Abstract

The simulated annealing method is used for retrieving the amplitude and phase from cross-phase modulation spectrograms. The method allows us to take into account the birefringence of the measurement fiber and resolution of the optical spectrum analyzer. The influence of the birefringence and analyzer resolution are discussed.

© 2004 Optical Society of America

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References

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    [CrossRef]
  2. R. Trebino, K.W. DeLong, D.N. Fittinghoff, J.N. Sweetser, M.A. Krumbuegel, and D.J. Kane, �??Measuring Ultrashort Laser Pulses in the Time-Frequency Domain Using Frequency-Resolved Optical Gating,�?? Review of Scientific Instruments 68, 3277�??3295 (1997).
    [CrossRef]
  3. K.W. DeLong, R. Trebino, J. Hunter, and W.E. White, �??Frequency-resolved optical gating with the use of 2ndharmonic generation,�?? J. Opt. Soc. Am. B 11, 2206�??2215 (1994).
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  5. J.M. Dudley, L.P. Barry, J.D. Harvey, et al., �??Complete characterization of ultrashort pulse sources at 1550 nm,�?? IEEE J. Quantum Electron. 35, 441�??450 (1999).
    [CrossRef]
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  7. P. Honzatko, J. Kanka, B. Vrany, Manuscript in preparation. Some details were presented in P. Honzatko, J. Kanka, B. Vrany, �??Alignment-free CPM FROG based on a microstructure optical fiber,�?? ETOS 2004, Cork, Ireland.
  8. V.V. Bryskin, M.P. Petrov, �??Passive mode locking in a birefringent fiber laser,�?? Tech. Phys. Lett. 22, 153�??155 (1996).
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  11. N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller, �??Equation of State Calculations by Fast Computing Machines,�?? J. Chem. Phys. 21, 1087�??1092 (1953).
    [CrossRef]
  12. S. Kirkpatrick, C. D. Gelatt Jr., M. P. Vecchi, �??Optimization by Simulated Annealing,�?? Science 220, 671�??680 (1983).
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  13. S. Geman, D. Geman, �??Stochastic relaxation, gibbs distributions, and the bayesian restoration of images,�?? IEEE Trans. on Pattern Analysis and Machine Intelligence 6, 721�??741 (1984).
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  14. M.A. Franco, H.R. Lange, J.-F. Ripoche, B.S. Prade, and A. Mysyrowicz, �??Characterization of ultra-short pulses by cross-phase modulation,�?? Opt. Commun. 140, 331�??340 (1997).
    [CrossRef]
  15. See pages of the GNU Scientific Library Project: <a href="http://www.gnu.org/software/gsl">http://www.gnu.org/software/gsl</a>

ETOS 2004 (1)

P. Honzatko, J. Kanka, B. Vrany, Manuscript in preparation. Some details were presented in P. Honzatko, J. Kanka, B. Vrany, �??Alignment-free CPM FROG based on a microstructure optical fiber,�?? ETOS 2004, Cork, Ireland.

IEEE J. Quantum Electron. (1)

J.M. Dudley, L.P. Barry, J.D. Harvey, et al., �??Complete characterization of ultrashort pulse sources at 1550 nm,�?? IEEE J. Quantum Electron. 35, 441�??450 (1999).
[CrossRef]

IEEE Trans. on Pattern Analysis and Mach (1)

S. Geman, D. Geman, �??Stochastic relaxation, gibbs distributions, and the bayesian restoration of images,�?? IEEE Trans. on Pattern Analysis and Machine Intelligence 6, 721�??741 (1984).
[CrossRef]

J. Chem. Phys. (1)

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller, �??Equation of State Calculations by Fast Computing Machines,�?? J. Chem. Phys. 21, 1087�??1092 (1953).
[CrossRef]

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

Meas. Sci. Technol. (1)

A.S. Kaminskii, E.L. Kosarev, and E.V. Lavrov, �??Using comb-like instrumental functions in high-resolution spectroscopy,�?? Meas. Sci. Technol. 8, 864�??870 (1997).
[CrossRef]

Opt. Commun. (1)

M.A. Franco, H.R. Lange, J.-F. Ripoche, B.S. Prade, and A. Mysyrowicz, �??Characterization of ultra-short pulses by cross-phase modulation,�?? Opt. Commun. 140, 331�??340 (1997).
[CrossRef]

