Abstract

Spectral phase compensation is crucial in the production of ultrafast laser pulses. To produce very short pulses, it is necessary to correct higher-order phase terms beyond the typical second-order and third-order corrections. It is helpful to have a pulse shaper to perform the compression, and to use an integrated, deterministic pulse-shaper-only method for pulse compression and characterization. While several algorithms exist for this purpose, it is desirable to know which method is optimal. Using a computer simulation, we investigate the speed of several existing approaches in several typical pulse shaping cases. We also present and demonstrate experimentally a new method named Spectral Phase of Electric field by Analytic Reconstruction (SPEAR), a variant of the Chirp Reversal Technique (CRT). The chirp-scan method, CRT, and SPEAR are found to be the fastest methods to achieve a desired level of accuracy, for the cases investigated.

© 2014 Optical Society of America

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2014

2013

2012

2010

2009

I. A. Walmsley and C. Dorrer, “Characterization of ultrashort electromagnetic pulses,” Adv. Opt. Photon. 1, 308–437 (2009).
[CrossRef]

S.-H. Shim and M. T. Zanni, “How to turn your pump-probe instrument into a multidimensional spectrometer: 2D IR and Vis spectroscopies via pulse shaping,” Phys. Chem. Chem. Phys. 11, 748–761 (2009).
[CrossRef]

2008

2007

P. Nuernberger, G. Vogt, T. Brixner, and G. Gerber, “Femtosecond quantum control of molecular dynamics in the condensed phase,” Phys. Chem. Chem. Phys. 9, 2470–2497 (2007).
[CrossRef]

Y. Coello, B. Xu, T. L. Miller, V. V. Lozovoy, and M. Dantus, “Group-velocity dispersion measurements of water, seawater, and ocular components using multiphoton intrapulse interference phase scan,” Appl. Opt. 46, 8394–8401 (2007).
[CrossRef]

2006

2004

2003

2000

M. E. Anderson, L. E. E. de Araujo, E. M. Kosik, and I. A. Walmsley, “The effects of noise on ultrashort-optical-pulse measurement using SPIDER,” Appl. Phys. B 70, S85–S93 (2000).
[CrossRef]

L. Gallmann, D. H. Sutter, N. Matuschek, G. Steinmeyer, and U. Keller, “Techniques for the characterization of sub-10-fs optical pulses: a comparison,” Appl. Phys. B 70, S67–S75 (2000).
[CrossRef]

E. Riedle, M. Beutter, S. Lochbrunner, J. Piel, S. Schenkl, S. Spörlein, and W. Zinth, “Generation of 10 to 50  fs pulses tunable through all of the visible and the NIR,” Appl. Phys. B 71, 457–465 (2000).
[CrossRef]

1999

1997

1995

R. H. Byrd, P. Lu, J. Nocedal, and C. Zhu, “A limited memory algorithm for bound constrained optimization,” SIAM J. Sci. Comput. 16, 1190–1208 (1995).
[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. Am. B 12, 1955–1967 (1995).
[CrossRef]

1993

1979

C. Ridders, “A new algorithm for computing a single root of a real continuous function,” IEEE Trans. Circuits Syst. 26, 979–980 (1979).
[CrossRef]

Alonso, B.

Anderson, M. E.

M. E. Anderson, L. E. E. de Araujo, E. M. Kosik, and I. A. Walmsley, “The effects of noise on ultrashort-optical-pulse measurement using SPIDER,” Appl. Phys. B 70, S85–S93 (2000).
[CrossRef]

Arnold, C. L.

Baltuška, A.

S. Yeremenko, A. Baltuška, M. S. Pshenichnikov, and D. A. Wiersma, “Phase-amplitude retrieval: SHG FROG vs. SPIDER,” in Conference on Lasers and Electro-Optics (2000), pp. 476–477.

Beaurepaire, E.

Beutter, M.

E. Riedle, M. Beutter, S. Lochbrunner, J. Piel, S. Schenkl, S. Spörlein, and W. Zinth, “Generation of 10 to 50  fs pulses tunable through all of the visible and the NIR,” Appl. Phys. B 71, 457–465 (2000).
[CrossRef]

Brenner, M. H.

