Abstract

Modified-spectrum auto-interferometric correlation (MOSAIC), derived from a conventional second order interferometric autocorrelation trace, is a sensitive and visual chirp diagnostic method for ultrashort laser pulses. We construct several pairs of example pulse shapes that have nearly identical MOSAIC traces and demonstrate that chirp ambiguity can result when the field amplitude or spectrum are not known, thus making MOSAIC a qualitative tool for chirped pulses. However, when the pulse spectrum is known, a unique chirp reconstruction is possible. With the help of a new reconstruction technique, we experimentally demonstrate complete pulse characterization using MOSAIC envelopes and the pulse spectrum.

© 2006 Optical Society of America

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References

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  1. J. C. M. Diels, J. J. Fontaine, I. C. McMichael, and F. Simoni, "Control and measurement of ultrashort pulse shapes (in amplitude and phase) with femtosecond accuracy," Appl. Opt. 24, 1270 - 82 (1985).
    [CrossRef] [PubMed]
  2. C. Yan and J. C. Diels, "Amplitude and phase recording of ultrashort pulses," J. Opt. Soc. Am. B 8, 1259 - 1263 (1991).
    [CrossRef]
  3. C. Spielmann, L. Xu, and F. Krausz, "Measurement of interferometric autocorrelations: comment," Appl. Opt. 36, 2523 - 2525 (1997).
    [CrossRef] [PubMed]
  4. T. Hirayama and M. Sheik-Bahae, "Real-time chirp diagnostic for ultrashort laser pulses," Opt. Lett. 27, 860 -862 (2002).
    [CrossRef]
  5. D. J. Kane and R. Trebino, "Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating," IEEE J. Quantum Electron. 29, 571 - 579 (1993).
    [CrossRef]
  6. P. O’Shea, M. Kimmel, X. Gu, and R. Trebino, "Highly simplified device for ultrashort-pulse measurement," Opt. Lett. 26, 932 - 934 (2001).
    [CrossRef]
  7. G. Stibenz and G. Steinmeyer, "Interferometric frequency-resolved optical gating," Opt. Express 13, 2617 - 2626 (2005).
    [CrossRef] [PubMed]
  8. C. Iaconis and I. A. Walmsley, "Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses," Opt. Lett. 23, 792 - 794 (1998).
    [CrossRef]
  9. J. K. Rhee, T. S. Sosnowski, A. C. Tien, and T. B. Norris, "Real-time dispersion analyzer of femtosecond laser pulses with use of a spectrally and temporally resolved upconversion technique," J. Opt. Soc. Am. B 13, 1780 - 1785 (1996).
    [CrossRef]
  10. J. W. Nicholson, J. Jasapara, W. Rudolph, F. G. Omenetto, and A. J. Taylor, "Full-field characterization of femtosecond pulses by spectrum and cross-correlation measurements," Opt. Lett. 24, 1774 - 1776 (1999).
    [CrossRef]
  11. R. G. M. P. Koumans and A. Yariv, "Time-resolved optical gating based on dispersive propagation: a new method to characterize optical pulses," IEEE J. Quantum Electron. 36, 137 - 144 (2000).
    [CrossRef]
  12. A. K. Sharma, P. A. Naik, and P. D. Gupta, "Estimation of higher order chirp in ultrashort laser pulses using modified spectrum auto-interferometric correlation," Opt. Commun. 233, 431 - 437 (2004).
    [CrossRef]
  13. A. K. Sharma, M. Raghuramaiah, P. A. Naik, and P. D. Gupta, "Use of commercial grade light emitting diode in auto-correlation measurements of femtosecond and picosecond laser pulses at 1054 nm," Opt. Commun. 246, 195 - 204 (2005).
    [CrossRef]
  14. D. A. Bender, M. P. Hasselbeck, and M. Sheik-Bahae, "Sensitive ultrashort pulse chirp measurement," Opt. Lett. 31, 122 - 124 (2006).
    [CrossRef] [PubMed]
  15. K. Naganuma, K. Modi, and H. Yamada, "General method for ultrashort light pulse chirp measurement," IEEE J. Quantum Electron. 25, 1225 - 1233 (1989).
    [CrossRef]
  16. R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik 35, 237 - 246 (1972).
  17. W. Press, B. Flannery, S. Teukosky, andW. Vetterling, Numerical Recepies in C - The Art of Scientific Computing (Cambridge University Press, Cambridge, 1986).
  18. For a 64 element matrix, the phase reconstruction required six seconds of computation in IDL on a Pentium M 1.6 GHz processor.

