Abstract

Linear pulse-characterization techniques based on electrically driven temporal modulators can measure the electric field of optical pulses with high sensitivity and accuracy. Synchronization of the electric-drive signal to the optical source under test is paramount to their implementation, and it is important to understand the impact of relative synchronization jitter on the measured experimental trace and on the reconstructed electric field. Derivations and simulations are presented for linear spectrography, spectral-shearing interferometry, and simplified chronocyclic tomography. For these three techniques, accurate characterization is obtained for relative jitter with a standard deviation as high as several times the pulse duration.

© 2008 Optical Society of America

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  1. P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H. G. Muller, and P. Agostini, "Observation of a train of attosecond pulses from high harmonic generation," Science 292, 1689-1692 (2001).
    [CrossRef] [PubMed]
  2. I. A. Walmsley and V. Wong, "Characterization of the electric field of ultrashort optical pulses," J. Opt. Soc. Am. B 13, 2453??2463 (1996).
    [CrossRef]
  3. C. Dorrer and I. Kang, "Linear self-referencing optical pulse characterization techniques," to be published in the J. Opt. Soc. Am. B (invited).
  4. C. Dorrer and I. Kang, "Simultaneous temporal characterization of telecommunication optical pulses and modulators by use of spectrograms," Opt. Lett. 27, 1315??1317 (2002).
    [CrossRef]
  5. J. Bromage, C. Dorrer, I. A. Begishev, N. G. Usechak, and J. D. Zuegel, "Highly sensitive, single-shot characterization for pulse widths from 0.4 to 85 ps using electro-optic shearing interferometry," Opt. Lett. 31, 3523??3525 (2006).
    [CrossRef] [PubMed]
  6. B. C. Thomsen, M. A. F. Roelens, R. T. Watts, and D. J. Richardson, "Comparison between nonlinear and linear spectrographic techniques for the complete characterization of high bit-rate pulses used in optical communications," IEEE Photon. Technol. Lett. 17, 1914??1916 (2005).
    [CrossRef]
  7. K. T. Vu, A. Malinowski, M. A. F. Roelens, M. Ibsen, P. Petropoulos, and D. J. Richardson, "Full characterisation of low power picosecond pulses from a gain-switched diode laser using electro-optic modulation based frog," presented at CLEO/QELS 2007, Baltimore, MD, 6??11 May 2007 (Paper CFF4).
  8. C. Dorrer and I. Kang, "Highly sensitive direct characterization of femtosecond pulses by electro-optic spectral shearing interferometry," Opt. Lett. 28, 477??479 (2003).
    [CrossRef] [PubMed]
  9. C. Dorrer and I. Kang, "Complete temporal characterization of short optical pulses by simplified chronocyclic tomography," Opt. Lett. 28, 1481??1483 (2003).
    [CrossRef] [PubMed]
  10. I. Kang, C. Dorrer, and F. Quochi, "Implementation of electro-optic spectral shearing interferometry for ultrashort pulse characterization," Opt. Lett. 28, 2264??2266 (2003).
    [CrossRef] [PubMed]
  11. C. Dorrer and I. A. Walmsley, "Accuracy criterion for ultrashort pulse characterization techniques: Application to spectral phase interferometry for direct electric field reconstruction," J. Opt. Soc. Am. B 19, 1019??1029 (2002).
    [CrossRef]
  12. C. Dorrer and I. Kang, "Real-time implementation of linear spectrograms for the characterization of high bit-rate optical pulse trains," IEEE Photon. Technol. Lett. 16, 858??860 (2004).
    [CrossRef]
  13. D. J. Kane, "Recent progress toward real-time measurement of ultrashort laser pulses," IEEE J. Quantum Electron. 35, 421??431 (1999).
    [CrossRef]
  14. R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweester, M. A. Krumbügel, B. A. Richman, and D. J. Kane, "Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating," Rev. Sci. Instrum. 68, 3277-3295 (1997).
    [CrossRef]
  15. C. Dorrer, "Investigation of the spectrogram techniques for the characterization of picosecond optical pulses," in Optical Fiber Communication Conference, 2005, Technical Digest, OFC/NOFEC (IEEE, New York, 2005), Vol. 2, Paper OTuB3.
  16. V. A. Zubov and T. I. Kuznetsova, "Solution of the phase problem for time-dependent optical signals by an interference system," Sov. J. Quantum Electron. 21, 1285??1286 (1991).
    [CrossRef]
  17. V. Wong and I. A. Walmsley, "Analysis of ultrashort pulse-shape measurement using linear interferometers," Opt. Lett. 19, 287??289 (1994).
    [CrossRef] [PubMed]
  18. I. Kang and C. Dorrer, "Highly sensitive differential tomographic technique for real-time ultrashort pulse characterization," Opt. Lett. 30, 1545??1547 (2005).
    [CrossRef] [PubMed]