Brent, R. P.

R. P. Brent, Algorithms for Minimization without Derivatives (Prentice-Hall, 1973).

Brixner, T.

P. Nuernberger, G. Vogt, T. Brixner, and G. Gerber, “Femtosecond quantum control of molecular dynamics in the condensed phase,” Phys. Chem. Chem. Phys. 9, 2470–2497 (2007).
[CrossRef]

Byrd, R. H.

R. H. Byrd, P. Lu, J. Nocedal, and C. Zhu, “A limited memory algorithm for bound constrained optimization,” SIAM J. Sci. Comput. 16, 1190–1208 (1995).
[CrossRef]

Cai, D.

Carriles, R.

Chambaret, J.-P.

Chandler, E. V.

Ciesielski, R.

Coello, Y.

Comin, A.

Crespo, H.

Crozatier, V.

Cruz, J. M. D.

Dahleh, M.

W. S. Warren, H. Rabitz, and M. Dahleh, “Coherent control of quantum dynamics: the dream is alive,” Science 259, 1581–1589 (1993).
[CrossRef]

Dantus, M.

de Araujo, L. E. E.

M. E. Anderson, L. E. E. de Araujo, E. M. Kosik, and I. A. Walmsley, “The effects of noise on ultrashort-optical-pulse measurement using SPIDER,” Appl. Phys. B 70, S85–S93 (2000).
[CrossRef]

de Beauvoir, B.

Débarre, D.

Dela Cruz, J.

DeLong, K. W.

Donkers, K.

Dorrer, C.

Field, J. J.

Fittinghoff, D. N.

Fordell, T.

Forget, N.

Fuller, F. D.

Gallmann, L.

L. Gallmann, D. H. Sutter, N. Matuschek, G. Steinmeyer, and U. Keller, “Techniques for the characterization of sub-10-fs optical pulses: a comparison,” Appl. Phys. B 70, S67–S75 (2000).
[CrossRef]

Garduño Mejía, J.

Gerber, G.

P. Nuernberger, G. Vogt, T. Brixner, and G. Gerber, “Femtosecond quantum control of molecular dynamics in the condensed phase,” Phys. Chem. Chem. Phys. 9, 2470–2497 (2007).
[CrossRef]

Gitzinger, G.

Greenaway, A.

Gunn, J. M.

Hartschuh, A.

Hoover, E. E.

Hughes, T. E.

Ito, R.

Joffre, M.

Kane, D. J.

Keller, U.

L. Gallmann, D. H. Sutter, N. Matuschek, G. Steinmeyer, and U. Keller, “Techniques for the characterization of sub-10-fs optical pulses: a comparison,” Appl. Phys. B 70, S67–S75 (2000).
[CrossRef]

Keusters, D.

P. Tian, D. Keusters, Y. Suzaki, and W. S. Warren, “Femtosecond phase-coherent two-dimensional spectroscopy,” Science 300, 1553–1555 (2003).
[CrossRef]

Kleinfeld, D.

Kondo, T.

Kosik, E. M.

M. E. Anderson, L. E. E. de Araujo, E. M. Kosik, and I. A. Walmsley, “The effects of noise on ultrashort-optical-pulse measurement using SPIDER,” Appl. Phys. B 70, S85–S93 (2000).
[CrossRef]

Kubota, S.

L’Huillier, A.

Ladera, C. L.

Le Blanc, C.

Lewis, K. L.

Lewis, K. L. M.

Lochbrunner, S.

E. Riedle, M. Beutter, S. Lochbrunner, J. Piel, S. Schenkl, S. Spörlein, and W. Zinth, “Generation of 10 to 50  fs pulses tunable through all of the visible and the NIR,” Appl. Phys. B 71, 457–465 (2000).
[CrossRef]

Loriot, V.

Lozovoy, V.

Lozovoy, V. V.

Lu, P.

R. H. Byrd, P. Lu, J. Nocedal, and C. Zhu, “A limited memory algorithm for bound constrained optimization,” SIAM J. Sci. Comput. 16, 1190–1208 (1995).
[CrossRef]

Martin, J.-L.

