Abstract

The spontaneous appearance of hexagon patterns in photorefractive crystals is treated as mirrorless coherent four-wave mixing oscillation. It is shown experimentally that the system has a well-defined coupling-strength threshold and behaves as other coherent optical oscillators near the threshold. A simple relation for the angle of the hexagon sideband as a function of the distance between the end mirror and the sample is derived and verified experimentally.

[Optical Society of America ]

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. T. Honda , Hexagonal pattern formation due to counterpropagation in KNbO 3 , Opt. Lett. OPLEDP 18 , 598 560 ( 1993
    [CrossRef]
  2. P. B. Banerjee , H.-L. Yu , D. A. Gregory , N. Kukhtarev , and H. J. Caulfield , Self-organization of scattering in photorefractive KNbO 3 into a reconfigurable hexagonal spot array , Opt. Lett. OPLEDP 20 , 10 12 ( 1995
    [CrossRef] [PubMed]
  3. T. Honda , Flow and controlled rotation of the spontaneous optical hexagons in KNbO 3 , Opt. Lett. OPLEDP 20 , 851 853 ( 1995
    [CrossRef] [PubMed]
  4. T. Honda and H. Matsumoto , Buildup of spontaneous hexagonal patterns in photorefractive BaTiO 3 with a feedback mirror , Opt. Lett. OPLEDP 20 , 1755 1757 ( 1995
    [CrossRef]
  5. N. Kukhtarev , N. Kukhtareva , H. J. Caulfield , P. B. Banerjee , H.-L. Yu , and L. Hesselink , Broadband dynamic, holographically selfrecorded, and static hexagonal scattering patterns in photorefractive KNbO 3 :Fe , Opt. Eng. OPEGAR 34 , 2261 2265 ( 1995
    [CrossRef]
  6. T. Honda , H. Matsumoto , M. Sedlatschek , C. Denz , and T. Tschudi , Spontaneous formation of hexagons, squares and squeezed hexagons in a photorefractive phase conjugator with virtually internal feedback mirror , Opt. Commun. OPCOB8 133 , 293 299 ( 1997
    [CrossRef]
  7. A. Mamaev and M. Saffman , Modulation instability and pattern formation in the field of noncollinear pump waves , Opt. Lett. OPLEDP 22 , 283 285 ( 1997
    [CrossRef] [PubMed]
  8. M. Saffman , A. A. Zozulya , and D. Anderson , Transverse instability of energy-exchanging counterpropagating waves in photorefractive media , J. Opt. Soc. Am. B JOBPDE 11 , 1409 1417 ( 1994
    [CrossRef]
  9. B. Sturman and A. Chernykh , Mechanism of transverse instability of counterpropagation in photorefractive media , J. Opt. Soc. Am. B JOBPDE 12 , 1384 1386 ( 1995
    [CrossRef]
  10. T. Honda and P. B. Banerjee , Threshold for spontaneous pattern formation in reflection-grating dominated photorefractive media with mirror feedback , Opt. Lett. OPLEDP 21 , 779 781 ( 1996
    [CrossRef] [PubMed]
  11. A. Chernykh , B. Sturman , M. Aguilar , and F. Agullo-Lopez , Threshold for pattern formation in a medium with a local photorefractive response , J. Opt. Soc. Am. B JOPBDE 14 , 1754 1760 ( 1997
    [CrossRef]
  12. A. Yariv and D. Pepper , Amplified reflection, phase conjugation, and oscillation in degenerate four-wave mixing , Opt. Lett. OPLEDP 1 , 16 18 ( 1977
    [CrossRef] [PubMed]
  13. 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. IEJQA7 QE-20 , 12 30 ( 1984
    [CrossRef]
  14. S. Odoulov , B. Sturman , and M. Goulkov , Parametric four-wave processes in photorefractive crystals , Phys. Rep. PRPLCM 275 , 197 254 ( 1997
  15. V. Lemeshko and V. Obukhovski , Autowaves of photoinduced light scattering , Sov. Tech. Phys. Lett. STPLD2 11 , 573 574 ( 1985
  16. V. Bazenov , S. Lyuksyutov , R. Jungen , S. Odoulov , and M. Soskin , in Amplitude and Intensity Spatial Interferometry , J. Breckinridge, ed. , Copper-vapour laser with adaptive holographic mirror based on photorefractive crystal , Proc. SPIE PSISDG 1237 , 48 53 ( 1990
    [CrossRef]
  17. G. Grynberg , A. Maistre , and A. Petrossian , Flowerlike patterns generated by a laser beam transmitted through a rubidium cell with single feedback mirror , Phys. Rev. Lett. PRLTAO 72 , 2379 2382 ( 1994
    [CrossRef] [PubMed]
  18. T. Ackemann , Yu. A. Logvin , A. Heuer , and W. Lange , Transitions between positive and negative hexagons in optical pattern formation , Phys. Rev. Lett. PRLTAO 75 , 3450 3454 ( 1995
    [CrossRef] [PubMed]
  19. M. Goulkov , S. Odoulov , and R. Trott , Dynamics of coherent oscillation in photorrefractive oscillator with BaTiO 3 , Ukr. Fiz. Zh. UFIZAW 36 , 402 406 ( 1991
  20. A. Zozulya , Fanning and photorefractive self-pumped four-wave mixing geometries , IEEE J. Quantum Electron. IEJQA7 29 , 538 555 ( 1993
    [CrossRef]
  21. D. Engin , S. Orlov , M. Segev , G. Valley , and A. Yariv , Order-disorder phase transition and critical slowing down in photorefractive self-oscillators , Phys. Rev. Lett. PRLTAO 74 , 1743 1746 ( 1995
    [CrossRef] [PubMed]