2006 (1)

2005 (2)

I. Kang and C. Dorrer, "Highly sensitive differential tomographic technique for real-time ultrashort pulse characterization," Opt. Lett. 30, 1545??1547 (2005).
[CrossRef] [PubMed]

B. C. Thomsen, M. A. F. Roelens, R. T. Watts, and D. J. Richardson, "Comparison between nonlinear and linear spectrographic techniques for the complete characterization of high bit-rate pulses used in optical communications," IEEE Photon. Technol. Lett. 17, 1914??1916 (2005).
[CrossRef]

2004 (1)

C. Dorrer and I. Kang, "Real-time implementation of linear spectrograms for the characterization of high bit-rate optical pulse trains," IEEE Photon. Technol. Lett. 16, 858??860 (2004).
[CrossRef]

2003 (3)

2002 (2)

2001 (1)

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H. G. Muller, and P. Agostini, "Observation of a train of attosecond pulses from high harmonic generation," Science 292, 1689-1692 (2001).
[CrossRef] [PubMed]

1999 (1)

D. J. Kane, "Recent progress toward real-time measurement of ultrashort laser pulses," IEEE J. Quantum Electron. 35, 421??431 (1999).
[CrossRef]

1997 (1)

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweester, M. A. Krumbügel, B. A. Richman, and D. J. Kane, "Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating," Rev. Sci. Instrum. 68, 3277-3295 (1997).
[CrossRef]

1996 (1)

1994 (1)

1991 (1)

V. A. Zubov and T. I. Kuznetsova, "Solution of the phase problem for time-dependent optical signals by an interference system," Sov. J. Quantum Electron. 21, 1285??1286 (1991).
[CrossRef]

Agostini, P.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H. G. Muller, and P. Agostini, "Observation of a train of attosecond pulses from high harmonic generation," Science 292, 1689-1692 (2001).
[CrossRef] [PubMed]

Augé, F.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H. G. Muller, and P. Agostini, "Observation of a train of attosecond pulses from high harmonic generation," Science 292, 1689-1692 (2001).
[CrossRef] [PubMed]

Balcou, Ph.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H. G. Muller, and P. Agostini, "Observation of a train of attosecond pulses from high harmonic generation," Science 292, 1689-1692 (2001).
[CrossRef] [PubMed]

Begishev, I. A.

Breger, P.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H. G. Muller, and P. Agostini, "Observation of a train of attosecond pulses from high harmonic generation," Science 292, 1689-1692 (2001).
[CrossRef] [PubMed]

Bromage, J.

DeLong, K. W.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweester, M. A. Krumbügel, B. A. Richman, and D. J. Kane, "Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating," Rev. Sci. Instrum. 68, 3277-3295 (1997).
[CrossRef]

Dorrer, C.

J. Bromage, C. Dorrer, I. A. Begishev, N. G. Usechak, and J. D. Zuegel, "Highly sensitive, single-shot characterization for pulse widths from 0.4 to 85 ps using electro-optic shearing interferometry," Opt. Lett. 31, 3523??3525 (2006).
[CrossRef] [PubMed]

I. Kang and C. Dorrer, "Highly sensitive differential tomographic technique for real-time ultrashort pulse characterization," Opt. Lett. 30, 1545??1547 (2005).
[CrossRef] [PubMed]

C. Dorrer and I. Kang, "Real-time implementation of linear spectrograms for the characterization of high bit-rate optical pulse trains," IEEE Photon. Technol. Lett. 16, 858??860 (2004).
[CrossRef]

