Abstract

The generation of multiple waves during near-oblique incidence of a 532  nm weakly focused beam on photorefractive iron-doped lithium niobate in a typical reflection geometry configuration is studied. It is shown that these waves are produced through two-wave coupling (self-diffraction) and four-wave mixing (parametric diffraction). One of these waves, the stimulated photorefractive backscatter produced from parametric diffraction, contains the self-phase conjugate. The dynamics of six-wave mixing and its dependence on crystal parameters, angle of incidence, and pump power are analyzed. What we believe to be a novel order analysis of the interaction equations provides further insight into experimental observations in the steady state. The quality of the backscatter is evaluated through image restoration, interference experiments, and visibility measurement. Reduction of two-wave coupling may significantly improve the quality of the self-phase conjugate.

© 2007 Optical Society of America

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References

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  1. I. F. Kanaev, V. K. Malinovski, and B. I. Sturman, "Induced reflection and bleaching effects in electro-optic crystals," Sov. Phys. JETP 47, 834-837 (1978).
  2. G. Valley, "Evolution of phase-conjugate waves in stimulated photorefractive backscattering," J. Opt. Soc. Am. A 9, 1440-1448 (1992).
    [CrossRef]
  3. A. V. Mamaev and V. V. Shkunov, "Transient phase self-conjugation in a lithium niobate crystal," Sov. J. Quantum Electron. 18, 829-830 (1988).
    [CrossRef]
  4. S. A. Korolkov, A. V. Mamaev, and V. V. Shkunov, "Stimulated diffusion backscattering with phase conjugation," Int. J. Nonlinear Opt. Phys. 2, 157-169 (1993), and references therein.
    [CrossRef]
  5. H. Qiao, Y. Tomita, J. Xu, Q. Wu, G. Zhang, and G. Zhang, "Observation of strong stimulated photorefractive scattering and self-pumped phase conjugation in LiNbO3:Mg in the ultraviolet," Opt. Express 13, 7666-7671 (2005).
    [CrossRef] [PubMed]
  6. N. V. Kukhtarev, T. Kukhtareva, H. J.Caulfield, P. Banerjee, H.-L. Yu, and L. Hesselink, "Broadband dynamic, holographically self recorded, and static hexagonal scattering patterns in photorefractive KNbO3:Fe," Opt. Eng. 34, 2261-2268 (1995).
    [CrossRef]
  7. N. Kukhtarev, T. Kukhtareva, R. Jones, J. Wang, and P. Banerjee, "Real-time holography for optical processing using photorefractive crystals," Proc. SPIE 3793, 90-96 (1999).
    [CrossRef]
  8. E. Shamonina, B. I. Sturman, S. G. Odoulov, and K. H. Ringhofer, "Investigation of stochastic photorefractive backscattering," J. Opt. Soc. Am. B 13, 2242-2251 (1996).
    [CrossRef]
  9. J. Feinberg, "Self-pumped, continuous-wave phase conjugator using internal reflection," Opt. Lett. 7, 486-488 (1982).
    [CrossRef] [PubMed]
  10. P. Buranasiri, P. P. Banerjee, V. Polejaev, and C. C. Sun, "Image correlation using isotropic and anisotropic higher-order generation and mutually pumped phase conjugation in photorefractive barium titanate," Proc. SPIE 5206, 215-222 (2003).
    [CrossRef]
  11. P. Suni and J. Falk, "Measurements of stimulated Brillouin scattering phase-conjugate fidelity," Opt. Lett. 12, 838-840 (1987).
    [CrossRef] [PubMed]
  12. M. D.Ewbank, "Mechanism for photorefractive phase conjugation using incoherent beams," Opt. Lett. 13, 47-49 (1988).
    [CrossRef] [PubMed]
  13. D. R. Evans, S. A. Basun, M. A. Saleh, T. P. Pottenger, G. Cook, T. J. Bunning, and S. Guha, "Elimination of photorefractive grating writing instabilities in iron-doped lithium niobate," IEEE J. Quantum Electron. 38, 1661-1663 (2001).
    [CrossRef]
  14. D. R. Evans, J. L. Gibson, S. A. Basun,M. A. Saleh, and G. Cook, "Understanding and eliminating photovoltaic induced instabilities during contradirectional two-beam coupling in photorefractive LiNbO3:Fe," Opt. Matter 27, 1730-1732 (2005).
    [CrossRef]
  15. S. Odoulov, B. Sturman, and E. Kratzig, "Seeded and spontaneous light hexagons in LiNbO3:Fe," Appl. Phys. B 70, 645-647 (2000).
    [CrossRef]
  16. E. Hecht, Optics (Addison-Wesley, 1987).
  17. G. Cook, D. C. Jones, C. J. Finnan, L. L. Taylor, and T. W. Vere, "Optical limiting with lithium niobate," Proc. SPIE 3798, 2-16 (1999).
    [CrossRef]
  18. M. Luenemann, K. Buse, and B. Sturman, "Coupling effects for counterpropagating light beams in lithium niobate crystals studied by grating translation technique for extremely high electric fields," J. Appl. Phys. 94, 6274-6279 (2003).
    [CrossRef]