2006 (1)

2005 (2)

G. Stibenz and G. Steinmeyer, "Interferometric frequency-resolved optical gating," Opt. Express 13, 2617 - 2626 (2005).
[CrossRef] [PubMed]

A. K. Sharma, M. Raghuramaiah, P. A. Naik, and P. D. Gupta, "Use of commercial grade light emitting diode in auto-correlation measurements of femtosecond and picosecond laser pulses at 1054 nm," Opt. Commun. 246, 195 - 204 (2005).
[CrossRef]

2004 (1)

A. K. Sharma, P. A. Naik, and P. D. Gupta, "Estimation of higher order chirp in ultrashort laser pulses using modified spectrum auto-interferometric correlation," Opt. Commun. 233, 431 - 437 (2004).
[CrossRef]

2002 (1)

2001 (1)

2000 (1)

R. G. M. P. Koumans and A. Yariv, "Time-resolved optical gating based on dispersive propagation: a new method to characterize optical pulses," IEEE J. Quantum Electron. 36, 137 - 144 (2000).
[CrossRef]

1999 (1)

1998 (1)

1997 (1)

1996 (1)

1993 (1)

D. J. Kane and R. Trebino, "Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating," IEEE J. Quantum Electron. 29, 571 - 579 (1993).
[CrossRef]

1991 (1)

1989 (1)

K. Naganuma, K. Modi, and H. Yamada, "General method for ultrashort light pulse chirp measurement," IEEE J. Quantum Electron. 25, 1225 - 1233 (1989).
[CrossRef]

1985 (1)

1972 (1)

R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik 35, 237 - 246 (1972).

Bender, D. A.

Diels, J. C.

Diels, J. C. M.

Fontaine, J. J.

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik 35, 237 - 246 (1972).

Gu, X.

Gupta, P. D.

A. K. Sharma, M. Raghuramaiah, P. A. Naik, and P. D. Gupta, "Use of commercial grade light emitting diode in auto-correlation measurements of femtosecond and picosecond laser pulses at 1054 nm," Opt. Commun. 246, 195 - 204 (2005).
[CrossRef]

A. K. Sharma, P. A. Naik, and P. D. Gupta, "Estimation of higher order chirp in ultrashort laser pulses using modified spectrum auto-interferometric correlation," Opt. Commun. 233, 431 - 437 (2004).
[CrossRef]

Hasselbeck, M. P.

Hirayama, T.

Iaconis, C.

Jasapara, J.

Kane, D. J.

D. J. Kane and R. Trebino, "Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating," IEEE J. Quantum Electron. 29, 571 - 579 (1993).
[CrossRef]

Kimmel, M.

Koumans, R. G. M. P.

R. G. M. P. Koumans and A. Yariv, "Time-resolved optical gating based on dispersive propagation: a new method to characterize optical pulses," IEEE J. Quantum Electron. 36, 137 - 144 (2000).
[CrossRef]

Krausz, F.

McMichael, I. C.

Modi, K.

K. Naganuma, K. Modi, and H. Yamada, "General method for ultrashort light pulse chirp measurement," IEEE J. Quantum Electron. 25, 1225 - 1233 (1989).
[CrossRef]

Naganuma, K.

K. Naganuma, K. Modi, and H. Yamada, "General method for ultrashort light pulse chirp measurement," IEEE J. Quantum Electron. 25, 1225 - 1233 (1989).
[CrossRef]

Naik, P. A.

