Abstract

It is shown that the saw-tooth variation of the cavity length in a photorefractive semilinear coherent oscillator can suppress the instability in the frequency domain and prevent a bifurcation in the oscillation spectrum. To achieve such a suppression the frequency of the cavity length modulation should be chosen appropriately. It depends on the photorefractive crystal parameters (electrooptic properties, photoconductivity, dimensions) and on the experimental conditions (pump intensity ratio, orientation of the pump and oscillation waves with respect to the crystallographic axes, polarization of the pump waves, etc.). It depends also strongly on a possible misalignment of the two pump waves. On the other hand, within a certain range of the experimental parameters the mirror vibration may lead to a further frequency splitting in the already existing two-mode oscillation spectrum.

©2007 Optical Society of America

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References

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  1. L. Curtis Foster, M. D. Ewy, and C. Burton Crumly, “Laser mode locking by an external Doppler cell,” Appl. Phys. Lett. 6, 6–8 (1965).
    [Crossref]
  2. L. P. Yatsenko, B. W. Shore, and K. Bergmann, “Theory of a frequency-shifted feedback laser,” Opt. Commun. 236, 183–202 (2004).
    [Crossref]
  3. V. V. Ogurtsov, L. P. Yatsenko, V. M. Khodakovskyy, B. W. Shore, G. Bonnet, and K. Bergmann, “Experimental characterization of an Yb3+-doped fiber ring laser with frequency shifted feedback,” Opt. Commun. 266, 627–637 (2006).
    [Crossref]
  4. L. Solymar, D. Webb, and A. Grunnet-Jepsen, “The Physics and Applications of Photorefractive Materials,” (Clarendon, Oxford, 1996).
  5. P. Mathey, S. Odoulov, and D. Rytz, “Instability of single frequency operation in semilinear photorefractive coherent oscillators,” Phys. Rev. Lett. 89, 053901-1-4 (2002).
    [Crossref]
  6. P. Mathey, S. Odoulov, and D. Rytz, “Oscillation spectra of semilinear photorefractive coherent oscillator with two pump waves,” J. Opt. Soc. Am. B 19, 2967–2977 (2002).
    [Crossref]
  7. P. A. Belanger, A. Hardy, and A. Siegman,“Resonant modes of optical cavities with phase-conjugate mirrors,” Appl. Opt. 19, 602–609 (1980).
    [Crossref] [PubMed]
  8. M. Grapinet, P. Mathey, S. Odoulov, and D. Rytz, “Semilinear coherent oscillator with reflection-type photorefractive gratings,” Appl. Phys. B 77, 551–554 (2003).
    [Crossref]
  9. George C. Valley, “Competition between forward-and backward-stimulated photorefractive scattering,” J. Opt. Soc. Am. B4, 14–19 (1987); Erratum: J. Opt. Soc. Am. B4, 934 (1987).
    [Crossref]
  10. P. Mathey, M. Grapinet, H. R. Jauslin, B. Sturman, D. Rytz, and S. Odoulov, “Threshold behavior of semi-linear photorefractive oscillator,” European Phys. J. D 39, 445–451 (2006).
    [Crossref]
  11. 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. QE-20, 12–20 (1984).
    [Crossref]

2006 (2)

V. V. Ogurtsov, L. P. Yatsenko, V. M. Khodakovskyy, B. W. Shore, G. Bonnet, and K. Bergmann, “Experimental characterization of an Yb3+-doped fiber ring laser with frequency shifted feedback,” Opt. Commun. 266, 627–637 (2006).
[Crossref]

P. Mathey, M. Grapinet, H. R. Jauslin, B. Sturman, D. Rytz, and S. Odoulov, “Threshold behavior of semi-linear photorefractive oscillator,” European Phys. J. D 39, 445–451 (2006).
[Crossref]

2004 (1)

L. P. Yatsenko, B. W. Shore, and K. Bergmann, “Theory of a frequency-shifted feedback laser,” Opt. Commun. 236, 183–202 (2004).
[Crossref]

