Abstract

A simple technique for the synthesis of optical pulse sequences is described, where the input laser spectrum is viewed as a superposition of independent but interlaced combs assigned to different sub-pulses. The devised concept enables intuitive programming of complex multi-pulse waveforms via one-dimensional phase-only shaping. Using this approach, we perform self-referenced cross-correlation measurements of various optical waveforms and demonstrate the generation and coding of shaped pulse sequences.

© 2009 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–639 (2000).
    [CrossRef] [PubMed]
  2. T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
    [CrossRef] [PubMed]
  3. Z. Jiang, C. B. Huang, D. E. Leaird, and A. M. Weiner, “Optical arbitrary waveform processing of more than 100 spectral comb lines,” Nat. Photonics 1(8), 463–467 (2007).
    [CrossRef]
  4. V. R. Supradeepa, C. B. Huang, D. E. Leaird, and A. M. Weiner, “Femtosecond pulse shaping in two dimensions: towards higher complexity optical waveforms,” Opt. Express 16(16), 11878–11887 (2008).
    [CrossRef] [PubMed]
  5. A typical ultrafast Ti:Sapphire laser oscillator, operating at 80 MHz and having 100-nm bandwidth, features about 106 comb lines within its spectrum. At the same time, the number of addressable pixels in a dispersive 4f pulse shaper with a linear SLM in its Fourier plane ranges from 100 to ~1,000.
  6. A. M. Weiner and D. E. Leaird, “Generation of Terahertz-Rate Trains of Femtosecond Pulses by Phase-Only Filtering,” Opt. Lett. 15(1), 51–53 (1990).
    [CrossRef] [PubMed]
  7. M. M. Wefers and K. A. Nelson, “Programmable Phase and Amplitude Femtosecond Pulse Shaping,” Opt. Lett. 18(23), 2032–2034 (1993).
    [CrossRef] [PubMed]
  8. A. M. Weiner, S. Oudin, D. E. Leaird, and D. H. Reitze, “Shaping of Femtosecond Pulses Using Phase-Only Filters Designed by Simulated Annealing,” J. Opt. Soc. Am. A 10(5), 1112–1120 (1993).
    [CrossRef]
  9. M. M. Wefers and K. A. Nelson, “Generation of High-Fidelity Programmable Ultrafast Optical Wave-Forms,” Opt. Lett. 20(9), 1047–1049 (1995).
    [CrossRef] [PubMed]
  10. M. A. Dugan, J. X. Tull, and W. S. Warren, “High-resolution acousto-optic shaping of unamplified and amplified femtosecond laser pulses,” J. Opt. Soc. Am. B 14(9), 2348–2358 (1997).
    [CrossRef]
  11. T. Brixner and G. Gerber, “Femtosecond polarization pulse shaping,” Opt. Lett. 26(8), 557–559 (2001).
    [CrossRef]
  12. D. Yelin, D. Meshulach, and Y. Silberberg, “Adaptive femtosecond pulse compression,” Opt. Lett. 22(23), 1793–1795 (1997).
    [CrossRef]
  13. T. Baumert, T. Brixner, V. Seyfried, M. Strehle, and G. Gerber, “Femtosecond pulse shaping by an evolutionary algorithm with feedback,” Appl. Phys. B 65(6), 779–782 (1997).
    [CrossRef]
  14. V. V. Lozovoy, I. Pastirk, and M. Dantus, “Multiphoton intrapulse interference. IV. Ultrashort laser pulse spectral phase characterization and compensation,” Opt. Lett. 29(7), 775–777 (2004).
    [CrossRef] [PubMed]
  15. B. W. Xu, J. M. Gunn, J. M. Dela Cruz, V. V. Lozovoy, and M. Dantus, “Quantitative investigation of the multiphoton intrapulse interference phase scan method for simultaneous phase measurement and compensation of femtosecond laser pulses,” J. Opt. Soc. Am. B 23(4), 750–759 (2006).
