Abstract

The second-order parametric lens effect shows a temporal limit as a saturable-absorber device for operation in the ultrafast time region. We present and discuss an extended theoretical model dealing with second-order cascaded processes in a nonstationary condition. Experimentally we report the detection of the time-averaged lens effect in the hundred-of-femtoseconds range, discussing the limits that arise in this ultrafast optical region.

© 1995 Optical Society of America

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References

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  1. D. Pierrottet, B. Berman, M. Vannini, D. McGraw, Opt. Lett. 18, 4 (1993).
    [CrossRef]
  2. R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, Opt. Lett. 17, 28 (1992).
    [CrossRef] [PubMed]
  3. D. J. Hagan, Z. Wang, G. Stegeman, E. W. Van Stryland, M. Sheik-Bahae, G. Assanto, Opt. Lett. 19, 17 (1994).
    [CrossRef]
  4. H. A. Haus, J. G. Fujimoto, E. P. Ippen, IEEE J. Quantum Electron. 28, 10 (1992).
  5. J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
    [CrossRef]
  6. J. T. Manassah, Appl. Opt. 27, 21, 4365 (1988).
    [CrossRef] [PubMed]
  7. K. A. Stankov, V. P. Tzolov, M. G. Mirkov, Opt. Lett. 16, 14 (1991).
  8. K. A. Stankov, Appl. Phys. B 54, 303 (1992).
    [CrossRef]

1994 (1)

D. J. Hagan, Z. Wang, G. Stegeman, E. W. Van Stryland, M. Sheik-Bahae, G. Assanto, Opt. Lett. 19, 17 (1994).
[CrossRef]

1993 (1)

1992 (3)

R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, Opt. Lett. 17, 28 (1992).
[CrossRef] [PubMed]

H. A. Haus, J. G. Fujimoto, E. P. Ippen, IEEE J. Quantum Electron. 28, 10 (1992).

K. A. Stankov, Appl. Phys. B 54, 303 (1992).
[CrossRef]

1991 (1)

K. A. Stankov, V. P. Tzolov, M. G. Mirkov, Opt. Lett. 16, 14 (1991).

1988 (1)

J. T. Manassah, Appl. Opt. 27, 21, 4365 (1988).
[CrossRef] [PubMed]

1962 (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Assanto, G.

D. J. Hagan, Z. Wang, G. Stegeman, E. W. Van Stryland, M. Sheik-Bahae, G. Assanto, Opt. Lett. 19, 17 (1994).
[CrossRef]

Berman, B.

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

DeSalvo, R.

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Fujimoto, J. G.

H. A. Haus, J. G. Fujimoto, E. P. Ippen, IEEE J. Quantum Electron. 28, 10 (1992).

Hagan, D. J.

D. J. Hagan, Z. Wang, G. Stegeman, E. W. Van Stryland, M. Sheik-Bahae, G. Assanto, Opt. Lett. 19, 17 (1994).
[CrossRef]

R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, Opt. Lett. 17, 28 (1992).
[CrossRef] [PubMed]

Haus, H. A.

H. A. Haus, J. G. Fujimoto, E. P. Ippen, IEEE J. Quantum Electron. 28, 10 (1992).

Ippen, E. P.

H. A. Haus, J. G. Fujimoto, E. P. Ippen, IEEE J. Quantum Electron. 28, 10 (1992).

Manassah, J. T.

J. T. Manassah, Appl. Opt. 27, 21, 4365 (1988).
[CrossRef] [PubMed]

McGraw, D.

Mirkov, M. G.

K. A. Stankov, V. P. Tzolov, M. G. Mirkov, Opt. Lett. 16, 14 (1991).

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Pierrottet, D.

Sheik-Bahae, M.

D. J. Hagan, Z. Wang, G. Stegeman, E. W. Van Stryland, M. Sheik-Bahae, G. Assanto, Opt. Lett. 19, 17 (1994).
[CrossRef]

R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, Opt. Lett. 17, 28 (1992).
[CrossRef] [PubMed]

Stankov, K. A.