C. Dorrer and I. Kang, "Highly sensitive direct characterization of femtosecond pulses by electro-optic spectral shearing interferometry," Opt. Lett. 28, 477??479 (2003).
[CrossRef] [PubMed]

C. Dorrer and I. Kang, "Complete temporal characterization of short optical pulses by simplified chronocyclic tomography," Opt. Lett. 28, 1481??1483 (2003).
[CrossRef] [PubMed]

I. Kang, C. Dorrer, and F. Quochi, "Implementation of electro-optic spectral shearing interferometry for ultrashort pulse characterization," Opt. Lett. 28, 2264??2266 (2003).
[CrossRef] [PubMed]

C. Dorrer and I. A. Walmsley, "Accuracy criterion for ultrashort pulse characterization techniques: Application to spectral phase interferometry for direct electric field reconstruction," J. Opt. Soc. Am. B 19, 1019??1029 (2002).
[CrossRef]

C. Dorrer and I. Kang, "Simultaneous temporal characterization of telecommunication optical pulses and modulators by use of spectrograms," Opt. Lett. 27, 1315??1317 (2002).
[CrossRef]

Fittinghoff, D. N.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweester, M. A. Krumbügel, B. A. Richman, and D. J. Kane, "Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating," Rev. Sci. Instrum. 68, 3277-3295 (1997).
[CrossRef]

Kane, D. J.

D. J. Kane, "Recent progress toward real-time measurement of ultrashort laser pulses," IEEE J. Quantum Electron. 35, 421??431 (1999).
[CrossRef]

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweester, M. A. Krumbügel, B. A. Richman, and D. J. Kane, "Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating," Rev. Sci. Instrum. 68, 3277-3295 (1997).
[CrossRef]

Kang, I.

Krumbügel, M. A.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweester, M. A. Krumbügel, B. A. Richman, and D. J. Kane, "Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating," Rev. Sci. Instrum. 68, 3277-3295 (1997).
[CrossRef]

Kuznetsova, T. I.

V. A. Zubov and T. I. Kuznetsova, "Solution of the phase problem for time-dependent optical signals by an interference system," Sov. J. Quantum Electron. 21, 1285??1286 (1991).
[CrossRef]

Muller, H. G.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H. G. Muller, and P. Agostini, "Observation of a train of attosecond pulses from high harmonic generation," Science 292, 1689-1692 (2001).
[CrossRef] [PubMed]

Mullot, G.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H. G. Muller, and P. Agostini, "Observation of a train of attosecond pulses from high harmonic generation," Science 292, 1689-1692 (2001).
[CrossRef] [PubMed]

Paul, P. M.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H. G. Muller, and P. Agostini, "Observation of a train of attosecond pulses from high harmonic generation," Science 292, 1689-1692 (2001).
[CrossRef] [PubMed]

Quochi, F.

Richardson, D. J.

B. C. Thomsen, M. A. F. Roelens, R. T. Watts, and D. J. Richardson, "Comparison between nonlinear and linear spectrographic techniques for the complete characterization of high bit-rate pulses used in optical communications," IEEE Photon. Technol. Lett. 17, 1914??1916 (2005).
[CrossRef]

Richman, B. A.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweester, M. A. Krumbügel, B. A. Richman, and D. J. Kane, "Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating," Rev. Sci. Instrum. 68, 3277-3295 (1997).
[CrossRef]

Roelens, M. A. F.

B. C. Thomsen, M. A. F. Roelens, R. T. Watts, and D. J. Richardson, "Comparison between nonlinear and linear spectrographic techniques for the complete characterization of high bit-rate pulses used in optical communications," IEEE Photon. Technol. Lett. 17, 1914??1916 (2005).
[CrossRef]

Sweester, J. N.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweester, M. A. Krumbügel, B. A. Richman, and D. J. Kane, "Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating," Rev. Sci. Instrum. 68, 3277-3295 (1997).
[CrossRef]

Thomsen, B. C.

B. C. Thomsen, M. A. F. Roelens, R. T. Watts, and D. J. Richardson, "Comparison between nonlinear and linear spectrographic techniques for the complete characterization of high bit-rate pulses used in optical communications," IEEE Photon. Technol. Lett. 17, 1914??1916 (2005).
[CrossRef]

Toma, E. S.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H. G. Muller, and P. Agostini, "Observation of a train of attosecond pulses from high harmonic generation," Science 292, 1689-1692 (2001).
[CrossRef] [PubMed]

Trebino, R.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweester, M. A. Krumbügel, B. A. Richman, and D. J. Kane, "Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating," Rev. Sci. Instrum. 68, 3277-3295 (1997).
[CrossRef]

Usechak, N. G.