2003 (1)

M. Grapinet, P. Mathey, S. Odoulov, and D. Rytz, “Semilinear coherent oscillator with reflection-type photorefractive gratings,” Appl. Phys. B 77, 551–554 (2003).
[Crossref]

2002 (2)

P. Mathey, S. Odoulov, and D. Rytz, “Instability of single frequency operation in semilinear photorefractive coherent oscillators,” Phys. Rev. Lett. 89, 053901-1-4 (2002).
[Crossref]

P. Mathey, S. Odoulov, and D. Rytz, “Oscillation spectra of semilinear photorefractive coherent oscillator with two pump waves,” J. Opt. Soc. Am. B 19, 2967–2977 (2002).
[Crossref]

1984 (1)

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. QE-20, 12–20 (1984).
[Crossref]

1980 (1)

1965 (1)

L. Curtis Foster, M. D. Ewy, and C. Burton Crumly, “Laser mode locking by an external Doppler cell,” Appl. Phys. Lett. 6, 6–8 (1965).
[Crossref]

Belanger, P. A.

Bergmann, K.

V. V. Ogurtsov, L. P. Yatsenko, V. M. Khodakovskyy, B. W. Shore, G. Bonnet, and K. Bergmann, “Experimental characterization of an Yb3+-doped fiber ring laser with frequency shifted feedback,” Opt. Commun. 266, 627–637 (2006).
[Crossref]

L. P. Yatsenko, B. W. Shore, and K. Bergmann, “Theory of a frequency-shifted feedback laser,” Opt. Commun. 236, 183–202 (2004).
[Crossref]

Bonnet, G.

V. V. Ogurtsov, L. P. Yatsenko, V. M. Khodakovskyy, B. W. Shore, G. Bonnet, and K. Bergmann, “Experimental characterization of an Yb3+-doped fiber ring laser with frequency shifted feedback,” Opt. Commun. 266, 627–637 (2006).
[Crossref]

Burton Crumly, C.

L. Curtis Foster, M. D. Ewy, and C. Burton Crumly, “Laser mode locking by an external Doppler cell,” Appl. Phys. Lett. 6, 6–8 (1965).
[Crossref]

Cronin-Golomb, M.

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. QE-20, 12–20 (1984).
[Crossref]

Curtis Foster, L.

L. Curtis Foster, M. D. Ewy, and C. Burton Crumly, “Laser mode locking by an external Doppler cell,” Appl. Phys. Lett. 6, 6–8 (1965).
[Crossref]

Ewy, M. D.

L. Curtis Foster, M. D. Ewy, and C. Burton Crumly, “Laser mode locking by an external Doppler cell,” Appl. Phys. Lett. 6, 6–8 (1965).
[Crossref]

Fischer, B.

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. QE-20, 12–20 (1984).
[Crossref]

Grapinet, M.

P. Mathey, M. Grapinet, H. R. Jauslin, B. Sturman, D. Rytz, and S. Odoulov, “Threshold behavior of semi-linear photorefractive oscillator,” European Phys. J. D 39, 445–451 (2006).
[Crossref]

M. Grapinet, P. Mathey, S. Odoulov, and D. Rytz, “Semilinear coherent oscillator with reflection-type photorefractive gratings,” Appl. Phys. B 77, 551–554 (2003).
[Crossref]

Grunnet-Jepsen, A.

L. Solymar, D. Webb, and A. Grunnet-Jepsen, “The Physics and Applications of Photorefractive Materials,” (Clarendon, Oxford, 1996).

Hardy, A.

Jauslin, H. R.

P. Mathey, M. Grapinet, H. R. Jauslin, B. Sturman, D. Rytz, and S. Odoulov, “Threshold behavior of semi-linear photorefractive oscillator,” European Phys. J. D 39, 445–451 (2006).
[Crossref]

Khodakovskyy, V. M.

