Abstract

We outline criteria for fast and accurate acquisition of collinear FROG (CFROG) trace and how it can be transformed into the more traditional noncollinear FROG trace. The CFROG has an intrinsically simple geometry that provides greater versatility as well as the ability for built-in delay calibration and enhanced error-checking. The procedure, based on data processing, allows conventional SHG-FROG retrieval algorithms to be used. This technique is tested numerically and experimentally giving excellent results. This work represents an attractive alternative to the traditional, more complex non-collinear FROG technique while, at the same time, extending its use to experiments where collinear geometry is imposed.

© 2004 Optical Society of America

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References

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IEEE J. Quantum Electron.

D. N. Fittinghoff, A. C. Millard, J. A. Squier, and M. Muller, "Frequency-resolved optical gating measurement of ultrashort pulses passing through a high numerical aperture objective," IEEE J. Quantum Electron. 35, 479-486 (1999). .
[CrossRef]

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

IEEE J. Selec. 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. Selec. Top. Quantum Electron. 7, 656-666 (2001).
[CrossRef]

J. Opt. A

G. Steinmeyer, "A review of ultrafast optics and optoelectronics," J. Opt. A 5, R1-R15 (2003).
[CrossRef]

J. Opt. Soc. Am. A

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. Am. A 10, 1101-1111 (1993).
[CrossRef]

J. Opt. Soc. Am B

Z. Y. Wang, E. Zeek, R. Trebino, and P. Kvam, "Determining error bars in measurements of ultrashort laser pulses," J. Opt. Soc. Am. B 20, 2400-2405 (2003).
[CrossRef]

Opt. Commun.

A. Watanabe, H. Saito, Y. Ishida, and T. Yajima, "Computer-Assisted Spectrum-Resolved Shg Autocorrelator for Monitoring Phase Characteristics of Femtosecond Pulses," Opt. Commun. 63, 320-324 (1987).
[CrossRef]

Opt. Lett.

Proc. SPIE

I. Amat-Roldán, G. Cormack, P. Loza-Alvarez, and D. Artigas, "Nonlinear microscopy pulse optimization at the sample plane using Second Harmonic Generation from starch." Proc. SPIE, 5463-09, 2004.

Rev. Sci Instrum.

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

A. V. Oppenheim and R. W. Schafer, Digital Signal Processing (Prentice-Hall, 1975).

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Figures (6)

Fig. 1.
Fig. 1.

Schematic representing the differences within the detected (a) collinear and (b) noncollinear signal.

Fig. 2.
Fig. 2.

Numerical results: (a) Multiple-pulse with cubic phase employed as input in our simulation tool (b) Interferometric Autocorrelation (c) CFROG trace (d) Fourier Transformed CFROG trace.

Fig. 3.
Fig. 3.

Numerical results: (a) filtered CFROG trace (b) FROG trace. G=2.7·10-7.

Fig. 4.
Fig. 4.

(a) Measured CFROG, (b) fourier transformed CFROG and (c) measured IA with a delay step of 1.76 fs and 512 samples.

Fig. 5.
Fig. 5.

(a) filtered fast-CFROG trace and (b) FROG trace. G=3.9·10-6.

Fig. 6.
Fig. 6.

(a) Marginal of the spectrum from the filtered CFROG trace (blue circles) and FROG trace (red line); (b) Intensity autocorrelation (delay marginal) from the filtered CFROG trace (blue dots) and the FROG trace (red line).

Equations (15)

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E ̂ ( t ) = E ( t ) exp ( j 2 π f 0 t )
( E ̂ ( t ) + E ̂ ( t τ ) ) 2 .
E ̂ ( t ) E ̂ ( t τ ) .
I FROG SHG ( τ , f ) E ̂ ( t ) E ̂ ( t τ ) exp ( j 2 π f t ) d t 2
I CFROG SHG ( τ , f ) ( E ̂ ( t ) + E ̂ ( t τ ) ) 2 exp ( j 2 π f t ) d t 2
I CFROG SHG ( τ , f ) 2 I SHG ( f )
+ 2 I SHG ( f ) cos ( 2 π ( 2 f 0 + f ) τ )
+ 4 Re { E SHG * ( f ) E FROG SHG ( τ , f ) ( exp ( j 2 π f 0 τ ) + exp ( j 2 π ( f 0 + f ) τ ) ) }
+ 4 I FROG SHG ( τ , f )
E SHG ( f ) E 2 ( t ) exp ( j 2 π f t ) d t
E FROG SHG ( τ , f ) E ( t ) E ( t τ ) exp ( j 2 π f t ) d t
k = k n · k span
Δ τ = n ± 1 3 f 0
Δ τ < τ IA 10
τ span = 1 Δ k 2 · τ IA

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