Abstract

A temperature study of a photorefractive coherent oscillation in a ring-loop resonator with the relaxor ferroelectric Sr0.61Ba0.39Nb2O6:Ce as a nonlinear element is presented. It is shown that the oscillation intensity as well as the oscillation onset time strongly depend on the crystal temperature. Strong influence of a resonator loop angle on the temperature dependence of coherent oscillation is reported and discussed via the dispersion of thermal spatial disorder and thermal decay versus various scales in the polar structure. Optimization of the output of a photorefractive oscillator via thermal tuning of material parameters of the crystal is shown.

© 2005 Optical Society of America

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References

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  1. P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, 1993).
  2. M. Cronin-Golomb, B. Fisher, J. P. White, and A. Yariv, "Theory and applications of four-wave mixing in photorefractive media," IEEE J. Quantum Electron. 20, 12-30 (1984).
    [CrossRef]
  3. S. Odoulov, M. Soskin, and A. Khizhnyak, Introduction to Photorefractive Nonlinear Optics (Harwood, 1998).
  4. M. Goulkov, M. Imlau, R. Pankrath, T. Granzow, U. Dörfler, and Th. Woike, "Temperature study of photo-induced wide-angle scattering in cerium-doped strontium barium niobate," J. Opt. Soc. Am. B 20, 307-313 (2003).
    [CrossRef]
  5. M. Goulkov, T. Granzow, U. Dörfler, Th. Woike, M. Imlau, and R. Pankrath, "Study of beam-fanning hysteresis in photorefractive SBN:Ce: light-induced and primary scattering as functions of polar structure," Appl. Phys. B 76, 407-416 (2003).
    [CrossRef]
  6. M. Goulkov, O. Shinkarenko, T. Granzow, Th. Woike, and M. Imlau, "Beam fanning used to study thermal disorder and decay of polar structures in the ferroelectric relaxor Sr0.61Ba0.39Nb2O6," Europhys. Lett. 66, 48-54 (2004).
    [CrossRef]
  7. M. Goul'kov, S. Odoulov, and R. Troth, "Temporal threshold of oscillation in ring-loop photorefractive resonator," Ukr. J. Phys. 36, 1007-1009 (1991).
  8. M. Cronin-Golomb, A. M. Biernacki, C. Lin, and H. Kong, "Photorefractive time differentiation of coherent optical images," Opt. Lett. 12, 1029-1031 (1987).
    [CrossRef] [PubMed]
  9. A. J. Fox, "Longitudinal electro-optic effects in barium strontium niobate (Sr1-xBaxNb2O6)," J. Appl. Phys. 44, 254-262 (1973).
    [CrossRef]
  10. G. Fogarty, B. Steiner, M. Cronin-Golomb, U. Laor, M. H. Garrett, J. Martin, and R. Uhrin, "Antiparallel ferroelectric domains in photorefractive barium titanate and strontium barium niobate observed by high-resolution x-ray diffraction imaging," J. Opt. Soc. Am. B 13, 2636-2643 (1996).
    [CrossRef]
  11. L. Ivleva, N. Bogodaev, N. Polozkov, and V. Osiko, "Growth of SBN single crystals by Stepanov technique for photorefractive applications," Opt. Mater. 4, 168-173 (1995).
    [CrossRef]
  12. M. Goulkov, T. Granzow, U. Dörfler, Th. Woike, M. Imlau, and R. Pankrath, "Temperature dependent determination of the linear electrooptic coefficient r33 in Sr0.61Ba0.39Nb2O6 single crystals by means of light-induced scattering," Opt. Commun. 218, 173-182 (2003).
    [CrossRef]

2004 (1)

M. Goulkov, O. Shinkarenko, T. Granzow, Th. Woike, and M. Imlau, "Beam fanning used to study thermal disorder and decay of polar structures in the ferroelectric relaxor Sr0.61Ba0.39Nb2O6," Europhys. Lett. 66, 48-54 (2004).
[CrossRef]

2003 (3)

M. Goulkov, T. Granzow, U. Dörfler, Th. Woike, M. Imlau, and R. Pankrath, "Study of beam-fanning hysteresis in photorefractive SBN:Ce: light-induced and primary scattering as functions of polar structure," Appl. Phys. B 76, 407-416 (2003).
[CrossRef]