V. V. Ogurtsov, L. P. Yatsenko, V. M. Khodakovskyy, B. W. Shore, G. Bonnet, and K. Bergmann, “Experimental characterization of an Yb3+-doped fiber ring laser with frequency shifted feedback,” Opt. Commun. 266, 627–637 (2006).
[Crossref]

Mathey, P.

P. Mathey, M. Grapinet, H. R. Jauslin, B. Sturman, D. Rytz, and S. Odoulov, “Threshold behavior of semi-linear photorefractive oscillator,” European Phys. J. D 39, 445–451 (2006).
[Crossref]

M. Grapinet, P. Mathey, S. Odoulov, and D. Rytz, “Semilinear coherent oscillator with reflection-type photorefractive gratings,” Appl. Phys. B 77, 551–554 (2003).
[Crossref]

P. Mathey, S. Odoulov, and D. Rytz, “Oscillation spectra of semilinear photorefractive coherent oscillator with two pump waves,” J. Opt. Soc. Am. B 19, 2967–2977 (2002).
[Crossref]

P. Mathey, S. Odoulov, and D. Rytz, “Instability of single frequency operation in semilinear photorefractive coherent oscillators,” Phys. Rev. Lett. 89, 053901-1-4 (2002).
[Crossref]

Odoulov, S.

P. Mathey, M. Grapinet, H. R. Jauslin, B. Sturman, D. Rytz, and S. Odoulov, “Threshold behavior of semi-linear photorefractive oscillator,” European Phys. J. D 39, 445–451 (2006).
[Crossref]

M. Grapinet, P. Mathey, S. Odoulov, and D. Rytz, “Semilinear coherent oscillator with reflection-type photorefractive gratings,” Appl. Phys. B 77, 551–554 (2003).
[Crossref]

P. Mathey, S. Odoulov, and D. Rytz, “Oscillation spectra of semilinear photorefractive coherent oscillator with two pump waves,” J. Opt. Soc. Am. B 19, 2967–2977 (2002).
[Crossref]

P. Mathey, S. Odoulov, and D. Rytz, “Instability of single frequency operation in semilinear photorefractive coherent oscillators,” Phys. Rev. Lett. 89, 053901-1-4 (2002).
[Crossref]

Ogurtsov, V. V.

V. V. Ogurtsov, L. P. Yatsenko, V. M. Khodakovskyy, B. W. Shore, G. Bonnet, and K. Bergmann, “Experimental characterization of an Yb3+-doped fiber ring laser with frequency shifted feedback,” Opt. Commun. 266, 627–637 (2006).
[Crossref]

Rytz, D.

P. Mathey, M. Grapinet, H. R. Jauslin, B. Sturman, D. Rytz, and S. Odoulov, “Threshold behavior of semi-linear photorefractive oscillator,” European Phys. J. D 39, 445–451 (2006).
[Crossref]

M. Grapinet, P. Mathey, S. Odoulov, and D. Rytz, “Semilinear coherent oscillator with reflection-type photorefractive gratings,” Appl. Phys. B 77, 551–554 (2003).
[Crossref]

P. Mathey, S. Odoulov, and D. Rytz, “Oscillation spectra of semilinear photorefractive coherent oscillator with two pump waves,” J. Opt. Soc. Am. B 19, 2967–2977 (2002).
[Crossref]

P. Mathey, S. Odoulov, and D. Rytz, “Instability of single frequency operation in semilinear photorefractive coherent oscillators,” Phys. Rev. Lett. 89, 053901-1-4 (2002).
[Crossref]

Shore, B. W.

V. V. Ogurtsov, L. P. Yatsenko, V. M. Khodakovskyy, B. W. Shore, G. Bonnet, and K. Bergmann, “Experimental characterization of an Yb3+-doped fiber ring laser with frequency shifted feedback,” Opt. Commun. 266, 627–637 (2006).
[Crossref]

L. P. Yatsenko, B. W. Shore, and K. Bergmann, “Theory of a frequency-shifted feedback laser,” Opt. Commun. 236, 183–202 (2004).
[Crossref]

Siegman, A.