2005 (2)

D. R. Evans, J. L. Gibson, S. A. Basun,M. A. Saleh, and G. Cook, "Understanding and eliminating photovoltaic induced instabilities during contradirectional two-beam coupling in photorefractive LiNbO3:Fe," Opt. Matter 27, 1730-1732 (2005).
[CrossRef]

H. Qiao, Y. Tomita, J. Xu, Q. Wu, G. Zhang, and G. Zhang, "Observation of strong stimulated photorefractive scattering and self-pumped phase conjugation in LiNbO3:Mg in the ultraviolet," Opt. Express 13, 7666-7671 (2005).
[CrossRef] [PubMed]

2003 (2)

M. Luenemann, K. Buse, and B. Sturman, "Coupling effects for counterpropagating light beams in lithium niobate crystals studied by grating translation technique for extremely high electric fields," J. Appl. Phys. 94, 6274-6279 (2003).
[CrossRef]

P. Buranasiri, P. P. Banerjee, V. Polejaev, and C. C. Sun, "Image correlation using isotropic and anisotropic higher-order generation and mutually pumped phase conjugation in photorefractive barium titanate," Proc. SPIE 5206, 215-222 (2003).
[CrossRef]

2001 (1)

D. R. Evans, S. A. Basun, M. A. Saleh, T. P. Pottenger, G. Cook, T. J. Bunning, and S. Guha, "Elimination of photorefractive grating writing instabilities in iron-doped lithium niobate," IEEE J. Quantum Electron. 38, 1661-1663 (2001).
[CrossRef]

2000 (1)

S. Odoulov, B. Sturman, and E. Kratzig, "Seeded and spontaneous light hexagons in LiNbO3:Fe," Appl. Phys. B 70, 645-647 (2000).
[CrossRef]

1999 (2)

G. Cook, D. C. Jones, C. J. Finnan, L. L. Taylor, and T. W. Vere, "Optical limiting with lithium niobate," Proc. SPIE 3798, 2-16 (1999).
[CrossRef]

N. Kukhtarev, T. Kukhtareva, R. Jones, J. Wang, and P. Banerjee, "Real-time holography for optical processing using photorefractive crystals," Proc. SPIE 3793, 90-96 (1999).
[CrossRef]

1996 (1)

1995 (1)

N. V. Kukhtarev, T. Kukhtareva, H. J.Caulfield, P. Banerjee, H.-L. Yu, and L. Hesselink, "Broadband dynamic, holographically self recorded, and static hexagonal scattering patterns in photorefractive KNbO3:Fe," Opt. Eng. 34, 2261-2268 (1995).
[CrossRef]

1993 (1)

S. A. Korolkov, A. V. Mamaev, and V. V. Shkunov, "Stimulated diffusion backscattering with phase conjugation," Int. J. Nonlinear Opt. Phys. 2, 157-169 (1993), and references therein.
[CrossRef]

1992 (1)

G. Valley, "Evolution of phase-conjugate waves in stimulated photorefractive backscattering," J. Opt. Soc. Am. A 9, 1440-1448 (1992).
[CrossRef]

1988 (2)

A. V. Mamaev and V. V. Shkunov, "Transient phase self-conjugation in a lithium niobate crystal," Sov. J. Quantum Electron. 18, 829-830 (1988).
[CrossRef]

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

1987 (1)

1982 (1)

1978 (1)

I. F. Kanaev, V. K. Malinovski, and B. I. Sturman, "Induced reflection and bleaching effects in electro-optic crystals," Sov. Phys. JETP 47, 834-837 (1978).

