the photorefractive effect in cubic crystals , Sov. Phys. Solid State SPSSA7 29 , 1754 1756 ( 1987
  16. J. E. Millerd , E. M. Garmire , M. B. Klein , B. A. Wechsler , F. P. Strohkendl , and G. A. Brost , Photorefractive response at high modulation depths in Bi 12 TiO 20 , J. Opt. Soc. Am. B JOBPDE 9 , 1449 1453 ( 1992
    [CrossRef]
  17. N. V. Kukhtarev , V. B. Markov , S. G. Odulov , M. S. Soskin , and V. L. Vinetskii , Holographic storage in electro-optic crystals. II. Beam coupling light amplification , Ferroelectrics FEROA8 22 , 961 964 ( 1979
    [CrossRef]
  18. A. A. Kamshilin , E. Raita , V. V. Prokofiev , and T. Jaaskelainen , Nonlinear self-channeling of a laser beam at the surface of a photorefractive fiber , Appl. Phys. Lett. APPLAB 67 , 3242 3244 ( 1995
    [CrossRef]
  19. A. A. Kamshilin , H. Tuovinen , V. V. Prokofiev , and T. Jaaskelainen , Coupling of mutually incoherent beams in photorefractive Bi 12 TiO 20 fiber , Opt. Commun. OPCOB8 109 , 312 317 ( 1994
    [CrossRef]
  20. Q. B. He , P. Yeh , C. Gu , and R. R. Neurgaonkar , Multigrating competition effects in photorefractive mutually pumped phase conjugation , J. Opt. Soc. Am. B JOBPDE 9 , 114 120 ( 1992
    [CrossRef]
  21. A. A. Kamshilin , E. Raita , and A. V. Khomenko , Intensity redistribution in a thin photorefractive crystal caused by strong fanning effect and internal reflections , J. Opt. Soc. Am. B JOBPDE 13 , 2536 2543 ( 1996
    [CrossRef]
  22. G. S. Garcia-Quirino , J. J. Sanchez-Mondragon , and S. I. Stepanov , Nonlinear surface optical waves in photorefractive crystals with a diffusion mechanism of nonlinearity , Phys. Rev. A PLRAAN 51 , 1571 1577 ( 1995
    [CrossRef] [PubMed]
  23. M. Cronin-Golomb , Photorefractive surface waves , Opt. Lett. OPLEDP 20 , 2075 2077 ( 1995
    [CrossRef] [PubMed]
  24. A. V. Khomenko , A. Garcia-Weidner , and A. A. Kamshilin , Amplification of optical signals in Bi 12 TiO 20 crystal by photorefractive surface waves , Opt. Lett. OPLEDP 21 , 1014 1016 ( 1996
    [CrossRef] [PubMed]

Hatkov, N. D

S. I. Stepanov , S. M. Shandarov , and N. D. Hat kov , Photoelastic contribution to the photorefractive effect in cubic crystals , Sov. Phys. Solid State SPSSA7 29 , 1754 1756 ( 1987

Monchalin, J.-P

P. Delaye , A. Blouin , D. Drolet , and J.-P. Monchalin , Heterodyne detection of ultrasound from rough surfaces using a double phase conjugate mirror , Appl. Phys. Lett. APPLAB 67 , 3251 3253 ( 1995
[CrossRef]

Other (24)

P. Delaye , A. Blouin , D. Drolet , and J.-P. Monchalin , Heterodyne detection of ultrasound from rough surfaces using a double phase conjugate mirror , Appl. Phys. Lett. APPLAB 67 , 3251 3253 ( 1995
[CrossRef]

V. V. Voronov , I. R. Dorosh , Y. S. Kuzminov , and N. V. Tkachenko , Photoinduced light scattering in cerium-doped barium strontium niobate crystals , Sov. J. Quantum Electron. SJQEAF 10 , 1346 1349 ( 1980
[CrossRef]

D. L. Staebler and J. J. Amodey , Coupled-wave analysis of holographic storage in LiNbO 3 , J. Appl. Phys. JAPIAU 43 , 1042 1049 ( 1972
[CrossRef]

S. I. Stepanov and M. P. Petrov , Efficient unstationary holographic recording in photorefractive crystals under an ex-ternal alternating electric field , Opt. Commun. OPCOB8 53 , 292 295 ( 1985
[CrossRef]

N. V. Kukhtarev , V. B. Markov , and S. G. Odulov , Transient energy transfer during hologram formation in LiNbO 3 in external electric field , Opt. Commun. OPCOB8 23 , 338 343 ( 1977
[CrossRef]