Banerjee, P. B

Kukhtareva, N

N. Kukhtarev , N. Kukhtareva , H. J. Caulfield , P. B. Banerjee , H.-L. Yu , and L. Hesselink , Broadband dynamic, holographically selfrecorded, and static hexagonal scattering patterns in photorefractive KNbO 3 :Fe , Opt. Eng. OPEGAR 34 , 2261 2265 ( 1995
[CrossRef]

Lemeshko, V

V. Lemeshko and V. Obukhovski , Autowaves of photoinduced light scattering , Sov. Tech. Phys. Lett. STPLD2 11 , 573 574 ( 1985

Maistre, A

G. Grynberg , A. Maistre , and A. Petrossian , Flowerlike patterns generated by a laser beam transmitted through a rubidium cell with single feedback mirror , Phys. Rev. Lett. PRLTAO 72 , 2379 2382 ( 1994
[CrossRef] [PubMed]

Obukhovski, V

V. Lemeshko and V. Obukhovski , Autowaves of photoinduced light scattering , Sov. Tech. Phys. Lett. STPLD2 11 , 573 574 ( 1985

Trott, R

M. Goulkov , S. Odoulov , and R. Trott , Dynamics of coherent oscillation in photorrefractive oscillator with BaTiO 3 , Ukr. Fiz. Zh. UFIZAW 36 , 402 406 ( 1991

Other (21)

T. Honda , Hexagonal pattern formation due to counterpropagation in KNbO 3 , Opt. Lett. OPLEDP 18 , 598 560 ( 1993
[CrossRef]

P. B. Banerjee , H.-L. Yu , D. A. Gregory , N. Kukhtarev , and H. J. Caulfield , Self-organization of scattering in photorefractive KNbO 3 into a reconfigurable hexagonal spot array , Opt. Lett. OPLEDP 20 , 10 12 ( 1995
[CrossRef] [PubMed]

T. Honda , Flow and controlled rotation of the spontaneous optical hexagons in KNbO 3 , Opt. Lett. OPLEDP 20 , 851 853 ( 1995
[CrossRef] [PubMed]

T. Honda and H. Matsumoto , Buildup of spontaneous hexagonal patterns in photorefractive BaTiO 3 with a feedback mirror , Opt. Lett. OPLEDP 20 , 1755 1757 ( 1995
[CrossRef]

N. Kukhtarev , N. Kukhtareva , H. J. Caulfield , P. B. Banerjee , H.-L. Yu , and L. Hesselink , Broadband dynamic, holographically selfrecorded, and static hexagonal scattering patterns in photorefractive KNbO 3 :Fe , Opt. Eng. OPEGAR 34 , 2261 2265 ( 1995
[CrossRef]

T. Honda , H. Matsumoto , M. Sedlatschek , C. Denz , and T. Tschudi , Spontaneous formation of hexagons, squares and squeezed hexagons in a photorefractive phase conjugator with virtually internal feedback mirror , Opt. Commun. OPCOB8 133 , 293 299 ( 1997
[CrossRef]

A. Mamaev and M. Saffman , Modulation instability and pattern formation in the field of noncollinear pump waves , Opt. Lett. OPLEDP 22 , 283 285 ( 1997
[CrossRef] [PubMed]

M. Saffman , A. A. Zozulya , and D. Anderson , Transverse instability of energy-exchanging counterpropagating waves in photorefractive media , J. Opt. Soc. Am. B JOBPDE 11 , 1409 1417 ( 1994
[CrossRef]

B. Sturman and A. Chernykh , Mechanism of transverse instability of counterpropagation in photorefractive media , J. Opt. Soc. Am. B JOBPDE 12 , 1384 1386 ( 1995
[CrossRef]