Opt. Lett. (3)

Review of Scientific Instruments (1)

R. Trebino, K.W. DeLong, D.N. Fittinghoff, J.N. Sweetser, M.A. Krumbuegel, and D.J. Kane, �??Measuring Ultrashort Laser Pulses in the Time-Frequency Domain Using Frequency-Resolved Optical Gating,�?? Review of Scientific Instruments 68, 3277�??3295 (1997).
[CrossRef]

Science (1)

S. Kirkpatrick, C. D. Gelatt Jr., M. P. Vecchi, �??Optimization by Simulated Annealing,�?? Science 220, 671�??680 (1983).
[CrossRef] [PubMed]

Tech. Phys. Lett. (1)

V.V. Bryskin, M.P. Petrov, �??Passive mode locking in a birefringent fiber laser,�?? Tech. Phys. Lett. 22, 153�??155 (1996).

Other (2)

R. Trebino ed., Frequency-resolved optical gating: The measurement of ultrashort laser pulses, (Kluwer Academic Publishers, Boston/Dodrecht/London 2002).
[CrossRef]

See pages of the GNU Scientific Library Project: <a href="http://www.gnu.org/software/gsl">http://www.gnu.org/software/gsl</a>

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Figures (4)

Fig. 1.
Fig. 1.

Schematic set-up for fiber FROG measurement.

Fig. 2.
Fig. 2.

Comparison of the numerically generated field and reconstructed field for test pulses. Figures a)–d) correspond to pulses no. 1–4 of Tab. 1, respectively.

Fig. 3.
Fig. 3.

a) Noisy spectrogram with contours in decibels. b) Original and reconstructed pulse.

Fig. 4.
Fig. 4.

a) Influence of walk-off and OSA resolution on the pulse reconstruction. b) Influence of walk-off between probe and cross-polarized pulse on the mean frequency of spectrogram.

Tables (1)

Tables Icon

Table 1. Summary of test pulses parameters. For all pulses v=0.

Equations (11)

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i z E x , y + β 2 2 tt E x , y ± i σ t E x , y ± κ E x , y + γ [ ( E x , y 2 + 2 3 E y , x 2 ) E x , y + 1 3 E y , x 2 E x , y * ] = 0 ,
E ˜ x = E x e i κ z , E ˜ y = E y e i κ z ,
i z E ˜ x , y + β 2 2 tt E ˜ x , y ± i σ t E ˜ x , y + γ ( E ˜ x , y | 2 + 2 3 E ˜ y , x | 2 ) E ˜ x , y + γ 3 E ˜ y , x 2 E ˜ x , y * e 4 i κ z = 0 ,
i z E ˜ x , y ± i σ t E ˜ x , y + γ ( E ˜ x , y 2 + 2 3 E ˜ y , x | 2 ) E ˜ x , y = 0 .
E x , y ( z , t ) = E x , y ( 0 , t σ z ) exp [ i γ E x , y ( 0 , t σ z ) | 2 z + i γ 3 z z E y , x ( 0 , t σ ξ ) | 2 d ξ ] .
E SIG ( t , τ ) = r E ( 0 , t σ L ) exp [ i γ r 2 E ( 0 , t σ L ) 2 z + i γ ( 1 r 2 ) 3 L L E ( 0 , t τ + σ ξ ) 2 d ξ ] ,
S ( ω , τ ) = E SIG ( t , τ ) exp [ i ω t ] d t 2 .
S ( ω , τ ) = S ( Ω , τ ) K ( ω Ω ) d Ω .
E ( t ) exp [ i ψ ( t ) ] i = 1 n p S i exp [ 2 l n ( 2 ) ( t t i / 2 T ) 2 ] ,
ψ ( t ) = a ( t T ) 2 + b ( t T ) 3 + c ( t T ) 4 + q E ( t ) 2 ,
E ( t ) = 𝓕 1 { exp [ i ξ ( ν ) ] 𝓕 [ E ( t ) ] ( ν ) } ( t ) , ξ ( ν ) = u ( ν T ) 3 + v ( ν T ) 4 + x ( ν T ) 5 .

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