J. M. Heaton and L. Solymar , Transient effects during dynamic hologram formation in BSO crystals: theory and experiment , IEEE J. Quantum Electron. IEJQA7 24 , 558 567 ( 1988
[CrossRef]

E. Raita , A. A. Kamshilin , V. V. Prokofiev , and T. Jaaskelainen , Fast mutually pumped phase conjugation using transient photorefractive coupling , Appl. Phys. Lett. APPLAB 70 , 1641 1643 ( 1997
[CrossRef]

N. V. Kukhtarev , V. B. Markov , S. G. Odulov , M. S. Soskin , and V. L. Vinetskii , Holographic storage in electrooptic crystals. I. Steady state , Ferroelectrics FEROA8 22 , 949 960 ( 1979
[CrossRef]

M. Cronin-Golomb , A. Yariv , and I. Ury , Coherent coupling of diode lasers by phase conjugation , Appl. Phys. Lett. APPLAB 48 , 1240 1242 ( 1986
[CrossRef]

N. V. Kukhtarev , V. B. Markov , S. G. Odulov , M. S. Soskin , and V. L. Vinetskii , Holographic storage in electro-optic crystals. II. Beam coupling light amplification , Ferroelectrics FEROA8 22 , 961 964 ( 1979
[CrossRef]

A. A. Kamshilin , E. Raita , V. V. Prokofiev , and T. Jaaskelainen , Nonlinear self-channeling of a laser beam at the surface of a photorefractive fiber , Appl. Phys. Lett. APPLAB 67 , 3242 3244 ( 1995
[CrossRef]

A. A. Kamshilin , H. Tuovinen , V. V. Prokofiev , and T. Jaaskelainen , Coupling of mutually incoherent beams in photorefractive Bi 12 TiO 20 fiber , Opt. Commun. OPCOB8 109 , 312 317 ( 1994
[CrossRef]

S. I. Stepanov , S. M. Shandarov , and N. D. Hat kov , Photoelastic contribution to the photorefractive effect in cubic crystals , Sov. Phys. Solid State SPSSA7 29 , 1754 1756 ( 1987

G. S. Garcia-Quirino , J. J. Sanchez-Mondragon , and S. I. Stepanov , Nonlinear surface optical waves in photorefractive crystals with a diffusion mechanism of nonlinearity , Phys. Rev. A PLRAAN 51 , 1571 1577 ( 1995
[CrossRef] [PubMed]

Q. B. He , P. Yeh , C. Gu , and R. R. Neurgaonkar , Multigrating competition effects in photorefractive mutually pumped phase conjugation , J. Opt. Soc. Am. B JOBPDE 9 , 114 120 ( 1992
[CrossRef]

J. E. Millerd , E. M. Garmire , M. B. Klein , B. A. Wechsler , F. P. Strohkendl , and G. A. Brost , Photorefractive response at high modulation depths in Bi 12 TiO 20 , J. Opt. Soc. Am. B JOBPDE 9 , 1449 1453 ( 1992
[CrossRef]

F. Vachss , Frequency-dependent photorefractive response in the presence of applied ac electric fields , J. Opt. Soc. Am. B JOBPDE 11 , 1045 1058 ( 1994
[CrossRef]

S. Sternklar , S. Weiss , M. Segev , and B. Fischer , Beam coupling and locking of lasers using photorefractive four-wave mixing , Opt. Lett. OPLEDP 11 , 528 530 ( 1986
[CrossRef] [PubMed]

M. D. Ewbank , Mechanism of photorefractive phase-conjugation using incoherent beams , Opt. Lett. OPLEDP 13 , 47 49 ( 1988
[CrossRef] [PubMed]

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 1647 ( 1993
[CrossRef] [PubMed]

A. A. Kamshilin , E. Raita , and A. V. Khomenko , Intensity redistribution in a thin photorefractive crystal caused by strong fanning effect and internal reflections , J. Opt. Soc. Am. B JOBPDE 13 , 2536 2543 ( 1996
[CrossRef]

M. Cronin-Golomb , Photorefractive surface waves , Opt. Lett. OPLEDP 20 , 2075 2077 ( 1995
[CrossRef] [PubMed]

H. Tuovinen , A. A. Kamshilin , and T. Jaaskelainen , Asymmetry of two-wave coupling in cubic photorefractive crystals , J. Opt. Soc. Am. B JOBPDE 14 , 3383 3392 ( 1997
[CrossRef]