A. K. Sharma, M. Raghuramaiah, P. A. Naik, and P. D. Gupta, "Use of commercial grade light emitting diode in auto-correlation measurements of femtosecond and picosecond laser pulses at 1054 nm," Opt. Commun. 246, 195 - 204 (2005).
[CrossRef]

A. K. Sharma, P. A. Naik, and P. D. Gupta, "Estimation of higher order chirp in ultrashort laser pulses using modified spectrum auto-interferometric correlation," Opt. Commun. 233, 431 - 437 (2004).
[CrossRef]

Nicholson, J. W.

Norris, T. B.

O’Shea, P.

Omenetto, F. G.

Raghuramaiah, M.

A. K. Sharma, M. Raghuramaiah, P. A. Naik, and P. D. Gupta, "Use of commercial grade light emitting diode in auto-correlation measurements of femtosecond and picosecond laser pulses at 1054 nm," Opt. Commun. 246, 195 - 204 (2005).
[CrossRef]

Rhee, J. K.

Rudolph, W.

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik 35, 237 - 246 (1972).

Sharma, A. K.

A. K. Sharma, M. Raghuramaiah, P. A. Naik, and P. D. Gupta, "Use of commercial grade light emitting diode in auto-correlation measurements of femtosecond and picosecond laser pulses at 1054 nm," Opt. Commun. 246, 195 - 204 (2005).
[CrossRef]

A. K. Sharma, P. A. Naik, and P. D. Gupta, "Estimation of higher order chirp in ultrashort laser pulses using modified spectrum auto-interferometric correlation," Opt. Commun. 233, 431 - 437 (2004).
[CrossRef]

Sheik-Bahae, M.

Simoni, F.

Sosnowski, T. S.

Spielmann, C.

Steinmeyer, G.

Stibenz, G.

Taylor, A. J.

Tien, A. C.

Trebino, R.

P. O’Shea, M. Kimmel, X. Gu, and R. Trebino, "Highly simplified device for ultrashort-pulse measurement," Opt. Lett. 26, 932 - 934 (2001).
[CrossRef]

D. J. Kane and R. Trebino, "Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating," IEEE J. Quantum Electron. 29, 571 - 579 (1993).
[CrossRef]

Walmsley, I. A.

Xu, L.

Yamada, H.

K. Naganuma, K. Modi, and H. Yamada, "General method for ultrashort light pulse chirp measurement," IEEE J. Quantum Electron. 25, 1225 - 1233 (1989).
[CrossRef]

Yan, C.

Yariv, A.

R. G. M. P. Koumans and A. Yariv, "Time-resolved optical gating based on dispersive propagation: a new method to characterize optical pulses," IEEE J. Quantum Electron. 36, 137 - 144 (2000).
[CrossRef]

Appl. Opt. (2)

IEEE J. Quantum Electron. (3)

D. J. Kane and R. Trebino, "Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating," IEEE J. Quantum Electron. 29, 571 - 579 (1993).
[CrossRef]

R. G. M. P. Koumans and A. Yariv, "Time-resolved optical gating based on dispersive propagation: a new method to characterize optical pulses," IEEE J. Quantum Electron. 36, 137 - 144 (2000).
[CrossRef]

K. Naganuma, K. Modi, and H. Yamada, "General method for ultrashort light pulse chirp measurement," IEEE J. Quantum Electron. 25, 1225 - 1233 (1989).
[CrossRef]

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

Opt. Commun. (2)

A. K. Sharma, P. A. Naik, and P. D. Gupta, "Estimation of higher order chirp in ultrashort laser pulses using modified spectrum auto-interferometric correlation," Opt. Commun. 233, 431 - 437 (2004).
[CrossRef]

A. K. Sharma, M. Raghuramaiah, P. A. Naik, and P. D. Gupta, "Use of commercial grade light emitting diode in auto-correlation measurements of femtosecond and picosecond laser pulses at 1054 nm," Opt. Commun. 246, 195 - 204 (2005).
[CrossRef]

Opt. Express (1)

Opt. Lett. (5)

Optik (1)

R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik 35, 237 - 246 (1972).