Appl. Phys. B (1)

S. Odoulov, B. Sturman, and E. Kratzig, "Seeded and spontaneous light hexagons in LiNbO3:Fe," Appl. Phys. B 70, 645-647 (2000).
[CrossRef]

IEEE J. Quantum Electron. (1)

D. R. Evans, S. A. Basun, M. A. Saleh, T. P. Pottenger, G. Cook, T. J. Bunning, and S. Guha, "Elimination of photorefractive grating writing instabilities in iron-doped lithium niobate," IEEE J. Quantum Electron. 38, 1661-1663 (2001).
[CrossRef]

Int. J. Nonlinear Opt. Phys. (1)

S. A. Korolkov, A. V. Mamaev, and V. V. Shkunov, "Stimulated diffusion backscattering with phase conjugation," Int. J. Nonlinear Opt. Phys. 2, 157-169 (1993), and references therein.
[CrossRef]

J. Appl. Phys. (1)

M. Luenemann, K. Buse, and B. Sturman, "Coupling effects for counterpropagating light beams in lithium niobate crystals studied by grating translation technique for extremely high electric fields," J. Appl. Phys. 94, 6274-6279 (2003).
[CrossRef]

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

G. Valley, "Evolution of phase-conjugate waves in stimulated photorefractive backscattering," J. Opt. Soc. Am. A 9, 1440-1448 (1992).
[CrossRef]

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

Opt. Eng. (1)

N. V. Kukhtarev, T. Kukhtareva, H. J.Caulfield, P. Banerjee, H.-L. Yu, and L. Hesselink, "Broadband dynamic, holographically self recorded, and static hexagonal scattering patterns in photorefractive KNbO3:Fe," Opt. Eng. 34, 2261-2268 (1995).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Opt. Matter (1)

D. R. Evans, J. L. Gibson, S. A. Basun,M. A. Saleh, and G. Cook, "Understanding and eliminating photovoltaic induced instabilities during contradirectional two-beam coupling in photorefractive LiNbO3:Fe," Opt. Matter 27, 1730-1732 (2005).
[CrossRef]

Proc. SPIE (3)

N. Kukhtarev, T. Kukhtareva, R. Jones, J. Wang, and P. Banerjee, "Real-time holography for optical processing using photorefractive crystals," Proc. SPIE 3793, 90-96 (1999).
[CrossRef]

P. Buranasiri, P. P. Banerjee, V. Polejaev, and C. C. Sun, "Image correlation using isotropic and anisotropic higher-order generation and mutually pumped phase conjugation in photorefractive barium titanate," Proc. SPIE 5206, 215-222 (2003).
[CrossRef]

G. Cook, D. C. Jones, C. J. Finnan, L. L. Taylor, and T. W. Vere, "Optical limiting with lithium niobate," Proc. SPIE 3798, 2-16 (1999).
[CrossRef]

Sov. J. Quantum Electron. (1)

A. V. Mamaev and V. V. Shkunov, "Transient phase self-conjugation in a lithium niobate crystal," Sov. J. Quantum Electron. 18, 829-830 (1988).
[CrossRef]

Sov. Phys. JETP (1)

I. F. Kanaev, V. K. Malinovski, and B. I. Sturman, "Induced reflection and bleaching effects in electro-optic crystals," Sov. Phys. JETP 47, 834-837 (1978).

Other (1)

E. Hecht, Optics (Addison-Wesley, 1987).

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Figures (7)

Fig. 1
Fig. 1

Schematic representation of the six waves inside the crystal. C 1 denotes the forward-propagating pump through the crystal. C 2 represents the result of six-wave mixing in the direction of the Fresnel reflection of the pump from the surface. C 3 and C 4 denote the waves generated in the crystal that are perpendicular to the interface and consequently along the c axis. C 5 and C 6 (the SPBS) make up the other two participating waves in the six-wave-mixing scheme.

Fig. 2
Fig. 2

(Color online) Schematic representation of the experimental arrangement. L1–L3, lenses; M1, M2, mirrors; BS1, BS2, beam splitters. The pump is collimated 532   nm light from a Verdi laser. Six-wave mixing is observed on screens S1 and S2. Lens L1 is used to focus the pump onto the PR sample, which is placed at its back focus for six-wave-mixing experiments. SPBS ( C 6 ) power is measured with the detector shown. Powers in C 1 C 5 are also recorded with similar detectors placed directly in the path of the beams after exit from the crystal in their respective directions. Lens L3 and screen S3 are used during interference experiments for determination of the quality of SPBS. The PR sample is first placed at an arbitrary distance from lens L1 and the SPBS interfered with a portion of the collimated pump reflected by the mirror M1 with lens L2 removed. Thereafter, the sample is reinserted at the back focal plane of L1 and the interference of the SPBS with a portion of the pump focused by L2 and reflected by the mirror M1 is monitored.

