Abstract

We present a simple and robust technique to retrieve the phase of ultrashort laser pulses, based on a chirped mirror and glass wedges compressor. It uses the compression system itself as a diagnostic tool, thereby making unnecessary the use of complementary diagnostic tools. We used this technique to compress and characterize 7.1 fs laser pulses from an ultrafast laser oscillator.

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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(9), 1270–1282 (1985).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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  14. J. A. Nelder and R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).
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    [CrossRef] [PubMed]
  16. A. Baltuška, M. S. Pshenichnikov, and D. A. Wiersma, “Amplitude and phase characterization of 4.5-fs pulses by frequency-resolved optical gating,” Opt. Lett. 23(18), 1474–1476 (1998).
    [CrossRef] [PubMed]
  17. A. Baltuška, M. S. Pshenichnikov, and D. A. Wiersma, “Second-harmonic generation frequency-resolved optical gating in the single-cycle regime,” IEEE J. Quantum Electron. 35(4), 459–478 (1999).
    [CrossRef]

2010 (1)

2008 (2)

2006 (2)

2004 (1)

1999 (3)

1998 (2)

1997 (1)

A. Baltuška, Z. Wei, M. S. Pshenichnikov, D. A. Wiersma, and R. Szipöcs, “All-solid-state cavity-dumped sub-5-fs laser,” Appl. Phys. B 65(2), 175–188 (1997).
[CrossRef]

1993 (2)

D. J. Kane and R. Trebino, “Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating,” IEEE J. Quantum Electron. 29(2), 571–579 (1993).
[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. Am. A 10(5), 1101–1111 (1993).
[CrossRef]

1989 (1)

K. Naganuma, K. Mogi, and H. Yamada, “General method for ultrashort light pulse chirp measurement,” IEEE J. Quantum Electron. 25(6), 1225–1233 (1989).
[CrossRef]

1985 (1)

1965 (1)

J. A. Nelder and R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).

Baltuška, A.

A. Baltuška, M. S. Pshenichnikov, and D. A. Wiersma, “Second-harmonic generation frequency-resolved optical gating in the single-cycle regime,” IEEE J. Quantum Electron. 35(4), 459–478 (1999).
[CrossRef]

A. Baltuška, M. S. Pshenichnikov, and D. A. Wiersma, “Amplitude and phase characterization of 4.5-fs pulses by frequency-resolved optical gating,” Opt. Lett. 23(18), 1474–1476 (1998).
[CrossRef] [PubMed]

A. Baltuška, Z. Wei, M. S. Pshenichnikov, D. A. Wiersma, and R. Szipöcs, “All-solid-state cavity-dumped sub-5-fs laser,” Appl. Phys. B 65(2), 175–188 (1997).
[CrossRef]

Birge, J. R.

Borukhovich, I.

Coello, Y.

Crespo, H. M.

Cruz, J. M. D.

Dantus, M.

Diels, J. C. M.

Fontaine, J. J.

Funk, D. J.

Gunaratne, T. C.

Gunn, J. M.

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(2), 571–579 (1993).
[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. Am. A 10(5), 1101–1111 (1993).
[CrossRef]

Kärtner, F. X.

Lozovoy, V. V.

McMichael, I. C.

Mead, R.

J. A. Nelder and R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).

Mogi, K.

K. Naganuma, K. Mogi, and H. Yamada, “General method for ultrashort light pulse chirp measurement,” IEEE J. Quantum Electron. 25(6), 1225–1233 (1989).
[CrossRef]

Naganuma, K.

K. Naganuma, K. Mogi, and H. Yamada, “General method for ultrashort light pulse chirp measurement,” IEEE J. Quantum Electron. 25(6), 1225–1233 (1989).
[CrossRef]

Nelder, J. A.

J. A. Nelder and R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).

Nicholson, J. W.

Omenetto, F. G.

Pastirk, I.

Pshenichnikov, M. S.

A. Baltuška, M. S. Pshenichnikov, and D. A. Wiersma, “Second-harmonic generation frequency-resolved optical gating in the single-cycle regime,” IEEE J. Quantum Electron. 35(4), 459–478 (1999).
[CrossRef]

A. Baltuška, M. S. Pshenichnikov, and D. A. Wiersma, “Amplitude and phase characterization of 4.5-fs pulses by frequency-resolved optical gating,” Opt. Lett. 23(18), 1474–1476 (1998).
[CrossRef] [PubMed]

A. Baltuška, Z. Wei, M. S. Pshenichnikov, D. A. Wiersma, and R. Szipöcs, “All-solid-state cavity-dumped sub-5-fs laser,” Appl. Phys. B 65(2), 175–188 (1997).
[CrossRef]

Rudolph, W.

Simoni, F.

Steinmeyer, G.

Stibenz, G.

Szipöcs, R.

A. Baltuška, Z. Wei, M. S. Pshenichnikov, D. A. Wiersma, and R. Szipöcs, “All-solid-state cavity-dumped sub-5-fs laser,” Appl. Phys. B 65(2), 175–188 (1997).
[CrossRef]

Taylor, A. J.

Trebino, R.

D. J. Kane and R. Trebino, “Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating,” IEEE J. Quantum Electron. 29(2), 571–579 (1993).
[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. Am. A 10(5), 1101–1111 (1993).
[CrossRef]

Tseng, C.-H.

Walmsley, I. A.

Wei, Z.