M. Goulkov, T. Granzow, U. Dörfler, Th. Woike, M. Imlau, and R. Pankrath, "Temperature dependent determination of the linear electrooptic coefficient r33 in Sr0.61Ba0.39Nb2O6 single crystals by means of light-induced scattering," Opt. Commun. 218, 173-182 (2003).
[CrossRef]

M. Goulkov, M. Imlau, R. Pankrath, T. Granzow, U. Dörfler, and Th. Woike, "Temperature study of photo-induced wide-angle scattering in cerium-doped strontium barium niobate," J. Opt. Soc. Am. B 20, 307-313 (2003).
[CrossRef]

1996 (1)

1995 (1)

L. Ivleva, N. Bogodaev, N. Polozkov, and V. Osiko, "Growth of SBN single crystals by Stepanov technique for photorefractive applications," Opt. Mater. 4, 168-173 (1995).
[CrossRef]

1991 (1)

M. Goul'kov, S. Odoulov, and R. Troth, "Temporal threshold of oscillation in ring-loop photorefractive resonator," Ukr. J. Phys. 36, 1007-1009 (1991).

1987 (1)

1984 (1)

M. Cronin-Golomb, B. Fisher, J. P. White, and A. Yariv, "Theory and applications of four-wave mixing in photorefractive media," IEEE J. Quantum Electron. 20, 12-30 (1984).
[CrossRef]

1973 (1)

A. J. Fox, "Longitudinal electro-optic effects in barium strontium niobate (Sr1-xBaxNb2O6)," J. Appl. Phys. 44, 254-262 (1973).
[CrossRef]

Biernacki, A. M.

Bogodaev, N.

L. Ivleva, N. Bogodaev, N. Polozkov, and V. Osiko, "Growth of SBN single crystals by Stepanov technique for photorefractive applications," Opt. Mater. 4, 168-173 (1995).
[CrossRef]

Cronin-Golomb, M.

Dörfler, U.

M. Goulkov, M. Imlau, R. Pankrath, T. Granzow, U. Dörfler, and Th. Woike, "Temperature study of photo-induced wide-angle scattering in cerium-doped strontium barium niobate," J. Opt. Soc. Am. B 20, 307-313 (2003).
[CrossRef]

M. Goulkov, T. Granzow, U. Dörfler, Th. Woike, M. Imlau, and R. Pankrath, "Study of beam-fanning hysteresis in photorefractive SBN:Ce: light-induced and primary scattering as functions of polar structure," Appl. Phys. B 76, 407-416 (2003).
[CrossRef]

M. Goulkov, T. Granzow, U. Dörfler, Th. Woike, M. Imlau, and R. Pankrath, "Temperature dependent determination of the linear electrooptic coefficient r33 in Sr0.61Ba0.39Nb2O6 single crystals by means of light-induced scattering," Opt. Commun. 218, 173-182 (2003).
[CrossRef]

Fisher, B.

M. Cronin-Golomb, B. Fisher, J. P. White, and A. Yariv, "Theory and applications of four-wave mixing in photorefractive media," IEEE J. Quantum Electron. 20, 12-30 (1984).
[CrossRef]

Fogarty, G.

Fox, A. J.

A. J. Fox, "Longitudinal electro-optic effects in barium strontium niobate (Sr1-xBaxNb2O6)," J. Appl. Phys. 44, 254-262 (1973).
[CrossRef]

Garrett, M. H.

Goulkov, M.

M. Goulkov, O. Shinkarenko, T. Granzow, Th. Woike, and M. Imlau, "Beam fanning used to study thermal disorder and decay of polar structures in the ferroelectric relaxor Sr0.61Ba0.39Nb2O6," Europhys. Lett. 66, 48-54 (2004).
[CrossRef]

M. Goulkov, T. Granzow, U. Dörfler, Th. Woike, M. Imlau, and R. Pankrath, "Temperature dependent determination of the linear electrooptic coefficient r33 in Sr0.61Ba0.39Nb2O6 single crystals by means of light-induced scattering," Opt. Commun. 218, 173-182 (2003).
[CrossRef]