Walmsley, I. A.

Watts, R. T.

B. C. Thomsen, M. A. F. Roelens, R. T. Watts, and D. J. Richardson, "Comparison between nonlinear and linear spectrographic techniques for the complete characterization of high bit-rate pulses used in optical communications," IEEE Photon. Technol. Lett. 17, 1914??1916 (2005).
[CrossRef]

Wong, V.

Zubov, V. A.

V. A. Zubov and T. I. Kuznetsova, "Solution of the phase problem for time-dependent optical signals by an interference system," Sov. J. Quantum Electron. 21, 1285??1286 (1991).
[CrossRef]

Zuegel, J. D.

IEEE J. Quantum Electron. (1)

D. J. Kane, "Recent progress toward real-time measurement of ultrashort laser pulses," IEEE J. Quantum Electron. 35, 421??431 (1999).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

C. Dorrer and I. Kang, "Real-time implementation of linear spectrograms for the characterization of high bit-rate optical pulse trains," IEEE Photon. Technol. Lett. 16, 858??860 (2004).
[CrossRef]

B. C. Thomsen, M. A. F. Roelens, R. T. Watts, and D. J. Richardson, "Comparison between nonlinear and linear spectrographic techniques for the complete characterization of high bit-rate pulses used in optical communications," IEEE Photon. Technol. Lett. 17, 1914??1916 (2005).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Lett. (7)

Rev. Sci. Instrum. (1)

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweester, M. A. Krumbügel, B. A. Richman, and D. J. Kane, "Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating," Rev. Sci. Instrum. 68, 3277-3295 (1997).
[CrossRef]

Science (1)

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H. G. Muller, and P. Agostini, "Observation of a train of attosecond pulses from high harmonic generation," Science 292, 1689-1692 (2001).
[CrossRef] [PubMed]

Sov. J. Quantum Electron. (1)

V. A. Zubov and T. I. Kuznetsova, "Solution of the phase problem for time-dependent optical signals by an interference system," Sov. J. Quantum Electron. 21, 1285??1286 (1991).
[CrossRef]

Other (3)

C. Dorrer, "Investigation of the spectrogram techniques for the characterization of picosecond optical pulses," in Optical Fiber Communication Conference, 2005, Technical Digest, OFC/NOFEC (IEEE, New York, 2005), Vol. 2, Paper OTuB3.

C. Dorrer and I. Kang, "Linear self-referencing optical pulse characterization techniques," to be published in the J. Opt. Soc. Am. B (invited).

K. T. Vu, A. Malinowski, M. A. F. Roelens, M. Ibsen, P. Petropoulos, and D. J. Richardson, "Full characterisation of low power picosecond pulses from a gain-switched diode laser using electro-optic modulation based frog," presented at CLEO/QELS 2007, Baltimore, MD, 6??11 May 2007 (Paper CFF4).

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Figures (7)

Fig. 1.
Fig. 1.

(a) Spectral intensity (black line) and phase of the Fourier transform (FT)-limited test pulse (blue line), pulse with second-order dispersion (green line), and pulse with third-order dispersion (red line). (b) Temporal intensity of the FT-limited pulse (blue line), pulse with second-order dispersion (green line), and pulse with third-order dispersion (red line).

Fig. 2.
Fig. 2.

Simulated spectrograms for a 10-ps gate and the Fourier transform–limited pulse, the pulse with second-order dispersion, and the pulse with third-order dispersion (from left to right) without jitter (first line) and with jitter with a standard deviation of 5 ps (second line).

Fig. 3.
Fig. 3.