A. V. Khomenko , A. Garcia-Weidner , and A. A. Kamshilin , Amplification of optical signals in Bi 12 TiO 20 crystal by photorefractive surface waves , Opt. Lett. OPLEDP 21 , 1014 1016 ( 1996
[CrossRef] [PubMed]

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Figures (10)

Fig. 1
Fig. 1

Calculated evolution of the beam-coupling gain factor during hologram formation for three values of the spatial frequency of a holographic grating: (a) 55 lines/mm, (b) 147 lines/mm, and (c) 220 lines/mm. These spatial frequencies correspond to angles between interacting beams of 2°, 5°, and 8°, respectively. The following material parameters were used for the calculations: NA=2×1016 cm-3, ND=1019 cm-3, μ=0.66×10-2 cm2/V s, and γ=3.5×10-11 cm3/s.The pump-beam intensity was 1.3 W/cm2.

Fig. 2
Fig. 2

Experimental geometry of the fiberlike BTO crystal and the typical steady-state fanning pattern emerging in the far field of the crystal. A horizontally polarized pump beam of the red He–Ne laser (λ=632.8 nm) is launched into the sample to propagate along the 〈110〉 axis. The vector of the external electric field is parallel to the 〈1̅11〉 axis. The white arrows show three angular positions of the photodetector in the experiment.

Fig. 3
Fig. 3

Temporal evolution of the transient amplification gain for three spatial frequencies, (a) 55 lines/mm, (b) 147 lines/mm, and (c) 220 lines/mm, corresponding to scattering angles of 2°, 5°, and 8°, respectively. Curves were measured after the rising front of a dc electric field with a 35-kV/cm amplitude was applied to the crystal. The pump-beam intensity was 2.25 W/cm2.

Fig. 4
Fig. 4

Angular distribution of the coupling gain at three moments of time during the process of fanning pattern formation. To show the transition of the amplification maximum in time, the angular distribution of the amplification gain was measured at (a) 8 ms, (b) 35 ms, and (c) 500 ms after application of the rising front of a dc electric field with an amplitude of 35 kV/cm.

Fig. 5
Fig. 5

Experimental setup for (a) conventional steady-state MPPC and for (b) novel transient MPPC. Horizontally polarized pump beams P1 and P2 are derived from the independent He–Ne lasers. PC1 and PC2 are the phase-conjugate responses. The angle between the incident pump beams is determined by the angular position of the steady-state fanning maximum in the case of steady-state MPPC. Transient MPPC is constructed such that the angle between pump beams is equal to 2°, corresponding to a spatial frequency of 55 lines/mm.

Fig. 6
Fig. 6

CCD-camera image of the transient phase-conjugate response. The phase-conjugate output is accompanied by a specific ring that is the result of the degeneration of Bragg-diffraction conditions when the plane-wave-front beams are used to pump a photorefractive phase conjugator.

Fig. 7
Fig. 7

Temporal evolution of the phase-conjugate response of (a) transient MPPC and of (b), (c) two fanning gratings involved in the MPPC process. Fanning-response curves are measured independently of each other when the crystal is illuminated by only one pump beam.

Fig. 8
Fig. 8

Response time of the transient phase conjugator as a function of the amplitude of the applied dc electric field. A BTO crystal is illuminated by two independent He–Ne laser beams with a total intensity of 2×2.25 W/cm2.

Fig. 9
Fig. 9

CCD-camera images showing the intensity redistribution at the output face of the fiberlike BTO crystal after the application of an external dc electric field. (a) Initial situation when no external electric field is applied. (b) Transient situation immediately after application of the rising front of a dc electric field with an amplitude of 35 kV/cm, demonstrating the effect of light-intensity self-channeling into a transient photorefractive surface wave that appears near the left-hand-side surface of the crystal. The steady-state situation with the dc electric field applied is shown in (c).

Fig. 10
Fig. 10

Intensity distribution across the output face of the crystal in the steady state with the dc electric field applied (lighter curve) and in the transient case immediately after the dc field has been switched on (heavier curve). The channel of the increased intensity corresponding to the transient photorefractive surface waves is clearly distinguished near the left-hand-side surface of the crystal.  

Equations (5)

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dE1dt+1-iEA/EQ1-iEA/EM E1τM=-EAτM(1-iEA/EM).
EAE0+iED,
EMγNAμKG,
EQeNA(ND-NA)0KGND,
EDKGkBTe.

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