M. Goulkov, T. Granzow, U. Dörfler, Th. Woike, M. Imlau, and R. Pankrath, "Study of beam-fanning hysteresis in photorefractive SBN:Ce: light-induced and primary scattering as functions of polar structure," Appl. Phys. B 76, 407-416 (2003).
[CrossRef]

M. Goulkov, M. Imlau, R. Pankrath, T. Granzow, U. Dörfler, and Th. Woike, "Temperature study of photo-induced wide-angle scattering in cerium-doped strontium barium niobate," J. Opt. Soc. Am. B 20, 307-313 (2003).
[CrossRef]

Goul'kov, M.

M. Goul'kov, S. Odoulov, and R. Troth, "Temporal threshold of oscillation in ring-loop photorefractive resonator," Ukr. J. Phys. 36, 1007-1009 (1991).

Granzow, T.

M. Goulkov, O. Shinkarenko, T. Granzow, Th. Woike, and M. Imlau, "Beam fanning used to study thermal disorder and decay of polar structures in the ferroelectric relaxor Sr0.61Ba0.39Nb2O6," Europhys. Lett. 66, 48-54 (2004).
[CrossRef]

M. Goulkov, T. Granzow, U. Dörfler, Th. Woike, M. Imlau, and R. Pankrath, "Study of beam-fanning hysteresis in photorefractive SBN:Ce: light-induced and primary scattering as functions of polar structure," Appl. Phys. B 76, 407-416 (2003).
[CrossRef]

M. Goulkov, M. Imlau, R. Pankrath, T. Granzow, U. Dörfler, and Th. Woike, "Temperature study of photo-induced wide-angle scattering in cerium-doped strontium barium niobate," J. Opt. Soc. Am. B 20, 307-313 (2003).
[CrossRef]

M. Goulkov, T. Granzow, U. Dörfler, Th. Woike, M. Imlau, and R. Pankrath, "Temperature dependent determination of the linear electrooptic coefficient r33 in Sr0.61Ba0.39Nb2O6 single crystals by means of light-induced scattering," Opt. Commun. 218, 173-182 (2003).
[CrossRef]

Imlau, M.

M. Goulkov, O. Shinkarenko, T. Granzow, Th. Woike, and M. Imlau, "Beam fanning used to study thermal disorder and decay of polar structures in the ferroelectric relaxor Sr0.61Ba0.39Nb2O6," Europhys. Lett. 66, 48-54 (2004).
[CrossRef]

M. Goulkov, T. Granzow, U. Dörfler, Th. Woike, M. Imlau, and R. Pankrath, "Temperature dependent determination of the linear electrooptic coefficient r33 in Sr0.61Ba0.39Nb2O6 single crystals by means of light-induced scattering," Opt. Commun. 218, 173-182 (2003).
[CrossRef]

M. Goulkov, T. Granzow, U. Dörfler, Th. Woike, M. Imlau, and R. Pankrath, "Study of beam-fanning hysteresis in photorefractive SBN:Ce: light-induced and primary scattering as functions of polar structure," Appl. Phys. B 76, 407-416 (2003).
[CrossRef]

M. Goulkov, M. Imlau, R. Pankrath, T. Granzow, U. Dörfler, and Th. Woike, "Temperature study of photo-induced wide-angle scattering in cerium-doped strontium barium niobate," J. Opt. Soc. Am. B 20, 307-313 (2003).
[CrossRef]

Ivleva, L.

L. Ivleva, N. Bogodaev, N. Polozkov, and V. Osiko, "Growth of SBN single crystals by Stepanov technique for photorefractive applications," Opt. Mater. 4, 168-173 (1995).
[CrossRef]

Khizhnyak, A.

S. Odoulov, M. Soskin, and A. Khizhnyak, Introduction to Photorefractive Nonlinear Optics (Harwood, 1998).

Kong, H.

Laor, U.

Lin, C.

Martin, J.

Odoulov, S.

M. Goul'kov, S. Odoulov, and R. Troth, "Temporal threshold of oscillation in ring-loop photorefractive resonator," Ukr. J. Phys. 36, 1007-1009 (1991).

