Abstract

We show that the introduction of an angular mismatch for the pump waves results, in the case of nonlocal photorefractive nonlinearity, in a strong almost twofold decrease of the threshold value of the coupling strength for the mirrorless optical oscillation. This surprising feature will lead to a strong modification of the threshold and near-threshold behavior of a vast variety of optical oscillators based on the photorefractive phase conjugation and involving finite-size light beams.

© 2008 Optical Society of America

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References

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  1. B. Y. Zeldovich, N. F. Pilipetsky, and V. V. Shkunov, in Springer Series in Optical Sciences (Springer-Verlag, 1985), vol. 42.
  2. A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 2003).
  3. A. Yariv and D. M. Pepper, Opt. Lett. 1, 16 (1977).
    [CrossRef] [PubMed]
  4. J. Feinberg and R. Hellwarth, Opt. Lett. 5, 519 (1980).
    [CrossRef] [PubMed]
  5. M. Cronin-Golomb, B. Fisher, J. O. White, and A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984).
    [CrossRef]
  6. L. Solymar, D. J. Webb, and A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Clarendon, 1996).
  7. P.Günter and J.-P.Huignard, eds., in Topics in Applied Physics (Springer-Verlag, 1989), vol. 62.
  8. S. Odoulov, M. Soskin, and A. Khyzhnyak, Optical Coherent Oscillators with Degenerate Four-Wave Mixing (Harwood Academic, 1991).
  9. P. Mathey, S. Odoulov, and D. Rytz, J. Opt. Soc. Am. B 19, 2967 (2002).
    [CrossRef]
  10. P. Mathey, M. Grapinet, H. R. Jauslin, B. Sturman, D. Rytz, and S. Odoulov, Eur. Phys. J. D 39, 445 (2006).
    [CrossRef]
  11. C. Denz, J. Golz, and T. Tschudi, Opt. Commun. 72, 129 (1989).
    [CrossRef]
  12. B. I. Sturman, S. G. Odoulov, and M. Yu. Goulkov, Phys. Rep. 275, 197 (1996).
    [CrossRef]
  13. R. Rebhi, P. Mathey, M. Grapinet, H. Jauslin, and S. Odoulov, Appl. Phys. B 91, 583 (2008).
    [CrossRef]
  14. M. Grapinet, P. Mathey, H. Jauslin, B. Sturman, D. Rytz, and S. Odoulov, Eur. Phys. J. D 41, 363 (2007).
    [CrossRef]

2008

R. Rebhi, P. Mathey, M. Grapinet, H. Jauslin, and S. Odoulov, Appl. Phys. B 91, 583 (2008).
[CrossRef]

2007

M. Grapinet, P. Mathey, H. Jauslin, B. Sturman, D. Rytz, and S. Odoulov, Eur. Phys. J. D 41, 363 (2007).
[CrossRef]

2006

P. Mathey, M. Grapinet, H. R. Jauslin, B. Sturman, D. Rytz, and S. Odoulov, Eur. Phys. J. D 39, 445 (2006).
[CrossRef]

2002

1996

B. I. Sturman, S. G. Odoulov, and M. Yu. Goulkov, Phys. Rep. 275, 197 (1996).
[CrossRef]

1989

C. Denz, J. Golz, and T. Tschudi, Opt. Commun. 72, 129 (1989).
[CrossRef]

1984

M. Cronin-Golomb, B. Fisher, J. O. White, and A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984).
[CrossRef]

1980

1977

Cronin-Golomb, M.

M. Cronin-Golomb, B. Fisher, J. O. White, and A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984).
[CrossRef]

Denz, C.

C. Denz, J. Golz, and T. Tschudi, Opt. Commun. 72, 129 (1989).
[CrossRef]

Feinberg, J.

Fisher, B.

M. Cronin-Golomb, B. Fisher, J. O. White, and A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984).
[CrossRef]

Golz, J.

C. Denz, J. Golz, and T. Tschudi, Opt. Commun. 72, 129 (1989).
[CrossRef]

Grapinet, M.

R. Rebhi, P. Mathey, M. Grapinet, H. Jauslin, and S. Odoulov, Appl. Phys. B 91, 583 (2008).
[CrossRef]

M. Grapinet, P. Mathey, H. Jauslin, B. Sturman, D. Rytz, and S. Odoulov, Eur. Phys. J. D 41, 363 (2007).
[CrossRef]

P. Mathey, M. Grapinet, H. R. Jauslin, B. Sturman, D. Rytz, and S. Odoulov, Eur. Phys. J. D 39, 445 (2006).
[CrossRef]

Grunnet-Jepsen, A.