Matuschek, N.

L. Gallmann, D. H. Sutter, N. Matuschek, G. Steinmeyer, and U. Keller, “Techniques for the characterization of sub-10-fs optical pulses: a comparison,” Appl. Phys. B 70, S67–S75 (2000).
[CrossRef]

Miller, T. L.

Miranda, M.

Myers, J. A.

Nakamura, H.

Nocedal, J.

R. H. Byrd, P. Lu, J. Nocedal, and C. Zhu, “A limited memory algorithm for bound constrained optimization,” SIAM J. Sci. Comput. 16, 1190–1208 (1995).
[CrossRef]

Nuernberger, P.

P. Nuernberger, G. Vogt, T. Brixner, and G. Gerber, “Femtosecond quantum control of molecular dynamics in the condensed phase,” Phys. Chem. Chem. Phys. 9, 2470–2497 (2007).
[CrossRef]

Ogilvie, J. P.

Ohdaira, K.

Okamoto, T.

Oksenhendler, T.

Pastirk, I.

Pestov, D.

Piel, J.

E. Riedle, M. Beutter, S. Lochbrunner, J. Piel, S. Schenkl, S. Spörlein, and W. Zinth, “Generation of 10 to 50  fs pulses tunable through all of the visible and the NIR,” Appl. Phys. B 71, 457–465 (2000).
[CrossRef]

T. Wilhelm, J. Piel, and E. Riedle, “Sub-20-fs pulses tunable across the visible from a blue-pumped single-pass noncollinear parametric converter,” Opt. Lett. 22, 1494–1496 (1997).
[CrossRef]

Piredda, G.

Pshenichnikov, M. S.

S. Yeremenko, A. Baltuška, M. S. Pshenichnikov, and D. A. Wiersma, “Phase-amplitude retrieval: SHG FROG vs. SPIDER,” in Conference on Lasers and Electro-Optics (2000), pp. 476–477.

Rabitz, H.

W. S. Warren, H. Rabitz, and M. Dahleh, “Coherent control of quantum dynamics: the dream is alive,” Science 259, 1581–1589 (1993).
[CrossRef]

Ranc, S.

Reid, D.

Ridders, C.

C. Ridders, “A new algorithm for computing a single root of a real continuous function,” IEEE Trans. Circuits Syst. 26, 979–980 (1979).
[CrossRef]

Riedle, E.

E. Riedle, M. Beutter, S. Lochbrunner, J. Piel, S. Schenkl, S. Spörlein, and W. Zinth, “Generation of 10 to 50  fs pulses tunable through all of the visible and the NIR,” Appl. Phys. B 71, 457–465 (2000).
[CrossRef]

T. Wilhelm, J. Piel, and E. Riedle, “Sub-20-fs pulses tunable across the visible from a blue-pumped single-pass noncollinear parametric converter,” Opt. Lett. 22, 1494–1496 (1997).
[CrossRef]

Rousseau, J.-P.

Rousseau, P.

Salin, F.

Schenkl, S.

E. Riedle, M. Beutter, S. Lochbrunner, J. Piel, S. Schenkl, S. Spörlein, and W. Zinth, “Generation of 10 to 50  fs pulses tunable through all of the visible and the NIR,” Appl. Phys. B 71, 457–465 (2000).
[CrossRef]

Sheetz, K. E.

Shim, S.-H.

S.-H. Shim and M. T. Zanni, “How to turn your pump-probe instrument into a multidimensional spectrometer: 2D IR and Vis spectroscopies via pulse shaping,” Phys. Chem. Chem. Phys. 11, 748–761 (2009).
[CrossRef]

Shoji, I.

Silva, F.

Solinas, X.

Spörlein, S.

E. Riedle, M. Beutter, S. Lochbrunner, J. Piel, S. Schenkl, S. Spörlein, and W. Zinth, “Generation of 10 to 50  fs pulses tunable through all of the visible and the NIR,” Appl. Phys. B 71, 457–465 (2000).
[CrossRef]

Squier, J. A.

Steinmeyer, G.