S. Odoulov, M. Soskin, and A. Khizhnyak, Introduction to Photorefractive Nonlinear Optics (Harwood, 1998).

Osiko, V.

L. Ivleva, N. Bogodaev, N. Polozkov, and V. Osiko, "Growth of SBN single crystals by Stepanov technique for photorefractive applications," Opt. Mater. 4, 168-173 (1995).
[CrossRef]

Pankrath, R.

M. Goulkov, T. Granzow, U. Dörfler, Th. Woike, M. Imlau, and R. Pankrath, "Study of beam-fanning hysteresis in photorefractive SBN:Ce: light-induced and primary scattering as functions of polar structure," Appl. Phys. B 76, 407-416 (2003).
[CrossRef]

M. Goulkov, M. Imlau, R. Pankrath, T. Granzow, U. Dörfler, and Th. Woike, "Temperature study of photo-induced wide-angle scattering in cerium-doped strontium barium niobate," J. Opt. Soc. Am. B 20, 307-313 (2003).
[CrossRef]

M. Goulkov, T. Granzow, U. Dörfler, Th. Woike, M. Imlau, and R. Pankrath, "Temperature dependent determination of the linear electrooptic coefficient r33 in Sr0.61Ba0.39Nb2O6 single crystals by means of light-induced scattering," Opt. Commun. 218, 173-182 (2003).
[CrossRef]

Polozkov, N.

L. Ivleva, N. Bogodaev, N. Polozkov, and V. Osiko, "Growth of SBN single crystals by Stepanov technique for photorefractive applications," Opt. Mater. 4, 168-173 (1995).
[CrossRef]

Shinkarenko, O.

M. Goulkov, O. Shinkarenko, T. Granzow, Th. Woike, and M. Imlau, "Beam fanning used to study thermal disorder and decay of polar structures in the ferroelectric relaxor Sr0.61Ba0.39Nb2O6," Europhys. Lett. 66, 48-54 (2004).
[CrossRef]

Soskin, M.

S. Odoulov, M. Soskin, and A. Khizhnyak, Introduction to Photorefractive Nonlinear Optics (Harwood, 1998).

Steiner, B.

Troth, R.

M. Goul'kov, S. Odoulov, and R. Troth, "Temporal threshold of oscillation in ring-loop photorefractive resonator," Ukr. J. Phys. 36, 1007-1009 (1991).

Uhrin, R.

White, J. P.

M. Cronin-Golomb, B. Fisher, J. P. White, and A. Yariv, "Theory and applications of four-wave mixing in photorefractive media," IEEE J. Quantum Electron. 20, 12-30 (1984).
[CrossRef]

Woike, Th.

M. Goulkov, O. Shinkarenko, T. Granzow, Th. Woike, and M. Imlau, "Beam fanning used to study thermal disorder and decay of polar structures in the ferroelectric relaxor Sr0.61Ba0.39Nb2O6," Europhys. Lett. 66, 48-54 (2004).
[CrossRef]

M. Goulkov, T. Granzow, U. Dörfler, Th. Woike, M. Imlau, and R. Pankrath, "Temperature dependent determination of the linear electrooptic coefficient r33 in Sr0.61Ba0.39Nb2O6 single crystals by means of light-induced scattering," Opt. Commun. 218, 173-182 (2003).
[CrossRef]

M. Goulkov, M. Imlau, R. Pankrath, T. Granzow, U. Dörfler, and Th. Woike, "Temperature study of photo-induced wide-angle scattering in cerium-doped strontium barium niobate," J. Opt. Soc. Am. B 20, 307-313 (2003).
[CrossRef]

M. Goulkov, T. Granzow, U. Dörfler, Th. Woike, M. Imlau, and R. Pankrath, "Study of beam-fanning hysteresis in photorefractive SBN:Ce: light-induced and primary scattering as functions of polar structure," Appl. Phys. B 76, 407-416 (2003).
[CrossRef]

Yariv, A.

M. Cronin-Golomb, B. Fisher, J. P. White, and A. Yariv, "Theory and applications of four-wave mixing in photorefractive media," IEEE J. Quantum Electron. 20, 12-30 (1984).
[CrossRef]

Yeh, P.

P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, 1993).

