Abstract

We demonstrate a novel variant of frequency-resolved optical gating (FROG) that is based on spectrally resolving a collinear interferometric autocorrelation rather than a noncollinear one. From the interferometric FROG trace, one can extract two terms, the standard SHG-FROG trace and a new phase-sensitive modulational component, which both allow for independent retrieval of the pulse shape. We compare the results of both methods and a separate SPIDER measurement using 6.5-fs pulses from a white-light continuum. We find that the novel modulational component allows for robust retrieval of pulse shapes in the few-cycle regime. Together with the added cross-checks, our method significantly enhances choices for pulse characterization in this regime.

© 2005 Optical Society of America

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  1. J.-C. Diels, E. Van Stryland, and G. Benedict, �??Generation and measurement of 200 femtosecond optical pulses,�?? Opt. Commun. 25, 93-95 (1978).
    [CrossRef]
  2. J.-C. Diels and W. Rudolph, �??Ultrashort Laser Pulse Phenomena,�?? Academic Press, San Diego, CA (1996).
  3. K. Naganuma, K. Mogi, and H. Yamada, �??General Method for Ultrashort Light Pulse Chirp Measurement,�?? IEEE J. Quantum Electron. 25, 1225-1233 (1989).
    [CrossRef]
  4. J.-H. Chung, and A. M. Weiner, �??Ambiguity of Ultrashort Pulse Shapes Retrieved From the Intensity Autocorrelation and the Power Spectrum,�?? IEEE J. Sel. Top. Quantum Electron. 7, 656-666 (2001).
    [CrossRef]
  5. R. Trebino, K.W. De Long, D. N. Fittinghoff, J. N. Sweetser, 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]
  6. R. Trebino, �??Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses,�?? Kluwer Academic Publishers, Boston, MA (2000).
  7. 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]
  8. C. Iaconis and I. A.Walmsley, �??Self-referencing spectral interferometry for measuring ultrashort optical pulses,�?? IEEE J. Quantum Electron. 35, 501-509 (1999).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  11. A. Baltu¡ska, T. Fuji, and T. Kobayashi, �??Visible pulse compression to 4 fs by optical parametric amplification and programmable dispersion control,�?? Opt. Lett. 27, 306-308 (2002).
    [CrossRef]
  12. K. Yamane, Z. G. Zhang, K. Oka, R. Morita, M. Yamashita, and A. Suguro, �??Optical pulse compression to 3.4 fs in the monocycle region by feedback phase compensation,�?? Opt. Lett. 28, 2258-2260 (2003).
    [CrossRef] [PubMed]
  13. F. Reynaud, F. Salin, and A. Barthelemy, �??Measurement of phase shifts introduced by nonlinear optical phenomena on subpicosecond pulses,�?? Opt. Lett. 14, 275-277 (1989).
    [CrossRef] [PubMed]
  14. A. Baltu¡ska, Z. Wei, M. S. Pshenichnikov, and R. Szipocs, �??All-solid-state cavity-dumped sub-5-fs laser,�?? Appl. Phys. B 65, 175-188 (1997).
    [CrossRef]
  15. I. A. Roldán, I. G. Cormack, P. Loza-Alvarez, E. J. Gualda, and D. Artigas, �??Ultrashort pulse characterization with SHG collinear-FROG,�?? Opt. Express 12, 1169�??1178 (2004), <a href "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-6-1169">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-6-1169</a>
    [CrossRef]
  16. Certain commercial instruments and software packages are identified in this paper only to facilitate experimental reproducibility and to adequately describe the experimental procedure. Such identification does not imply any recommendation, nor does it imply that the equipment identified are necessarily the best available for the purpose.
  17. G. Sansone, G. Steinmeyer, C. Vozzi, S. Stagira, M. Nisoli, S. De Silvestri, K. Starke, D. Ristau, B. Schenkel, J. Biegert, A. Gosteva, and U. Keller, �??Mirror dispersion control of a hollow fiber supercontinuum,�?? Appl. Phys. B, 78, 551-555, (2004).
    [CrossRef]
  18. L. Cohen, �??Time-frequency distributions - a review,�?? Proc. IEEE 77, 941-981 (1989).
    [CrossRef]
  19. FROG software Ver. 3.0, <a href"=http://www.femtosoft.biz/"> http://www.femtosoft.biz/</a>
  20. M. Takeda, H. Ina, and S. Kobayashi, �??Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,�?? J. Opt. Soc. Am. 72, 156 (1982).
    [CrossRef]
  21. K. W. DeLong, D. N. Fittinghoff,R. Trebino,B. Kohler, and K. Wilson, �??Pulse Retrieval in Frequency-Resolved Optical Gating Based on the Method of Generalized Projections,�?? Opt. Lett. 19, 2152�??2154 (1994).
    [CrossRef] [PubMed]
  22. D. T. Reid, �??Algorithm for complete and rapid retrieval of ultrashort pulse amplitude and phase from a sonogram,�?? IEEE J. Quant. El. 35, 1584�??1589 (1999).
    [CrossRef]
  23. W. H. Press, S. A. Teukolsky, W. T. Vetterlin, and B. P. Flannery, �??Numerical Recipes in C,�??, 2nd ed., ch. 10.5, pp. 412, Cambridge University Press, Cambridge, UK, 1992.
  24. G. Stibenz and G. Steinmeyer, �??High dynamic range characterization of ultrabroadband white-light continuum pulses,�?? Opt. Express 12, 6319�??6325 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-25-6319">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-25-6319</a>
    [CrossRef] [PubMed]