L. Gallmann, D. H. Sutter, N. Matuschek, G. Steinmeyer, and U. Keller, “Techniques for the characterization of sub-10-fs optical pulses: a comparison,” Appl. Phys. B 70, S67–S75 (2000).
[CrossRef]

Sutter, D. H.

L. Gallmann, D. H. Sutter, N. Matuschek, G. Steinmeyer, and U. Keller, “Techniques for the characterization of sub-10-fs optical pulses: a comparison,” Appl. Phys. B 70, S67–S75 (2000).
[CrossRef]

Suzaki, Y.

P. Tian, D. Keusters, Y. Suzaki, and W. S. Warren, “Femtosecond phase-coherent two-dimensional spectroscopy,” Science 300, 1553–1555 (2003).
[CrossRef]

Swanson, J. A.

Sylvester, A. W.

Tatsuki, K.

Tekavec, P. F.

Tian, P.

P. Tian, D. Keusters, Y. Suzaki, and W. S. Warren, “Femtosecond phase-coherent two-dimensional spectroscopy,” Science 300, 1553–1555 (2003).
[CrossRef]

Tillo, S. E.

Trebino, R.

Vogt, G.

P. Nuernberger, G. Vogt, T. Brixner, and G. Gerber, “Femtosecond quantum control of molecular dynamics in the condensed phase,” Phys. Chem. Chem. Phys. 9, 2470–2497 (2007).
[CrossRef]

Walmsley, I. A.

I. A. Walmsley and C. Dorrer, “Characterization of ultrashort electromagnetic pulses,” Adv. Opt. Photon. 1, 308–437 (2009).
[CrossRef]

M. E. Anderson, L. E. E. de Araujo, E. M. Kosik, and I. A. Walmsley, “The effects of noise on ultrashort-optical-pulse measurement using SPIDER,” Appl. Phys. B 70, S85–S93 (2000).
[CrossRef]

Walowicz, K.

Warren, W. S.

P. Tian, D. Keusters, Y. Suzaki, and W. S. Warren, “Femtosecond phase-coherent two-dimensional spectroscopy,” Science 300, 1553–1555 (2003).
[CrossRef]

W. S. Warren, H. Rabitz, and M. Dahleh, “Coherent control of quantum dynamics: the dream is alive,” Science 259, 1581–1589 (1993).
[CrossRef]

Weigand, R.

Weiner, A. M.

A. M. Weiner, Ultrafast Optics (Wiley, 2009).

Wiersma, D. A.

S. Yeremenko, A. Baltuška, M. S. Pshenichnikov, and D. A. Wiersma, “Phase-amplitude retrieval: SHG FROG vs. SPIDER,” in Conference on Lasers and Electro-Optics (2000), pp. 476–477.

Wilcox, D. E.

Wilhelm, T.

Xu, B.

Yeremenko, S.

S. Yeremenko, A. Baltuška, M. S. Pshenichnikov, and D. A. Wiersma, “Phase-amplitude retrieval: SHG FROG vs. SPIDER,” in Conference on Lasers and Electro-Optics (2000), pp. 476–477.

Zanni, M. T.

S.-H. Shim and M. T. Zanni, “How to turn your pump-probe instrument into a multidimensional spectrometer: 2D IR and Vis spectroscopies via pulse shaping,” Phys. Chem. Chem. Phys. 11, 748–761 (2009).
[CrossRef]

Zhu, C.

R. H. Byrd, P. Lu, J. Nocedal, and C. Zhu, “A limited memory algorithm for bound constrained optimization,” SIAM J. Sci. Comput. 16, 1190–1208 (1995).
[CrossRef]

Zinth, W.

E. Riedle, M. Beutter, S. Lochbrunner, J. Piel, S. Schenkl, S. Spörlein, and W. Zinth, “Generation of 10 to 50  fs pulses tunable through all of the visible and the NIR,” Appl. Phys. B 71, 457–465 (2000).
[CrossRef]

Adv. Opt. Photon.

Appl. Opt.

