Abstract

We show that the usual phase-matching-bandwidth constraint in ultrashort-laser-pulse measurement techniques is overly restrictive. Specifically, the phase-matching bandwidth need not exceed the pulse bandwidth on every pulse. Instead, only the phase-matching bandwidth integrated over the measurement period need exceed the pulse bandwidth. We show that angle-dithering a second-harmonic-generation crystal that is otherwise too narrowband (that is, too thick) can yield sufficient phase-matching bandwidth and an accurate pulse measurement. We apply this technique to frequency-resolved optical gating (FROG) and show that accurate pulse measurements can be made using a comparatively very thick and hence narrowband crystal. An additional advantage of using a thick crystal is increased signal strength.

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References

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  1. J. L. A. Chilla and O. E. Martinez, "Direct Determination of the Amplitude and the Phase of Femtosecond Light Pulses," Opt. Lett. 16, 39-41 (1991).
    [CrossRef] [PubMed]
  2. K. W. DeLong, R. Trebino, J. Hunter, and W. E. White, "Frequency-Resolved Optical Gating With the Use of Second-Harmonic Generation," J. Opt. Soc. Amer. B 11, 2206-2215 (1994).
    [CrossRef]
  3. R. Trebino and D. J. Kane, "Using Phase Retrieval to Measure the Intensity and Phase of Ultrashort Pulses: Frequency-Resolved Optical Gating," J. Opt. Soc. Amer. A 10, 1101-1111 (1993).
    [CrossRef]
  4. D. N. Fittinghoff, J. L. Bowie, J. N. Sweetser, R. T. Jennings, M. A. Krumbügel, K. W. DeLong, R. Trebino, and I. A. Walmsley, "Measurement of the Intensity and Phase of Ultraweak, Ultrashort Laser Pulse," Opt. Lett. 21, 884-886 (1996).
    [CrossRef] [PubMed]
  5. R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, 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. T. S. Clement, A. J. Taylor, and D. J. Kane, "Single-shot measurement of the amplitude and phase of ultrashort laser pulses in the violet," Opt. Lett. 20, 70-72 (1995).
    [CrossRef] [PubMed]
  7. K. W. DeLong, C. L. Ladera, R. Trebino, B. Kohler, and K. R. Wilson, "Ultrashort-Pulse Measurement Using Noninstantaneous Nonlinearities: Raman Effects in Frequency-Resolved Optical Gating," Opt. Lett. 20, 486-488 (1995).
    [CrossRef] [PubMed]
  8. K. W. DeLong, D. N. Fittinghoff, and R. Trebino, "Practical Issues in Ultrashort-Laser-Pulse Measurement Using Frequency-Resolved Optical Gating," IEEE J. Quant. Electron. 32, 1253-1264 (1996).
    [CrossRef]
  9. S. A. Diddams, H. K. Eaton, A. A. Zozulya, and T. S. Clement, "Amplitude and phase measurements of femtosecond pulse splitting in nonlinear dispersive media," Opt. Lett. 23, 379-381 (1998).
    [CrossRef]
  10. D. N. Fittinghoff, J. A. Squier, C. P. T. Barty, J. N. Sweetser, R. Trebino, and M. Muller, "Collinear type II second-harmonic-generation frequency-resolved optical gating for use with high-numerical-aperture objectives," Opt. Lett. 23, 1046-1048 (1998).
    [CrossRef]
  11. D. J. Kane and R. Trebino, "Single-Shot Measurement of the Intensity and Phase of an Arbitrary Ultrashort Pulse By Using Frequency-Resolved Optical Gating," Opt. Lett. 18, 823-825 (1993).
    [CrossRef] [PubMed]
  12. G. Taft, A. Rundquist, M. M. Murnane, I. P. Christov, H. C. Kapteyn, K. W. DeLong, D. N. Fittinghoff, M. A. Krumbügel, J. N. Sweetser, and R. Trebino, "Measurement of 10-fs Laser Pulses," Selected Topics in Quantum Electronics 2, Special Issue on Ultrafast Phenomena, 575-585 (1996).
    [CrossRef]
  13. D. N. Fittinghoff, K. W. DeLong, R. Trebino, and C. L. Ladera, "Noise Sensitivity in Frequency-Resolved-Optical- Gating Measurements of Ultrashort Pulses," J. Opt. Soc. Amer. B 12, 1955-1967 (1995).
    [CrossRef]
  14. A. M. Weiner, "Effect of Group Velocity Mismatch on the Measurement of Ultrashort Optical Pulses via Second Harmonic Generation," IEEE J. Quant. Electronics QE-19, 1276-1283 (1983).
    [CrossRef]
  15. C. Nacke, W. Bathe, F. Kieseling, M. Seemann, H. Stolz, C. Heyn, S. Bargstaedt-Franke, W. Hansen, and D. Heitmann, "Phase sensitive resonant ultrafast reflection from GaAs quantum wells," Physica Status Solidi B Conference Title: Phys. Status Solidi B (Germany) 206, 307-314 (1998).
  16. D. J. Kane and R. Trebino, "Characterization of Arbitrary Femtosecond Pulses Using Frequency Resolved Optical Gating," IEEE J. Quant. Electron. 29, 571-579 (1993).
    [CrossRef]
  17. A. Baltuska, M. S. Pshenichnikov, and D. A. Wiersma, "Second-Harmonic Generation Frequency-Resolved Optical Gating in the Single-Cycle Regime," IEEE J. Quant. Electron. 35, 459-478 (1999).
    [CrossRef]
  18. C. Iaconis and I. A. Walmsley, "Self-Referencing Spectral Interferometry for Measuring Ultrashort Optical Pulses," IEEE J. Quant. Electron. 35, 501-509 (1999).
    [CrossRef]