T. Honda and P. B. Banerjee , Threshold for spontaneous pattern formation in reflection-grating dominated photorefractive media with mirror feedback , Opt. Lett. OPLEDP 21 , 779 781 ( 1996
[CrossRef] [PubMed]

A. Chernykh , B. Sturman , M. Aguilar , and F. Agullo-Lopez , Threshold for pattern formation in a medium with a local photorefractive response , J. Opt. Soc. Am. B JOPBDE 14 , 1754 1760 ( 1997
[CrossRef]

A. Yariv and D. Pepper , Amplified reflection, phase conjugation, and oscillation in degenerate four-wave mixing , Opt. Lett. OPLEDP 1 , 16 18 ( 1977
[CrossRef] [PubMed]

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. IEJQA7 QE-20 , 12 30 ( 1984
[CrossRef]

S. Odoulov , B. Sturman , and M. Goulkov , Parametric four-wave processes in photorefractive crystals , Phys. Rep. PRPLCM 275 , 197 254 ( 1997

V. Lemeshko and V. Obukhovski , Autowaves of photoinduced light scattering , Sov. Tech. Phys. Lett. STPLD2 11 , 573 574 ( 1985

V. Bazenov , S. Lyuksyutov , R. Jungen , S. Odoulov , and M. Soskin , in Amplitude and Intensity Spatial Interferometry , J. Breckinridge, ed. , Copper-vapour laser with adaptive holographic mirror based on photorefractive crystal , Proc. SPIE PSISDG 1237 , 48 53 ( 1990
[CrossRef]

G. Grynberg , A. Maistre , and A. Petrossian , Flowerlike patterns generated by a laser beam transmitted through a rubidium cell with single feedback mirror , Phys. Rev. Lett. PRLTAO 72 , 2379 2382 ( 1994
[CrossRef] [PubMed]

T. Ackemann , Yu. A. Logvin , A. Heuer , and W. Lange , Transitions between positive and negative hexagons in optical pattern formation , Phys. Rev. Lett. PRLTAO 75 , 3450 3454 ( 1995
[CrossRef] [PubMed]

M. Goulkov , S. Odoulov , and R. Trott , Dynamics of coherent oscillation in photorrefractive oscillator with BaTiO 3 , Ukr. Fiz. Zh. UFIZAW 36 , 402 406 ( 1991

A. Zozulya , Fanning and photorefractive self-pumped four-wave mixing geometries , IEEE J. Quantum Electron. IEJQA7 29 , 538 555 ( 1993
[CrossRef]

D. Engin , S. Orlov , M. Segev , G. Valley , and A. Yariv , Order-disorder phase transition and critical slowing down in photorefractive self-oscillators , Phys. Rev. Lett. PRLTAO 74 , 1743 1746 ( 1995
[CrossRef] [PubMed]

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 (6)

Fig. 1
Fig. 1

A, Orientation of the incident and generated light beams in hexagon formation. B, C, Elementary backward-wave four-wave mixing processes, and D, E, diffraction from the principal grating. The wave vectors k are shown as the solid arrows in B–E; the grating vectors are shown by dotted lines.

Fig. 2
Fig. 2

Schematic of the experimental setup: VBA, variable beam attenuator; λ/4, quarter-wave plate; P, O, objective; BS1, BS2, beam splitters; PRC, BaTiO3:Co sample; M, highly reflecting mirror; S, screen. Shutter Sh is used to open the erasing beam. The vectors e and c define the polarization of the pump wave and the orientation of the crystal polar axis, respectively. In some experiments, instead of a screen a high-pass spatial filter and a lens focusing the radiation of six hexagon spots to the photodetector (not shown in the figure) are installed.

Fig. 3
Fig. 3

Temporal development of the sideband intensity. At t=0 the pump waves start to illuminate the sample in which all photorefractive gratings were previously erased by an additional coherent light wave. Dashed line, 10% level from the saturation intensity of the hexagon sideband; Δt, delay time of the oscillation switch-on.

Fig. 4
Fig. 4

Polarization angle of hexagon sidebands ψh versus polarization angle of incident pump wave ψp.

Fig. 5
Fig. 5

A, Hexagon sideband intensity, and B, oscillation switch-on time versus polarization angle ψp of the incident pump wave. Dashed lines are guides for the eye.

Fig. 6
Fig. 6

Angle θ between the hexagon sideband and the pump beam versus the distance L between the sample and the backreflecting mirror. The solid curve is the best fit to relation (2) with N=1.

Equations (2)

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

LN=Λ2N/λ,
θ(λN/2L)1/2,

Metrics