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

Hellwarth, R.

Jauslin, H.

R. Rebhi, P. Mathey, M. Grapinet, H. Jauslin, and S. Odoulov, Appl. Phys. B 91, 583 (2008).
[CrossRef]

M. Grapinet, P. Mathey, H. Jauslin, B. Sturman, D. Rytz, and S. Odoulov, Eur. Phys. J. D 41, 363 (2007).
[CrossRef]

Jauslin, H. R.

P. Mathey, M. Grapinet, H. R. Jauslin, B. Sturman, D. Rytz, and S. Odoulov, Eur. Phys. J. D 39, 445 (2006).
[CrossRef]

Khyzhnyak, A.

S. Odoulov, M. Soskin, and A. Khyzhnyak, Optical Coherent Oscillators with Degenerate Four-Wave Mixing (Harwood Academic, 1991).

Mathey, P.

R. Rebhi, P. Mathey, M. Grapinet, H. Jauslin, and S. Odoulov, Appl. Phys. B 91, 583 (2008).
[CrossRef]

M. Grapinet, P. Mathey, H. Jauslin, B. Sturman, D. Rytz, and S. Odoulov, Eur. Phys. J. D 41, 363 (2007).
[CrossRef]

P. Mathey, M. Grapinet, H. R. Jauslin, B. Sturman, D. Rytz, and S. Odoulov, Eur. Phys. J. D 39, 445 (2006).
[CrossRef]

P. Mathey, S. Odoulov, and D. Rytz, J. Opt. Soc. Am. B 19, 2967 (2002).
[CrossRef]

Odoulov, S.

R. Rebhi, P. Mathey, M. Grapinet, H. Jauslin, and S. Odoulov, Appl. Phys. B 91, 583 (2008).
[CrossRef]

M. Grapinet, P. Mathey, H. Jauslin, B. Sturman, D. Rytz, and S. Odoulov, Eur. Phys. J. D 41, 363 (2007).
[CrossRef]

P. Mathey, M. Grapinet, H. R. Jauslin, B. Sturman, D. Rytz, and S. Odoulov, Eur. Phys. J. D 39, 445 (2006).
[CrossRef]

P. Mathey, S. Odoulov, and D. Rytz, J. Opt. Soc. Am. B 19, 2967 (2002).
[CrossRef]

S. Odoulov, M. Soskin, and A. Khyzhnyak, Optical Coherent Oscillators with Degenerate Four-Wave Mixing (Harwood Academic, 1991).

Odoulov, S. G.

B. I. Sturman, S. G. Odoulov, and M. Yu. Goulkov, Phys. Rep. 275, 197 (1996).
[CrossRef]

Pepper, D. M.

Pilipetsky, N. F.

B. Y. Zeldovich, N. F. Pilipetsky, and V. V. Shkunov, in Springer Series in Optical Sciences (Springer-Verlag, 1985), vol. 42.

Rebhi, R.

R. Rebhi, P. Mathey, M. Grapinet, H. Jauslin, and S. Odoulov, Appl. Phys. B 91, 583 (2008).
[CrossRef]

Rytz, D.

M. Grapinet, P. Mathey, H. Jauslin, B. Sturman, D. Rytz, and S. Odoulov, Eur. Phys. J. D 41, 363 (2007).
[CrossRef]

P. Mathey, M. Grapinet, H. R. Jauslin, B. Sturman, D. Rytz, and S. Odoulov, Eur. Phys. J. D 39, 445 (2006).
[CrossRef]

P. Mathey, S. Odoulov, and D. Rytz, J. Opt. Soc. Am. B 19, 2967 (2002).
[CrossRef]

Shkunov, V. V.

B. Y. Zeldovich, N. F. Pilipetsky, and V. V. Shkunov, in Springer Series in Optical Sciences (Springer-Verlag, 1985), vol. 42.

Solymar, L.

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

Soskin, M.

S. Odoulov, M. Soskin, and A. Khyzhnyak, Optical Coherent Oscillators with Degenerate Four-Wave Mixing (Harwood Academic, 1991).

Sturman, B.

M. Grapinet, P. Mathey, H. Jauslin, B. Sturman, D. Rytz, and S. Odoulov, Eur. Phys. J. D 41, 363 (2007).
[CrossRef]

P. Mathey, M. Grapinet, H. R. Jauslin, B. Sturman, D. Rytz, and S. Odoulov, Eur. Phys. J. D 39, 445 (2006).
[CrossRef]

Sturman, B. I.

B. I. Sturman, S. G. Odoulov, and M. Yu. Goulkov, Phys. Rep. 275, 197 (1996).
[CrossRef]

Tschudi, T.