Other

J. L. A. Chilla and O. E. Martinez, "Direct Determination of the Amplitude and the Phase of Femtosecond Light Pulses," Opt. Lett. 16, 39-41 (1991).
[CrossRef] [PubMed]

K. W. DeLong, R. Trebino, J. Hunter, and W. E. White, "Frequency-Resolved Optical Gating With the Use of Second-Harmonic Generation," J. Opt. Soc. Amer. B 11, 2206-2215 (1994).
[CrossRef]

R. Trebino and D. J. Kane, "Using Phase Retrieval to Measure the Intensity and Phase of Ultrashort Pulses: Frequency-Resolved Optical Gating," J. Opt. Soc. Amer. A 10, 1101-1111 (1993).
[CrossRef]

D. N. Fittinghoff, J. L. Bowie, J. N. Sweetser, R. T. Jennings, M. A. Krumbügel, K. W. DeLong, R. Trebino, and I. A. Walmsley, "Measurement of the Intensity and Phase of Ultraweak, Ultrashort Laser Pulse," Opt. Lett. 21, 884-886 (1996).
[CrossRef] [PubMed]

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, 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]

T. S. Clement, A. J. Taylor, and D. J. Kane, "Single-shot measurement of the amplitude and phase of ultrashort laser pulses in the violet," Opt. Lett. 20, 70-72 (1995).
[CrossRef] [PubMed]

K. W. DeLong, C. L. Ladera, R. Trebino, B. Kohler, and K. R. Wilson, "Ultrashort-Pulse Measurement Using Noninstantaneous Nonlinearities: Raman Effects in Frequency-Resolved Optical Gating," Opt. Lett. 20, 486-488 (1995).
[CrossRef] [PubMed]

K. W. DeLong, D. N. Fittinghoff, and R. Trebino, "Practical Issues in Ultrashort-Laser-Pulse Measurement Using Frequency-Resolved Optical Gating," IEEE J. Quant. Electron. 32, 1253-1264 (1996).
[CrossRef]

S. A. Diddams, H. K. Eaton, A. A. Zozulya, and T. S. Clement, "Amplitude and phase measurements of femtosecond pulse splitting in nonlinear dispersive media," Opt. Lett. 23, 379-381 (1998).
[CrossRef]

D. N. Fittinghoff, J. A. Squier, C. P. T. Barty, J. N. Sweetser, R. Trebino, and M. Muller, "Collinear type II second-harmonic-generation frequency-resolved optical gating for use with high-numerical-aperture objectives," Opt. Lett. 23, 1046-1048 (1998).
[CrossRef]

D. J. Kane and R. Trebino, "Single-Shot Measurement of the Intensity and Phase of an Arbitrary Ultrashort Pulse By Using Frequency-Resolved Optical Gating," Opt. Lett. 18, 823-825 (1993).
[CrossRef] [PubMed]

G. Taft, A. Rundquist, M. M. Murnane, I. P. Christov, H. C. Kapteyn, K. W. DeLong, D. N. Fittinghoff, M. A. Krumbügel, J. N. Sweetser, and R. Trebino, "Measurement of 10-fs Laser Pulses," Selected Topics in Quantum Electronics 2, Special Issue on Ultrafast Phenomena, 575-585 (1996).
[CrossRef]