A. Baltuška, Z. Wei, M. S. Pshenichnikov, D. A. Wiersma, and R. Szipöcs, “All-solid-state cavity-dumped sub-5-fs laser,” Appl. Phys. B 65(2), 175–188 (1997).
[CrossRef]

Weinacht, T.

Wiersma, D. A.

A. Baltuška, M. S. Pshenichnikov, and D. A. Wiersma, “Second-harmonic generation frequency-resolved optical gating in the single-cycle regime,” IEEE J. Quantum Electron. 35(4), 459–478 (1999).
[CrossRef]

A. Baltuška, M. S. Pshenichnikov, and D. A. Wiersma, “Amplitude and phase characterization of 4.5-fs pulses by frequency-resolved optical gating,” Opt. Lett. 23(18), 1474–1476 (1998).
[CrossRef] [PubMed]

A. Baltuška, Z. Wei, M. S. Pshenichnikov, D. A. Wiersma, and R. Szipöcs, “All-solid-state cavity-dumped sub-5-fs laser,” Appl. Phys. B 65(2), 175–188 (1997).
[CrossRef]

Wyatt, A. S.

Xu, B.

Yamada, H.

K. Naganuma, K. Mogi, and H. Yamada, “General method for ultrashort light pulse chirp measurement,” IEEE J. Quantum Electron. 25(6), 1225–1233 (1989).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

A. Baltuška, Z. Wei, M. S. Pshenichnikov, D. A. Wiersma, and R. Szipöcs, “All-solid-state cavity-dumped sub-5-fs laser,” Appl. Phys. B 65(2), 175–188 (1997).
[CrossRef]

Comput. J. (1)

J. A. Nelder and R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).

IEEE J. Quantum Electron. (3)

A. Baltuška, M. S. Pshenichnikov, and D. A. Wiersma, “Second-harmonic generation frequency-resolved optical gating in the single-cycle regime,” IEEE J. Quantum Electron. 35(4), 459–478 (1999).
[CrossRef]

K. Naganuma, K. Mogi, and H. Yamada, “General method for ultrashort light pulse chirp measurement,” IEEE J. Quantum Electron. 25(6), 1225–1233 (1989).
[CrossRef]

D. J. Kane and R. Trebino, “Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating,” IEEE J. Quantum Electron. 29(2), 571–579 (1993).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (3)

Opt. Express (1)

Opt. Lett. (6)

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Figures (5)

Fig. 1
Fig. 1

Example of simulated dispersion scans, where the spectral phase plots on the left correspond to zero insertion in the scans on the right. (a) Fourier limited pulse. (b) Linearly chirped pulse (second-order dispersion only) – this causes mostly a translation of the trace with respect to the glass insertion, but since the glass itself doesn’t introduce pure second order dispersion, the pulse is never completely compressed for any insertion, so it appears slightly tilted. (c) Pulse with third-order dispersion only, around 800 nm, which results in a clear tilt in the trace with respect to the previous cases. (d) A more complex phase curve, mostly third-order dispersion and some phase ringing.

Fig. 2
Fig. 2

Example of scan and phase retrievals from Fig. 1 (h).

Fig. 3
Fig. 3

Example of simulated traces including spectral filters in the SHG process. (a) Simulated spectrum, where the retrieved phase shown is for the worst case scenario, (d). (b) Ideal trace. (c) Ideal trace multiplied by a typical SHG crystal efficiency curve. (d) Same as (c), but clipped at around 370nm and 440nm. (e) Retrieved “ideal” scan from scan (d) – the retrieved scan is supposed to be identical to scan (b). (f) Applied and retrieved spectral filters from (c). The retrieved filter is made up of the error minimizing coefficients μ‘s for each wavelength.

Fig. 4
Fig. 4

Experimental setup. The laser is a Femtolasers Rainbow CEP (80 MHz repetition rate, energy per pulse of 2.5 nJ, FWHM Fourier limit of 6 fs), SHG is a 20 μm thick BBO crystal. The double chirped mirrors (DCM) are made in matched pairs to minimize phase ringing, and the aluminum off-axis parabola has a 50 mm focal length.

Fig. 5
Fig. 5

Measured and retrieved scans. (a) Raw scan, made up of 250 spectra. (b) Scan made from 50 spectra out of the raw scan. (c) Calibrated scan, by using the frequency marginals in Eq. (6)d) Retrieved scan from (c) - either retrieving from (c) or (b), the results are very similar. Plots (e) and (f) show a bootstrap analysis on spectrum and time, from 10 different retrievals. From the original scan with 250 spectra, 5 different scans were obtained using different data sets. The two different techniques were used on each data set. The red curve is the average value, and the blue curves are one standard deviation above and below the average. Retrieved pulse width at FWHM was 7.1 ± 0.1 fs.

Equations (8)

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U ˜ (ω)=| U ˜ (ω) |exp{iϕ(ω)}.
S(ω,z)= | ( U ˜ (Ω)exp{ izk(Ω) }exp(iΩt) dΩ ) 2 exp(iωt)dt | 2
G= 1 N i N j i,j ( S meas ( ω i , z j )μ S sim ( ω i , z j ) ) 2
μ= i,j S meas ( ω i , z j ) S sim ( ω i , z j ) i,j S sim ( ω i , z j ) 2 ,
S meas (ω,z)= S ideal (ω,z)R(ω),
M(ω)= + S(ω,z)dz
μ i = j S meas ( ω i , z j ) S sim ( ω i , z j ) j S sim ( ω i , z j ) 2
G= 1 N i N j i,j ( S meas ( ω i , z j ) μ i S sim ( ω i , z j ) ) 2 .

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