Appl. Phys. B

M. E. Anderson, L. E. E. de Araujo, E. M. Kosik, and I. A. Walmsley, “The effects of noise on ultrashort-optical-pulse measurement using SPIDER,” Appl. Phys. B 70, S85–S93 (2000).
[CrossRef]

L. Gallmann, D. H. Sutter, N. Matuschek, G. Steinmeyer, and U. Keller, “Techniques for the characterization of sub-10-fs optical pulses: a comparison,” Appl. Phys. B 70, S67–S75 (2000).
[CrossRef]

E. Riedle, M. Beutter, S. Lochbrunner, J. Piel, S. Schenkl, S. Spörlein, and W. Zinth, “Generation of 10 to 50  fs pulses tunable through all of the visible and the NIR,” Appl. Phys. B 71, 457–465 (2000).
[CrossRef]

IEEE Trans. Circuits Syst.

C. Ridders, “A new algorithm for computing a single root of a real continuous function,” IEEE Trans. Circuits Syst. 26, 979–980 (1979).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Express

J. J. Field, R. Carriles, K. E. Sheetz, E. V. Chandler, E. E. Hoover, S. E. Tillo, T. E. Hughes, A. W. Sylvester, D. Kleinfeld, and J. A. Squier, “Optimizing the fluorescent yield in two-photon laser scanning microscopy with dispersion compensation,” Opt. Express 18, 13661–13672 (2010).
[CrossRef]

P. F. Tekavec, J. A. Myers, K. L. M. Lewis, F. D. Fuller, and J. P. Ogilvie, “Effects of chirp on two-dimensional Fourier transform electronic spectra,” Opt. Express 18, 11015–11024 (2010).
[CrossRef]

J. P. Ogilvie, D. Débarre, X. Solinas, J.-L. Martin, E. Beaurepaire, and M. Joffre, “Use of coherent control for selective two-photon fluorescence microscopy in live organisms,” Opt. Express 14, 759–766 (2006).
[CrossRef]

I. Pastirk, J. Dela Cruz, K. Walowicz, V. Lozovoy, and M. Dantus, “Selective two-photon microscopy with shaped femtosecond pulses,” Opt. Express 11, 1695–1701 (2003).
[CrossRef]

M. H. Brenner, D. Cai, J. A. Swanson, and J. P. Ogilvie, “Two-photon imaging of multiple fluorescent proteins by phase-shaping and linear unmixing with a single broadband laser,” Opt. Express 21, 17256–17264 (2013).
[CrossRef]

J. A. Myers, K. L. Lewis, P. F. Tekavec, and J. P. Ogilvie, “Two-color two-dimensional Fourier transform electronic spectroscopy with a pulse-shaper,” Opt. Express 16, 17420–17428 (2008).
[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

(a) Measured c(ω), which is a measure of spectral intensity. (b) Measured and true group delay as a function of wavelength relative to the group delay of 590 nm. (c) Difference between measured and true group delay. Red solid line, true group delay based on the published dispersion formula. Black dotted line, average of five independent measurements of group delay using the SPEAR method. Blue shaded area, the range of those five measurements showing excellent repeatability and accuracy everywhere there is significant spectral intensity. Vertical green lines, boundaries of the region of interest over which there is significant spectral intensity.

Fig. 2.
Fig. 2.

Depiction of the four test cases being used to evaluate pulse-shaper-only spectral phase measurements. Left column, spectral intensity and group delay; right column, temporal intensity and phase. Blue dotted line, spectral or temporal intensity; red solid line, spectral group delay or temporal phase; vertical thin green lines, edges of region of interest with appreciable spectral intensity.

Fig. 3.
Fig. 3.

Simulated spectral group delay and retrieved distribution of spectral group delay for the case 1 pulse under the methods being simulated. Retrieved group delays from FROG were artificially rectified to have the correct direction of time. Red line, simulated true spectral group delay. Dark shaded area, the 30th–70th percentiles of the retrieved group delay; light shaded area, the 10th–90th percentiles. Vertical green lines, boundaries of the spectral region of interest. The retrieved group-delay errors are RMS deviations between retrieved and true group delay over the region of interest.

Fig. 4.
Fig. 4.