D. N. Fittinghoff, K. W. DeLong, R. Trebino, and C. L. Ladera, "Noise Sensitivity in Frequency-Resolved-Optical- Gating Measurements of Ultrashort Pulses," J. Opt. Soc. Amer. B 12, 1955-1967 (1995).
[CrossRef]

A. M. Weiner, "Effect of Group Velocity Mismatch on the Measurement of Ultrashort Optical Pulses via Second Harmonic Generation," IEEE J. Quant. Electronics QE-19, 1276-1283 (1983).
[CrossRef]

C. Nacke, W. Bathe, F. Kieseling, M. Seemann, H. Stolz, C. Heyn, S. Bargstaedt-Franke, W. Hansen, and D. Heitmann, "Phase sensitive resonant ultrafast reflection from GaAs quantum wells," Physica Status Solidi B Conference Title: Phys. Status Solidi B (Germany) 206, 307-314 (1998).

D. J. Kane and R. Trebino, "Characterization of Arbitrary Femtosecond Pulses Using Frequency Resolved Optical Gating," IEEE J. Quant. Electron. 29, 571-579 (1993).
[CrossRef]

A. Baltuska, M. S. Pshenichnikov, and D. A. Wiersma, "Second-Harmonic Generation Frequency-Resolved Optical Gating in the Single-Cycle Regime," IEEE J. Quant. Electron. 35, 459-478 (1999).
[CrossRef]

C. Iaconis and I. A. Walmsley, "Self-Referencing Spectral Interferometry for Measuring Ultrashort Optical Pulses," IEEE J. Quant. Electron. 35, 501-509 (1999).
[CrossRef]

Supplementary Material (1)

» Media 1: MOV (96 KB)     

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Figures (2)

Fig. 1.
Fig. 1.

(116K) Animation of angle dithering to increase the effective bandwidth. While a “thick” SHG crystal may not phasematch the entire pulse at once, dithering the crystal can cover the full bandwidth of the pulse. Dithering much more quickly than the integration time of the measurement can increase the effective overall bandwidth of otherwise too-thick crystals.

Fig. 2.
Fig. 2.

The measured and retrieved FROG traces and retrieved intensities and phases for 3 different setups. (a1), (b1), and (c1) are the measured FROG traces for the 100 µm KDP crystal, the dithered 1 mm BBO crystal, and the undithered BBO crystal, respectively. (a2), (b2), and (c2) are the corresponding retrieved traces. Note the clipping of frequencies in the undithered BBO crystal. Shown in (d) and (e) are the temporal and spectral retrieved intensities and phases of all 3 cases (solid lines are intensities, dashed lines are phases). Note the undithered BBO retrieval obtains a clipped spectrum and an incorrect temporal and spectral phase, despite the appearance of the temporal intensity being correct.

Tables (1)

Tables Icon

Table 1. The measured temporal and spectral widths, FROG errors, and time-bandwidth products (TBP) for FROG measurements made using three different nonlinear-optical crystals. Note the excellent agreement between measurements made using the thin KDP crystal and the angle-dithered thick BBO crystal. Note also the significantly reduced spectrum and TBP obtained using the undithered thick BBO crystal.

Equations (11)

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I FROG ( ω , τ ) = E ˜ sig ( ω , τ ) 2
E ˜ sig ( ω , τ ) = F { E sig ( t , τ ) }
E sig ( t , τ ) = E ( t ) E ( t τ )
E ˜ sig ( ω , τ , θ ) F { E ( t ) E ( t τ ) } F ( ω , θ )
F ( ω , θ ) sinc { [ n i ( 2 ω , θ ) n j ( ω , θ ) ] ω L 2 c } = sinc { β L [ ω ω 0 ( θ ) ] }
E ˜ sig ( ω , τ , θ ) F { E ( t ) E ( t τ ) }
I FROG dither ( ω , τ ) = π π E ˜ sig ( ω , τ , θ ) 2 g ( θ )
= π π F { E ( t ) E ( t τ ) } F ( ω , θ ) 2 g ( θ )
I FROG ( ω , τ ) = F { E ( t ) E ( t τ ) } 2 Φ ( ω )
Φ ( ω ) π π F ( ω , θ ) 2 g ( θ )
E ( t ) = Re { I ( t ) exp ( i ω 0 t i φ ( t ) ) }

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