Appl. Phys. B

A. Baltu¡ska, Z. Wei, M. S. Pshenichnikov, and R. Szipocs, �??All-solid-state cavity-dumped sub-5-fs laser,�?? Appl. Phys. B 65, 175-188 (1997).
[CrossRef]

G. Sansone, G. Steinmeyer, C. Vozzi, S. Stagira, M. Nisoli, S. De Silvestri, K. Starke, D. Ristau, B. Schenkel, J. Biegert, A. Gosteva, and U. Keller, �??Mirror dispersion control of a hollow fiber supercontinuum,�?? Appl. Phys. B, 78, 551-555, (2004).
[CrossRef]

IEEE J. Quant. El.

D. T. Reid, �??Algorithm for complete and rapid retrieval of ultrashort pulse amplitude and phase from a sonogram,�?? IEEE J. Quant. El. 35, 1584�??1589 (1999).
[CrossRef]

IEEE J. Quantum Electron.

K. Naganuma, K. Mogi, and H. Yamada, �??General Method for Ultrashort Light Pulse Chirp Measurement,�?? IEEE J. Quantum Electron. 25, 1225-1233 (1989).
[CrossRef]

C. Iaconis and I. A.Walmsley, �??Self-referencing spectral interferometry for measuring ultrashort optical pulses,�?? IEEE J. Quantum Electron. 35, 501-509 (1999).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

J.-H. Chung, and A. M. Weiner, �??Ambiguity of Ultrashort Pulse Shapes Retrieved From the Intensity Autocorrelation and the Power Spectrum,�?? IEEE J. Sel. Top. Quantum Electron. 7, 656-666 (2001).
[CrossRef]

J. Opt. Soc. Am.

Opt. Commun.

J.-C. Diels, E. Van Stryland, and G. Benedict, �??Generation and measurement of 200 femtosecond optical pulses,�?? Opt. Commun. 25, 93-95 (1978).
[CrossRef]

Opt. Express

Opt. Lett.

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]

K. W. DeLong, D. N. Fittinghoff,R. Trebino,B. Kohler, and K. Wilson, �??Pulse Retrieval in Frequency-Resolved Optical Gating Based on the Method of Generalized Projections,�?? Opt. Lett. 19, 2152�??2154 (1994).
[CrossRef] [PubMed]

A. Baltu¡ska, M. S. Pshenichnikov, and D. A.Wiersma �??Amplitude and phase characterization of 4.5-fs pulses by frequency-resolved optical gating,�?? Opt. Lett. 23, 1474-1476 (1998).
[CrossRef]

L. Gallmann, D. H. Sutter, N. Matuschek, G. Steinmeyer, U. Keller, C. Iaconis, and I. A. Walmsley, �??Characterization of sub-6-fs optical pulses with spectral phase interferometry for direct-field reconstruction,�?? Opt. Lett. 24, 1314-1316 (1999).
[CrossRef]

A. Baltu¡ska, T. Fuji, and T. Kobayashi, �??Visible pulse compression to 4 fs by optical parametric amplification and programmable dispersion control,�?? Opt. Lett. 27, 306-308 (2002).
[CrossRef]

K. Yamane, Z. G. Zhang, K. Oka, R. Morita, M. Yamashita, and A. Suguro, �??Optical pulse compression to 3.4 fs in the monocycle region by feedback phase compensation,�?? Opt. Lett. 28, 2258-2260 (2003).
[CrossRef] [PubMed]

F. Reynaud, F. Salin, and A. Barthelemy, �??Measurement of phase shifts introduced by nonlinear optical phenomena on subpicosecond pulses,�?? Opt. Lett. 14, 275-277 (1989).
[CrossRef] [PubMed]

Proc. IEEE

L. Cohen, �??Time-frequency distributions - a review,�?? Proc. IEEE 77, 941-981 (1989).
[CrossRef]

Rev. Sci. Instrum.

R. Trebino, K.W. De Long, D. N. Fittinghoff, J. N. Sweetser, 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]

Other

R. Trebino, �??Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses,�?? Kluwer Academic Publishers, Boston, MA (2000).