Solymar, L.

L. Solymar, D. Webb, and A. Grunnet-Jepsen, “The Physics and Applications of Photorefractive Materials,” (Clarendon, Oxford, 1996).

Sturman, B.

P. Mathey, M. Grapinet, H. R. Jauslin, B. Sturman, D. Rytz, and S. Odoulov, “Threshold behavior of semi-linear photorefractive oscillator,” European Phys. J. D 39, 445–451 (2006).
[Crossref]

Valley, George C.

George C. Valley, “Competition between forward-and backward-stimulated photorefractive scattering,” J. Opt. Soc. Am. B4, 14–19 (1987); Erratum: J. Opt. Soc. Am. B4, 934 (1987).
[Crossref]

Webb, D.

L. Solymar, D. Webb, and A. Grunnet-Jepsen, “The Physics and Applications of Photorefractive Materials,” (Clarendon, Oxford, 1996).

White, J. O.

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. QE-20, 12–20 (1984).
[Crossref]

Yariv, A.

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. QE-20, 12–20 (1984).
[Crossref]

Yatsenko, L. P.

V. V. Ogurtsov, L. P. Yatsenko, V. M. Khodakovskyy, B. W. Shore, G. Bonnet, and K. Bergmann, “Experimental characterization of an Yb3+-doped fiber ring laser with frequency shifted feedback,” Opt. Commun. 266, 627–637 (2006).
[Crossref]

L. P. Yatsenko, B. W. Shore, and K. Bergmann, “Theory of a frequency-shifted feedback laser,” Opt. Commun. 236, 183–202 (2004).
[Crossref]

Appl. Opt. (1)

Appl. Phys. B (1)

M. Grapinet, P. Mathey, S. Odoulov, and D. Rytz, “Semilinear coherent oscillator with reflection-type photorefractive gratings,” Appl. Phys. B 77, 551–554 (2003).
[Crossref]

Appl. Phys. Lett. (1)

L. Curtis Foster, M. D. Ewy, and C. Burton Crumly, “Laser mode locking by an external Doppler cell,” Appl. Phys. Lett. 6, 6–8 (1965).
[Crossref]

European Phys. J. D (1)

P. Mathey, M. Grapinet, H. R. Jauslin, B. Sturman, D. Rytz, and S. Odoulov, “Threshold behavior of semi-linear photorefractive oscillator,” European Phys. J. D 39, 445–451 (2006).
[Crossref]

IEEE J. Quantum Electron. (1)

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. QE-20, 12–20 (1984).
[Crossref]

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

Opt. Commun. (2)

L. P. Yatsenko, B. W. Shore, and K. Bergmann, “Theory of a frequency-shifted feedback laser,” Opt. Commun. 236, 183–202 (2004).
[Crossref]

V. V. Ogurtsov, L. P. Yatsenko, V. M. Khodakovskyy, B. W. Shore, G. Bonnet, and K. Bergmann, “Experimental characterization of an Yb3+-doped fiber ring laser with frequency shifted feedback,” Opt. Commun. 266, 627–637 (2006).
[Crossref]

Phys. Rev. Lett. (1)

P. Mathey, S. Odoulov, and D. Rytz, “Instability of single frequency operation in semilinear photorefractive coherent oscillators,” Phys. Rev. Lett. 89, 053901-1-4 (2002).
[Crossref]

Other (2)

George C. Valley, “Competition between forward-and backward-stimulated photorefractive scattering,” J. Opt. Soc. Am. B4, 14–19 (1987); Erratum: J. Opt. Soc. Am. B4, 934 (1987).
[Crossref]

L. Solymar, D. Webb, and A. Grunnet-Jepsen, “The Physics and Applications of Photorefractive Materials,” (Clarendon, Oxford, 1996).