Appl. Phys. B (1)

M. Goulkov, T. Granzow, U. Dörfler, Th. Woike, M. Imlau, and R. Pankrath, "Study of beam-fanning hysteresis in photorefractive SBN:Ce: light-induced and primary scattering as functions of polar structure," Appl. Phys. B 76, 407-416 (2003).
[CrossRef]

Europhys. Lett. (1)

M. Goulkov, O. Shinkarenko, T. Granzow, Th. Woike, and M. Imlau, "Beam fanning used to study thermal disorder and decay of polar structures in the ferroelectric relaxor Sr0.61Ba0.39Nb2O6," Europhys. Lett. 66, 48-54 (2004).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Cronin-Golomb, B. Fisher, J. P. White, and A. Yariv, "Theory and applications of four-wave mixing in photorefractive media," IEEE J. Quantum Electron. 20, 12-30 (1984).
[CrossRef]

J. Appl. Phys. (1)

A. J. Fox, "Longitudinal electro-optic effects in barium strontium niobate (Sr1-xBaxNb2O6)," J. Appl. Phys. 44, 254-262 (1973).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Commun. (1)

M. Goulkov, T. Granzow, U. Dörfler, Th. Woike, M. Imlau, and R. Pankrath, "Temperature dependent determination of the linear electrooptic coefficient r33 in Sr0.61Ba0.39Nb2O6 single crystals by means of light-induced scattering," Opt. Commun. 218, 173-182 (2003).
[CrossRef]

Opt. Lett. (1)

Opt. Mater. (1)

L. Ivleva, N. Bogodaev, N. Polozkov, and V. Osiko, "Growth of SBN single crystals by Stepanov technique for photorefractive applications," Opt. Mater. 4, 168-173 (1995).
[CrossRef]

Ukr. J. Phys. (1)

M. Goul'kov, S. Odoulov, and R. Troth, "Temporal threshold of oscillation in ring-loop photorefractive resonator," Ukr. J. Phys. 36, 1007-1009 (1991).

Other (2)

P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, 1993).

S. Odoulov, M. Soskin, and A. Khizhnyak, Introduction to Photorefractive Nonlinear Optics (Harwood, 1998).

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Figures (8)

Fig. 1
Fig. 1

The ring-loop resonator is built with a crystal of SBN:Ce and two plane mirrors Mr1 and Mr2. The pump beam 2 ( λ = 488 nm ) impinges upon the crystal at the angle θ p = 1 ° . The resonator cavity angle was adjusted to three different values θ loop : 27°, 14.5°, and 4.5°.

Fig. 2
Fig. 2

Dynamics of coherent oscillation at different temperatures in a ring-loop resonator with loop angle θ loop of (a) 27°, (b) 14.5°, and (c) 4.5°.

Fig. 3
Fig. 3

Normalized intensity of coherent oscillation versus crystal temperature for different angles θ loop : 27°, 14.5°, and 4.5°.

Fig. 4
Fig. 4

Oscillation onset time t on versus crystal temperature for different angles θ loop : 27°, 14.5°, and 4.5°.

Fig. 5
Fig. 5

Oscillation time decay versus crystal temperature for different angles θ loop : 27°, 14.5°, and 4.5°.

Fig. 6
Fig. 6

Threshold transmission coefficient of a ring-loop resonator M th versus crystal temperature for different angles θ loop : 27°, 14.5°, and 4.5°.

Fig. 7
Fig. 7

Stationary coupling strength versus crystal temperature for different angles θ loop : 27°, 14.5°, and 4.5°.

Fig. 8
Fig. 8

Ratio Γ o t dec versus crystal temperature for different angles θ loop : 27°, 14.5°, and 4.5°.

Equations (5)

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( Γ l ) ( t ) = ( Γ l ) o [ 1 exp ( t τ di ) ] ,
( Γ l ) th = 2 M + 1 M 1 ln M + 1 2 M ,
t on = τ di ln [ 1 + 2 ( M + 1 ) ( Γ l ) o ( M 1 ) ln M + 1 2 M ] ,
r eff = 2 g P s ϵ ϵ o ,
θ s = 2 arcsin ( λ 2 Λ d ) .

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