C. Denz, J. Golz, and T. Tschudi, Opt. Commun. 72, 129 (1989).
[CrossRef]

Webb, D. J.

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

White, J. O.

M. Cronin-Golomb, B. Fisher, J. O. White, and A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984).
[CrossRef]

Yariv, A.

M. Cronin-Golomb, B. Fisher, J. O. White, and A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984).
[CrossRef]

A. Yariv and D. M. Pepper, Opt. Lett. 1, 16 (1977).
[CrossRef] [PubMed]

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 2003).

Yeh, P.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 2003).

Yu. Goulkov, M.

B. I. Sturman, S. G. Odoulov, and M. Yu. Goulkov, Phys. Rep. 275, 197 (1996).
[CrossRef]

Zeldovich, B. Y.

B. Y. Zeldovich, N. F. Pilipetsky, and V. V. Shkunov, in Springer Series in Optical Sciences (Springer-Verlag, 1985), vol. 42.

Appl. Phys. B

R. Rebhi, P. Mathey, M. Grapinet, H. Jauslin, and S. Odoulov, Appl. Phys. B 91, 583 (2008).
[CrossRef]

Eur. Phys. J. D

M. Grapinet, P. Mathey, H. Jauslin, B. Sturman, D. Rytz, and S. Odoulov, Eur. Phys. J. D 41, 363 (2007).
[CrossRef]

P. Mathey, M. Grapinet, H. R. Jauslin, B. Sturman, D. Rytz, and S. Odoulov, Eur. Phys. J. D 39, 445 (2006).
[CrossRef]

IEEE J. Quantum Electron.

M. Cronin-Golomb, B. Fisher, J. O. White, and A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

C. Denz, J. Golz, and T. Tschudi, Opt. Commun. 72, 129 (1989).
[CrossRef]

Opt. Lett.

Phys. Rep.

B. I. Sturman, S. G. Odoulov, and M. Yu. Goulkov, Phys. Rep. 275, 197 (1996).
[CrossRef]

Other

B. Y. Zeldovich, N. F. Pilipetsky, and V. V. Shkunov, in Springer Series in Optical Sciences (Springer-Verlag, 1985), vol. 42.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 2003).

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

P.Günter and J.-P.Huignard, eds., in Topics in Applied Physics (Springer-Verlag, 1989), vol. 62.

S. Odoulov, M. Soskin, and A. Khyzhnyak, Optical Coherent Oscillators with Degenerate Four-Wave Mixing (Harwood Academic, 1991).

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Figures (3)

Fig. 1
Fig. 1

Schematic of the PC for the cases of dominating (a) transmission and (b) reflection grating; l is the crystal thickness, and the parallel dotted lines illustrate the index fringes.

Fig. 2
Fig. 2

Threshold values of g versus Δ l for the mirrorless oscillation at (a) r = exp ( π ) ; (b) corresponding values of Ω t r . The four lowest branches, j = 1 , 1, 2, and 3, are shown.

Fig. 3
Fig. 3

Contour plots g ( Δ l , r ) = 3.73 , 3.75, 3.8, and 3.9 illustrating the minimum coupling strength for the mirrorless oscillation. The cental dot corresponds to g 3.726 .

Equations (12)

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

a 1 e i k 1 r + a 2 e i k 2 r + a 3 e i k 3 r + i ( Δ 2 ) z + a 4 e i k 4 r + i ( Δ 2 ) z + c.c. ,
a 1 z = u * a 4 ,
a 2 z = u a 3 ,
( z + i Δ 2 ) a 3 = s u * a 2 ,
( z + i Δ 2 ) a 4 = s u a 1 ,
t r u t + u = γ I 0 ( a 1 * a 4 + a 2 a 3 * ) ,
d d z ( a 3 * a 4 ) = ( S 33 S 34 S 43 S 44 ) ( a 3 * a 4 ) ,
S 33 = s γ a 2 2 I 0 ( 1 i Ω t r ) + i Δ 2 , S 34 = s γ a 1 * a 2 * I 0 ( 1 i Ω t r ) ,
S 44 = s γ a 1 2 I 0 ( 1 i Ω t r ) i Δ 2 , S 43 = s γ a 1 a 2 I 0 ( 1 i Ω t r ) .
Γ ± = h ± h 2 d ,
ρ = S 43 1 ( e Γ + l e Γ l ) ( Γ + S 44 ) 1 e Γ + l ( Γ S 44 ) 1 e Γ l .
exp [ ( Γ + Γ ) l ] = ( Γ S 44 ) ( Γ + S 44 ) .

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