Simulation results for accuracy and consistency of linear spectrography in the presence of jitter. (a)–(c) correspond to the field error εE versus rms jitter σ, the trace error εS versus rms jitter σ, and the field error εE versus trace error εS , for a 10-ps gate and the three test pulses (FT-limited pulse, pulse with second-order dispersion, and pulse with third-order dispersion; blue, green, and red lines, respectively). (d)–(f) correspond to the field error εE versus rms jitter σ, the trace error εS versus rms jitter σ, and the field error εE versus trace error εS , for a 30-ps gate and the three test pulses (FT-limited pulse, pulse with second-order dispersion, and pulse with third-order dispersion; blue, green, and red lines, respectively).

Fig. 4.
Fig. 4.

Simulated interferograms for jitter with standard deviation of 5 ps. (a)–(c) correspond to one or two shears equal to 2% of the FWHM of the pulse. (d)–(f) correspond to one or two shears equal to 10% of the FWHM of the pulse. The plots correspond from left to right to: a single shear, two opposite shears with uncorrelated jitters, and two opposite shears with identical jitter.

Fig. 5.
Fig. 5.

(a)–(c) Spectrum (black line), differential signal in the absence of jitter (red line), and differential signal with a jitter having 5-ps standard deviation (red markers) for the characterization of the Fourier transform–limited pulse, the pulse with second-order dispersion, and the pulse with third-order dispersion, respectively.

Fig. 6.
Fig. 6.

Spectrum (black line) and phase error (red line) for the characterization of (a) the Fourier transform–limited pulse, (b) the pulse with second-order dispersion, and (c) the pulse with third-order dispersion with an experimental trace averaged over a 5-ps jitter.

Fig. 7.
Fig. 7.

Field error εE versus standard deviation of the jitter for the FT-limited pulse, the pulse with second-order dispersion, and the pulse with third-order dispersion, (blue, green, and red lines, respectively) for an amplitude of the temporal phase modulation 4×1020 s−2, 2×1021 s−2, and 1022 s−2 [(a), (b), and (c), respectively].

Equations (15)

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ε E = min τ , φ E 1 ( t ) E 2 ( t τ ) exp ( i φ ) 2 d t ,
S ( ω , τ ) = E ( t ) R ( t τ ) exp ( i ω t ) d t 2 ,
ε S = i , j [ S simulated ( ω i , t j ) S calculated ( ω i , t j ) ] 2 N ,
S ( ω ) = E ~ ( ω Ω 1 ) + E ~ ( ω Ω 2 ) exp ( i ω τ ) 2 .
E ( t ) exp [ i Ω ( t + δ t ) ] = E ( t ) exp ( i Ω t ) exp ( i Ω δ t ) .
S ( ω ) = E ~ ( ω Ω 1 ) exp ( i Ω 1 δ t 1 ) + E ~ ( ω Ω 2 ) exp ( i ω τ ) exp ( i Ω 2 δ t 2 ) 2 .
I ( ω ) = E ~ ( ω Ω 1 ) E ~ * ( ω Ω 2 ) exp ( i ω τ ) exp [ i ( Ω 1 δ t 1 Ω 2 δ t 2 ) ] ,
E ~ ( ω Ω 1 ) E ~ * ( ω Ω 2 ) exp ( i ω τ ) [ 1 + i ( Ω 1 δ t 1 Ω 2 δ t 2 ) ( Ω 1 δ t 1 Ω 2 δ t 2 ) 2 2 ] .
I ( ω ) = E ~ ( ω Ω 1 ) E ~ * ( ω Ω 2 ) exp ( i ω τ ) [ 1 ( Ω 1 δ t 1 Ω 2 δ t 2 ) 2 2 ] ,
lim ψ 0 S ψ ψ = ω [ S φ ω ] .
S ψ , δ t ( ω ) = E ( t ) exp [ i ψ ( t δ t ) 2 2 ] exp ( i ω t ) d t 2 ,
S ψ , δ t ( ω ) = E ( t ) exp ( i ψ t 2 2 ) exp [ i ( ω ψ δ t ) t ] d t 2 .
S ψ , δ t ( ω ) = S ψ ( ω ψ δ t ) = S ψ ( ω ) ψ δ t S ψ ω + ψ 2 δ t 2 2 S ψ ω 2 2 .
S ψ , δ t ( ω ) = S ψ ( ω ) + ψ 2 δ t 2 2 S ψ ( ω ) ω 2 2 .
lim ψ 0 S ψ , δ t ψ = lim ψ 0 S ψ ψ ;

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