Simulated spectral group delay and retrieved distribution of spectral group delay for the case 2 pulse under the methods being simulated. Retrieved group delays from FROG were artificially rectified to have the correct direction of time. Red line, simulated true spectral group delay. Dark shaded area, the 30th–70th percentiles of the retrieved group delay; light shaded area, the 10th–90th percentiles. Vertical green lines, boundaries of the spectral region of interest. Retrieved group-delay errors are RMS deviations between retrieved and true group delay over the region of interest.

Fig. 5.
Fig. 5.

Simulated spectral group delay and retrieved distribution of spectral group delay for the case 3 pulse under the methods being simulated. Retrieved group delays from FROG were artificially rectified to have the correct direction of time. Red line, simulated true spectral group delay. Dark shaded area, the 30th–70th percentiles of the retrieved group delay; light shaded area, the 10th–90th percentiles. Vertical green lines, boundaries of the spectral region of interest. Retrieved group-delay errors are RMS deviations between retrieved and true group delay over the region of interest.

Fig. 6.
Fig. 6.

Simulated spectral group delay and retrieved distribution of spectral group delay for the case 4 pulse under the methods being simulated. Retrieved group delays from FROG were artificially rectified to have the correct direction of time. Red line, simulated true spectral group delay. Dark shaded area, the 30th–70th percentiles of the retrieved group delay; light shaded area, the 10th–90th percentiles. Vertical green lines, boundaries of the spectral region of interest. Retrieved group-delay errors are RMS deviations between retrieved and true group delay over the region of interest.

Fig. 7.
Fig. 7.

Intensity of the spectral filter associated with the finite phase-matching bandwidth of a 10 μm thick BBO crystal, cut at 42°. The cut angle was chosen to ensure there was appreciable amplitude over the full second-harmonic laser bandwidth.

Tables (1)

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Table 1. Comparison of Different Methods’ Speed, both Laser Time and Computation Time

Equations (19)

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E(ω)=|E(ω)|exp(iφ(ω)).
Ei(ω)=|E(ω)|exp(iφ(ω)i2ϕ2(i)(ωω0)2),
ISHG(i)(2ω)=β|1φ(ω)+ϕ2(i)||E(ω)|4,
φ(ω)ϕ2(1)ISHG(1)(2ω)+ϕ2(2)ISHG(2)(2ω)ISHG(1)(2ω)+ISHG(2)(2ω).
L(c,b)=i,ωWi(ω)(ISHG(i)(2ω)|c(ω)b(ω)+ϕ2(i)|)2.
Wi(ω)=1r+ISHG(i)(2ω),
L(c,b)=i,ωWi(ω)(ISHG(i)(2ω)si·c(ω)b(ω)+ϕ2(i))2.
[isi·Wi(ω)ISHG(i)(2ω)b(ω)+ϕ2(i)][iWi(ω)(b(ω)+ϕ2(i))3]=[iWi(ω)(b(ω)+ϕ2(i))2][isi·Wi(ω)ISHG(i)(2ω)(b(ω)+ϕ2(i))2].
c(ω)=isi·Wi(ω)ISHG(i)(2ω)b(ω)+ϕ2(i)iWi(ω)(b(ω)+ϕ2(i))2.
2x2En2c22t2E=χ(2)c22t2E2.
2x2E1stn2c22t2E1st=0;
2x2E2ndn2c22t2E2nd=χ(2)c22t2E1st2.
E(x,y,z,t)=F(x,t)12πσexp(y2+z24σ2).
F2nd(x,ω)=χ(2)ω4n(ω)c12πσ×exp(iT(k(ω)+ω/vg2ω02dndω|ω0/c))1(k(ω)+ω/vg2ω02dndω|ω0/c)×dteiωtF1st2(t).
L=dωiRi,weighted2(ω),
Ri,weighted(ω)=1nestimate(i)(ω)[Imeasured(i)(ω)Vi(ω)],
Vi(ω)=Ui(ω)Ui*(ω),
Ui(ω)=Ftω{Ti2(t)},
Ti(t)=Fωt1{Si(ω)E(ω)}.

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