Other (2)

W. Press, B. Flannery, S. Teukosky, andW. Vetterling, Numerical Recepies in C - The Art of Scientific Computing (Cambridge University Press, Cambridge, 1986).

For a 64 element matrix, the phase reconstruction required six seconds of computation in IDL on a Pentium M 1.6 GHz processor.

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Figures (6)

Fig. 1.
Fig. 1.

Illustration of an IAC and its corresponding MOSAIC traces. (a) Second order interferometric autocorrelation trace. (b) Fringe resolved MOSAIC trace. (c) and (d) Envelopes of MOSAIC trace on linear and log scales.

Fig. 2.
Fig. 2.

Gerchberg-Saxton like algorithm for the construction of an electric field E(t) that has a nearly identical MOSAIC trace as the input field Ei (t).

Fig. 3.
Fig. 3.

Numerical results of the reconstruction algorithm. Red curves and image correspond to the input field, Ei (τ) and blue represents the reconstructed field, E(τ). (a) MOSAIC traces. (b) Intensity and phase of the electric fields. (c) Spectrum of E(τ) and Ei (τ). (d) and (e) Adaptation errors, Δ I ˜ ( Ω ) = Σ I ˜ ( Ω ) I ˜ i ( Ω ) Σ I ˜ i ( Ω ) and Δ E ˜ 2 ( Ω ) = Σ E ˜ 2 ( Ω ) E ˜ i 2 ( Ω ) Σ E ˜ i 2 ( Ω ) as a function iteration number. (f) and (g) Numerical second harmonic FROG traces for Ei (τ) and E(τ).

Fig. 4.
Fig. 4.

Reconstruction results corresponding to a secant hyperbolic initial field (red), Ei (τ), with higher order temporal phase similar to Ref. [14]. Green and blue represent reconstructions for two different initial conditions. (a), (b) MOSAIC traces, (c), (d) Temporal intensity and phase, (e), (f) and (g) comparison of SHG FROG traces.

Fig. 5.
Fig. 5.

Reconstruction of pulse intensity and chirp using MOSAIC envelopes and pulse spectral magnitude. Complete and unambiguous pulse characterization is possible with this approach. Solid lines correspond to the original pulse (Ei (τ)) in Fig. 3 and the symbols represent ambiguity free reconstruction.

Fig. 6.
Fig. 6.

(a) Solid red lines represent experimentally measured MOSAIC envelopes and blue symbols represent reconstruction results. (b) Red curve is an experimentally measured pulse spectral intensity and the blue curve is the reconstructed phase. (c) Reconstructed pulse intensity and phase in time.

Equations (10)

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S IAC ( τ ) = 1 + 2 A 0 ( τ ) + 2 Re [ A 1 ( τ ) exp ( i ω 0 τ ) ] + Re [ A 2 ( τ ) exp ( 2 i ω 0 τ ) ] ,
A 0 ( τ ) = I ( t ) I ( t τ ) d t ,
A 1 ( τ ) = [ I ( t ) + I ( t τ ) ] E ( t ) E * ( t τ ) d t ,
A 2 ( τ ) = E 2 ( t ) E * 2 ( t τ ) d t ,
I ( t ) = E ( t ) E * ( t ) .
S MOSIAC ( τ ) = 1 + 2 A 0 ( τ ) + 2 Re [ A 2 ( τ ) exp ( 2 i ω 0 τ ) ] .
S MOSIAC min ( τ ) = A 0 ( τ ) A 2 ( τ ) .
A ˜ 0 ( Ω ) = I ˜ ( Ω ) 2 ,
A ˜ 2 ( Ω ) = E ~ 2 ( Ω ) 2 ,
Δ = Σ i ( I ˜ g ( Ω i ) 2 I ˜ ( Ω i ) 2 ) 2 + Σ i ( E ˜ g 2 ( Ω i ) 2 E ˜ 2 ( Ω i ) 2 ) 2 ,

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