FROG software Ver. 3.0, <a href"=http://www.femtosoft.biz/"> http://www.femtosoft.biz/</a>

Certain commercial instruments and software packages are identified in this paper only to facilitate experimental reproducibility and to adequately describe the experimental procedure. Such identification does not imply any recommendation, nor does it imply that the equipment identified are necessarily the best available for the purpose.

J.-C. Diels and W. Rudolph, �??Ultrashort Laser Pulse Phenomena,�?? Academic Press, San Diego, CA (1996).

W. H. Press, S. A. Teukolsky, W. T. Vetterlin, and B. P. Flannery, �??Numerical Recipes in C,�??, 2nd ed., ch. 10.5, pp. 412, Cambridge University Press, Cambridge, UK, 1992.

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Figures (6)

Fig. 1.
Fig. 1.

Experimental arrangement of a dispersion balanced interferometric autocorrelator. Spectrally resolving the autocorrelation signal results in an interferometric FROG trace (See Fig. 2). The fringe substructure of the IFROG trace is preserved by triggering a fast camera with the encoder signal of a constant moving delay stage. ENC, encoder; OMA, optical multichannel analyzer.

Fig. 2.
Fig. 2.

Interferometric FROG. (a) Spectrally resolved interferometric autocorrelation (IFROG) trace. (b) Fourier transform of (a) along the delay axis. The dc baseband, two modulation side bands at the fundamental frequency ω 0, and two second harmonic side bands (at 2ω 0) are clearly separable. The dashed lines mark the borders of a super-Gaussian filter that was used for isolating the individual components.

Fig. 3.
Fig. 3.

Pulse retrieval from the dc part of the IFROG trace. (a) SH-FROG trace, as extracted from the IFROG trace. (b) Reconstructed SH-FROG trace. The FROG error of this reconstruction is 0.005. The retrieved temporal and spectral phase and intensity profiles of the pulse are plotted in Fig. 6(c) and (d).

Fig. 4.
Fig. 4.

Red curve: Frequency marginal after compensating the bandwidth limitation of the conversion process. Black dashed line: Convolution of the fundamental pulse spectrum.

Fig. 5.
Fig. 5.

Pulse retrieval from the ac part of the IFROG trace. (a) FM-FROG trace, i.e. modulated part at the interference period of the fundamental, phase-sensitively extracted from the IFROG data in Fig. 2(a). (b) Reconstructed FM-FROG trace derived by the implementation of a modified generalized projection method for the pulse-retrieval. The FROG error of this reconstruction is 0.0085. The retrieved temporal and spectral phase and intensity profiles of the pulse are plotted in Fig. 6(e) and (f).

Fig. 6.
Fig. 6.

Comparison of pulse shapes retrieved by SPIDER (a,b), SH-FROG (c,d), and FM-FROG (e,f). Temporal shapes are shown in (a, c, and e), reconstructed spectra are shown in (d) and (f). An independent measurement of the pulse spectrum, which also served for the marginal test, is shown in (b) together with the spectral phase measured in SPIDER. Intensities are shown in black, phases in red. The FWHM pulse durations are: 6.5 fs for SPIDER, 7.4 fs for SH-FROG, and 6.8 fs for FM-FROG.

Equations (12)

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𝓔 ( t ) = E ( t ) exp ( i ω 0 t )
I IFROG ( ω , τ ) = ( 𝓔 ( t ) + 𝓔 ( t τ ) ) 2 exp ( i ω t ) d t 2 .
E FROG ( Δ ω , τ ) = E ( t ) E ( t τ ) exp ( i Δ ω t ) d t
E SH ( Δ ω ) = E FROG ( Δ ω , τ = 0 ) = E 2 ( t ) exp ( i Δ ω t ) d t ,
I IFROG ( ω , τ ) = ( 1 + exp ( i ( 2 ω 0 + Δ ω ) τ ) ) E SH ( Δ ω ) + 2 exp ( i ω 0 τ ) E FROG ( Δ ω , τ ) 2 .
I IFROG ( ω , τ ) = 2 E SH ( Δ ω ) 2 + 4 E FROG ( Δ ω , τ ) 2
+ 8 cos [ ( ω 0 + Δ ω 2 ) τ ] Re [ E FROG ( Δ ω , τ ) E SH * ( Δ ω ) exp ( i Δ ω 2 τ ) ]
+ 2 cos [ ( 2 ω 0 + Δ ω ) τ ] E SH ( Δ ω ) 2 .
I FMFROG ( Δ ω , τ ) = E FROG ( Δ ω , τ ) E FROG ( Δ ω , τ = 0 ) ×
cos ( φ FROG ( Δ ω , τ ) φ FROG ( Δ ω , τ = 0 ) + Δ ω 2 τ )
Z = i , j = 1 N I FMFROG meas ( Δ ω i , τ j ) I FMFROG ( k ) ( Δ ω i , τ j ) 2 .
E ( k + 1 ) ( t i ) = E ( k ) ( t i ) + μ ( Z Re [ E ( t i ) ] ) + i μ ( Z Im [ E ( t i ) ] )

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