Fig. 3
Fig. 3

Calculation of contributions to SPBS ( C 6 ) using scattering diagrams, following Eq. (1.6). The thin lines on the right-hand side refer to k vectors of waves participating in the grating, whereas the dark lines represent the k vector of the wave reading the grating.

Fig. 4
Fig. 4

(Color online) (a) Backscattered beam C 6 and linearly reflected light in the direction of C 2 . Although the latter is instantaneously generated, C 6 forms between 100 ms and 10 s after the pump beam is turned on. The pump beam, in the direction of C 1 passes through a hole on screen S1. (b) Subsequent generation of C 2 and C 3 is seen on screen S1. The bright spot along C 2 also includes the instantaneously generated Fresnel-reflected light.

Fig. 5
Fig. 5

Time dynamics of six-wave mixing for crystal A at an angle of incidence of 4° (in air) for the pump. Screens S1 and S2 in Fig. 2 are replaced by detectors and C 1 C 5 are focused onto the detectors. The beams are recorded in pairs, with C 1 being common in all cases. The lighter traces correspond to 6 independent traces each for C 2 C 6 and 30 traces for C 1 . The average in each case is shown in black. Note that the total optical power in the direction of C 2 is plotted; the horizontal dashed line in this graph indicates the component of light in the direction of C 2 due to Fresnel reflection from the crystal surfaces.

Fig. 6
Fig. 6

(Color online) Interference with the reference (pump) when the crystal (or the mirror) is placed at a distance approximately f / 2 from lens L1. (a) Interference pattern between the reference and the phase conjugate from BaTiO 3 :Ce . Note the absence of circular fringes due to phase correction from phase conjugation. Inset shows linear fringes when the mirror M1 that reflects the reference is tilted. (b) Interference between the reference and reflection from a plane mirror placed at the location of the crystal. (c) Interference pattern between the reference and the SPBS from LiNbO 3 :Fe .

Fig. 7
Fig. 7

(Color online) Quantification of the coherence of the SPBS through visibility measurement from interference patterns. (a) Interference pattern between the reference and the SPBS from LiNbO 3 :Fe . (b) Interference pattern between the reference and a reflection from a plane mirror placed at the location of the crystal. (c) Intensity patterns along a vertical cut through both interference patterns recorded in (a) and (b), which is used for visibility calculations.

Tables (1)

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Table 1 Relevant Parameters for All the LiNbO3:Fe Crystals Used

Equations (13)

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L 1 C 1 = n 12 C 2 + n 13 C 3 + n 16 C 6 + n 46 C 3 + n 56 C 2 ,
L 2 C 2 = n 21 C 1 + n 24 C 4 + n 25 C 5 + n 65 C 1 + n 35 C 4 ,
L 3 C 3 = n 31 C 1 + n 34 C 4 + n 35 C 5 + n 64 C 1 + n 24 C 5 ,
L 4 C 4 = n 42 C 2 + n 43 C 3 + n 46 C 6 + n 53 C 2 + n 13 C 6 ,
L 5 C 5 = n 52 C 2 + n 53 C 3 + n 56 C 6 + n 12 C 6 + n 42 C 3 ,
L 6 C 6 = n 61 C 1 + n 64 C 4 + n 65 C 5 + n 21 C 5 + n 31 C 4 ,
τ i j n i j / t = γ i j C i C j * β i j n i j ,
L 1 C 1 = n 13 C 3 ( O : δ 1 ε 0 ) + n 12 C 2 ( O : δ 1 ε 1 ) ,
L 2 C 2 = n 21 C 1 ( O : δ 1 ε 0 ) ,
    L 3 C 3 = n 31 C 1 ( O : δ 1 ε 1 ) ,
L 4 C 4 = n 42 C 2 ( O : δ 4 ε 1 ) ,
L 5 C 5 = ( n 12 C 6 + n 42 C 3 ) ( O : δ 4 ε 2 ) + n 52 C 2 ( O : δ 6 ε 2 ) ,
L 6 C 6 = ( n 61 C 1 + n 31 C 4 ) ( O : δ 3 ε 2 ) + n 21 C 5 ( O : δ 5 ε 2 ) .

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