K. A. Stankov, Appl. Phys. B 54, 303 (1992).
[CrossRef]

K. A. Stankov, V. P. Tzolov, M. G. Mirkov, Opt. Lett. 16, 14 (1991).

Stegeman, G.

D. J. Hagan, Z. Wang, G. Stegeman, E. W. Van Stryland, M. Sheik-Bahae, G. Assanto, Opt. Lett. 19, 17 (1994).
[CrossRef]

R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, Opt. Lett. 17, 28 (1992).
[CrossRef] [PubMed]

Tzolov, V. P.

K. A. Stankov, V. P. Tzolov, M. G. Mirkov, Opt. Lett. 16, 14 (1991).

Van Stryland, E. W.

D. J. Hagan, Z. Wang, G. Stegeman, E. W. Van Stryland, M. Sheik-Bahae, G. Assanto, Opt. Lett. 19, 17 (1994).
[CrossRef]

R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, Opt. Lett. 17, 28 (1992).
[CrossRef] [PubMed]

Vannini, M.

Wang, Z.

D. J. Hagan, Z. Wang, G. Stegeman, E. W. Van Stryland, M. Sheik-Bahae, G. Assanto, Opt. Lett. 19, 17 (1994).
[CrossRef]

Appl. Opt. (1)

J. T. Manassah, Appl. Opt. 27, 21, 4365 (1988).
[CrossRef] [PubMed]

Appl. Phys. B (1)

K. A. Stankov, Appl. Phys. B 54, 303 (1992).
[CrossRef]

IEEE J. Quantum Electron. (1)

H. A. Haus, J. G. Fujimoto, E. P. Ippen, IEEE J. Quantum Electron. 28, 10 (1992).

Opt. Lett. (4)

D. Pierrottet, B. Berman, M. Vannini, D. McGraw, Opt. Lett. 18, 4 (1993).
[CrossRef]

R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, Opt. Lett. 17, 28 (1992).
[CrossRef] [PubMed]

D. J. Hagan, Z. Wang, G. Stegeman, E. W. Van Stryland, M. Sheik-Bahae, G. Assanto, Opt. Lett. 19, 17 (1994).
[CrossRef]

K. A. Stankov, V. P. Tzolov, M. G. Mirkov, Opt. Lett. 16, 14 (1991).

Phys. Rev. (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Temporal evolution along the pulse duration of the dioptric power of a nonlinear lens normalized to the peak value in a stationary condition. Dashed curve, stationary interaction (σ = 0); solid curve, nonstationary interaction (σ = 1); dotted curve, fundamental pulse amplitude profile.

Fig. 2
Fig. 2

Experimental setup.

Fig. 3
Fig. 3

Spot size versus the total power of the fundamental beam; their relative phase difference with respect to Θ is 85° ± 5°. The spot-size modulation amplitude is Δw2/w2 = ±1.5%, with 〈η̄2〉 = 1.5%.

Equations (8)

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σ = L γ / 2 τ p ,
( z + 1 u 1 t ) ρ 1 = i K ρ 1 * ρ 2 ,
( z + 1 u 2 t ) ρ 2 = i K ρ 1 2 ,
ρ 1 ( t , L ) = ρ 10 exp ( i ϕ 10 ) g ( U 1 ) [ 1 + r 2 ( sin Θ - i cos Θ ) × η ¯ 2 ( τ 1 / τ 2 ) δ 1 ( t ) - η ¯ 2 δ 2 ( t ) ] ,
δ 1 ( τ ) = L eff - 1 0 L h [ U 1 + ζ γ + Δ t ] d ζ ,
δ 2 ( τ ) = L eff - 2 0 L d ζ 0 ζ g 2 [ U 1 + ( ζ - ζ ) γ ] d ζ .
1 / f ( Θ , t ) = - ( 4 η ¯ 2 / k 1 ω 2 2 ) r 2 ( τ 1 / τ 2 ) δ 1 ( t ) cos Θ ,
P 1 ( Θ , t ) = P 10 g 2 ( t ) [ 1 + 2 r 2 η ¯ 2 ( τ 1 / τ 2 ) δ 1 ( t ) × sin Θ - 2 η ¯ 2 δ 2 ( t ) ] .

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