Supplementary Material (5)

» Media 1: MOV (316 KB)     
» Media 2: MOV (434 KB)     
» Media 3: MOV (299 KB)     
» Media 4: MOV (686 KB)     
» Media 5: MOV (824 KB)     

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Figures (6)

Fig. 1.
Fig. 1.

Schematic representation of a semilinear coherent oscillator. Two counterpropagating pump waves (1,2) with the frequency ωpump impinge upon the sample. The oscillation occurs between the photorefractive crystal that serves as an amplifying phase conjugate mirror (PCM) and the conventional mirror M mounted on a piezoceramic holder. An aperture D is placed inside the cavity for the transverse mode control.

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Fig. 2.
Fig. 2.

Diagrams of oscillation frequency self-reproduction in the cavity formed by a phase conjugate mirror (PCM) and a conventional mirror that can be immobile (M) or can move (vibrating mirror VM). The central horizontal line in each frame marks the temporal frequency of the pump wave ωpump . The displacement up and down from this line marks positive and negative detuning with respect to the pump frequency, respectively. The numbers inside the cavity (3, 3′, 4, 4′) label the particular components of the oscillation mode, the arrows show the direction of propagation. The frames (a,b) depict the cavity with the immobile conventional mirror while frames [Media 1] [Media 2] (c,d,e) depict those with the saw-tooth modulation of the mirror position [Media 3] [Media 4] [Media 5].

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Fig. 3.
Fig. 3.

Oscillation frequency versus frequency detuning introduced by a piezo-mirror. The pump intensity ratio is r=120. The data related with the oscillation waves 3 and 4 are in red and blue, respectively.

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Fig. 4.
Fig. 4.

Oscillation frequency versus frequency detuning introduced by a piezo-mirror. The pump intensity ratio is r=2.7. The data related with the oscillation waves 3 and 4 are in red and blue, respectively.

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Fig. 5.
Fig. 5.

Oscillation frequency versus frequency detuning introduced by a piezo-mirror. The pump ratio is r=2.7. The data related with the oscillation waves 3 and 4 are in red and blue, respectively. The pump waves are tilted for 0.1 mrad with respect to the alignment of previous figure.

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Fig. 6.
Fig. 6.

Calculated threshold coupling strength versus frequency detuning of the oscillation which is controlled by the feedback frequency shift Ω M for R=1 and r=1.5.

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Equations (12)

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

∂ A 3 ∂ z = v * A 2 ℓ ,
∂ A 4 ∂ z = v A 1 0 ,
τ ∂ v ∂ t + v = γ I 0 ( A 1 0 * A 4 + A 2 ℓ A 3 * ) .
A 4 ( ℓ , t ) = R A 3 ( ℓ , t ) exp ( i Ω M t ) ,
A 3 ( 0 , t ) = 0 .
A 3 ( z , t ) = a 3 ( z ) exp [ ( p − i Ω M ⁄ 2 ) t ] ,
A 4 ( z , t ) = a 4 ( z ) exp [ ( p + i Ω M ⁄ 2 ) t ] ,
v ( z , t ) = n ( z ) exp [ ( p + i Ω M ⁄ 2 ) t ] .
R r = exp ( 2 a ) + 2 r exp ( a ) cos ⁡ b + r 2 exp ( 2 a ) − 2 exp ( a ) cos ⁡ b + 1 ,
a = γ ℓ ( 1 + τ p ) ( 1 + τ p ) 2 + ( Ω M τ ⁄ 2 ) 2 ,
b = γ ℓ Ω M τ ⁄ 2 ( 1 + τ p ) 2 + ( Ω M τ ⁄ 2 ) 2 ,
R pc = sinh ⁡ 2 ( a ⁄ 2 ) + sin ⁡ 2 ( b ⁄ 2 ) cosh ⁡ 2 [ ( a ⁄ 2 ) − ( ln r ) ⁄ 2 ] − sin ⁡ 2 ( b ⁄ 2 ) .

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