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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  1. R. Trebino ed., Frequency-resolved optical gating: The measurement of ultrashort laser pulses, (Kluwer Academic Publishers, Boston/Dodrecht/London2002).
    [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 2nd-harmonic generation,” J. Opt. Soc. Am. B 11, 2206–2215 (1994).
    [Crossref]
  4. M.D. Thomson, J.M. Dudley, and L.P. Barry, et al., “Complete pulse characterization at 1.5 mu m by cross-phase modulation in optical fibers,” Opt. Lett. 23, 1582–1584 (1998).
    [Crossref]
  5. J.M. Dudley, L.P. Barry, and J.D. Harvey, et al., “Complete characterization of ultrashort pulse sources at 1550 nm,” IEEE J. Quantum Electron. 35, 441–450 (1999).
    [Crossref]
  6. J.W. Nicholson, F.G. Omenetto, D.J. Funk, and A.J. Taylor, “Evolving FROGS: phase retrieval from frequency-resolved optical gating measurements by use of genetic algorithms,” Opt. Lett. 24, 490–492 (1999).
    [Crossref]
  7. P. Honzatko, J. Kanka, and 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 and M.P. Petrov, “Passive mode locking in a birefringent fiber laser,” Tech. Phys. Lett. 22, 153–155 (1996).
  9. M. Horowitz and Y. Silberberg, “Nonlinear filtering by use of intensity-dependent polarization rotation in birefringent fibers,” Opt. Lett. 22, 1760–1762 (1997).
    [Crossref]
  10. 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]
  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, and M. P. Vecchi, “Optimization by Simulated Annealing,” Science 220, 671–680 (1983).
    [Crossref] [PubMed]
  13. S. Geman and 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]
  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: http://www.gnu.org/software/gsl

1999 (2)

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

J.W. Nicholson, F.G. Omenetto, D.J. Funk, and A.J. Taylor, “Evolving FROGS: phase retrieval from frequency-resolved optical gating measurements by use of genetic algorithms,” Opt. Lett. 24, 490–492 (1999).
[Crossref]

1998 (1)

1997 (4)

M. Horowitz and Y. Silberberg, “Nonlinear filtering by use of intensity-dependent polarization rotation in birefringent fibers,” Opt. Lett. 22, 1760–1762 (1997).
[Crossref]

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]

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]

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]

1996 (1)

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

1994 (1)

1984 (1)

S. Geman and 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]

1983 (1)

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by Simulated Annealing,” Science 220, 671–680 (1983).
[Crossref] [PubMed]

1953 (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]

Barry, L.P.

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

M.D. Thomson, J.M. Dudley, and L.P. Barry, et al., “Complete pulse characterization at 1.5 mu m by cross-phase modulation in optical fibers,” Opt. Lett. 23, 1582–1584 (1998).
[Crossref]

Bryskin, V.V.

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

DeLong, K.W.

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]

K.W. DeLong, R. Trebino, J. Hunter, and W.E. White, “Frequency-resolved optical gating with the use of 2nd-harmonic generation,” J. Opt. Soc. Am. B 11, 2206–2215 (1994).
[Crossref]

Dudley, J.M.

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

M.D. Thomson, J.M. Dudley, and L.P. Barry, et al., “Complete pulse characterization at 1.5 mu m by cross-phase modulation in optical fibers,” Opt. Lett. 23, 1582–1584 (1998).
[Crossref]

Fittinghoff, D.N.

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]

Franco, M.A.

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]

Funk, D.J.

Gelatt, C. D.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by Simulated Annealing,” Science 220, 671–680 (1983).
[Crossref] [PubMed]

Geman, D.

S. Geman and 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]

Geman, S.

S. Geman and 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]

Harvey, J.D.

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

Honzatko, P.

P. Honzatko, J. Kanka, and 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.

Horowitz, M.

Hunter, J.

Kaminskii, A.S.

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]

Kane, D.J.

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]

Kanka, J.

P. Honzatko, J. Kanka, and 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.

Kirkpatrick, S.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by Simulated Annealing,” Science 220, 671–680 (1983).
[Crossref] [PubMed]

Kosarev, E.L.

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]

Krumbuegel, M.A.

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]

Lange, H.R.

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]

Lavrov, E.V.

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]

Metropolis, N.

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]

Mysyrowicz, A.

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]

Nicholson, J.W.

Omenetto, F.G.

Petrov, M.P.

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

Prade, B.S.

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]

Ripoche, J.-F.

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]

Rosenbluth, A.

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]

Rosenbluth, M.

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]

Silberberg, Y.

Sweetser, J.N.

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]

Taylor, A.J.

Teller, A.

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]

Teller, E.

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]

Thomson, M.D.

Trebino, R.

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]

K.W. DeLong, R. Trebino, J. Hunter, and W.E. White, “Frequency-resolved optical gating with the use of 2nd-harmonic generation,” J. Opt. Soc. Am. B 11, 2206–2215 (1994).
[Crossref]

Vecchi, M. P.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by Simulated Annealing,” Science 220, 671–680 (1983).
[Crossref] [PubMed]

Vrany, B.

P. Honzatko, J. Kanka, and 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.

White, W.E.

IEEE J. Quantum Electron. (1)

J.M. Dudley, L.P. Barry, and 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 Machine Intelligence (1)

S. Geman and 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, and M. P. Vecchi, “Optimization by Simulated Annealing,” Science 220, 671–680 (1983).
[Crossref] [PubMed]

Tech. Phys. Lett. (1)

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

Other (3)

R. Trebino ed., Frequency-resolved optical gating: The measurement of ultrashort laser pulses, (Kluwer Academic Publishers, Boston/Dodrecht/London2002).
[Crossref]

P. Honzatko, J. Kanka, and 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.

See pages of the GNU Scientific Library Project: http://www.gnu.org/software/gsl

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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)

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

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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