    [CrossRef]
  16. B. von Vacano, T. Buckup, and M. Motzkus, “In situ broadband pulse compression for multiphoton microscopy using a shaper-assisted collinear SPIDER,” Opt. Lett. 31(8), 1154–1156 (2006).
    [CrossRef] [PubMed]
  17. A. Galler and T. Feurer, “Pulse shaper assisted short laser pulse characterization,” Appl. Phys. B 90(3-4), 427–430 (2008).
    [CrossRef]
  18. D. Meshulach and Y. Silberberg, “Coherent quantum control of two-photon transitions by a femtosecond laser pulse,” Nature 396(6708), 239–242 (1998).
    [CrossRef]
  19. T. Brixner, N. H. Damrauer, P. Niklaus, and G. Gerber, “Photoselective adaptive femtosecond quantum control in the liquid phase,” Nature 414(6859), 57–60 (2001).
    [CrossRef] [PubMed]
  20. N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature 418(6897), 512–514 (2002).
    [CrossRef] [PubMed]
  21. T. Hornung, J. C. Vaughan, T. Feurer, and K. A. Nelson, “Degenerate four-wave mixing spectroscopy based on two-dimensional femtosecond pulse shaping,” Opt. Lett. 29(17), 2052–2054 (2004).
    [CrossRef] [PubMed]
  22. E. M. Grumstrup, S. H. Shim, M. A. Montgomery, N. H. Damrauer, and M. T. Zanni, “Facile collection of two-dimensional electronic spectra using femtosecond pulse-shaping Technology,” Opt. Express 15(25), 16681–16689 (2007).
    [CrossRef] [PubMed]
  23. J. C. Vaughan, T. Hornung, T. Feurer, and K. A. Nelson, “Diffraction-based femtosecond pulse shaping with a two-dimensional spatial light modulator,” Opt. Lett. 30(3), 323–325 (2005).
    [CrossRef] [PubMed]
  24. J. W. Wilson, P. Schlup, and R. A. Bartels, “Ultrafast phase and amplitude pulse shaping with a single, one-dimensional, high-resolution phase mask,” Opt. Express 15(14), 8979–8987 (2007).
    [CrossRef] [PubMed]
  25. E. Frumker and Y. Silberberg, “Phase and amplitude pulse shaping with two-dimensional phase-only spatial light modulators,” J. Opt. Soc. Am. B 24(12), 2940–2947 (2007).
    [CrossRef]
  26. The experimental data reported in this work were partially presented at SPIE Photonics West 2009 (San Jose, CA - January 24–29, 2009)
  27. A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71(5), 1929–1960 (2000).
    [CrossRef]

2008 (2)

2007 (4)

2006 (2)

2005 (1)

2004 (2)

2002 (2)

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
[CrossRef] [PubMed]

N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature 418(6897), 512–514 (2002).
[CrossRef] [PubMed]

2001 (2)

T. Brixner, N. H. Damrauer, P. Niklaus, and G. Gerber, “Photoselective adaptive femtosecond quantum control in the liquid phase,” Nature 414(6859), 57–60 (2001).
[CrossRef] [PubMed]

T. Brixner and G. Gerber, “Femtosecond polarization pulse shaping,” Opt. Lett. 26(8), 557–559 (2001).
[CrossRef]

2000 (2)

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71(5), 1929–1960 (2000).
[CrossRef]

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–639 (2000).
[CrossRef] [PubMed]

1998 (1)

D. Meshulach and Y. Silberberg, “Coherent quantum control of two-photon transitions by a femtosecond laser pulse,” Nature 396(6708), 239–242 (1998).
[CrossRef]

1997 (3)

1995 (1)

1993 (2)

1990 (1)

Bartels, R. A.

Baumert, T.

T. Baumert, T. Brixner, V. Seyfried, M. Strehle, and G. Gerber, “Femtosecond pulse shaping by an evolutionary algorithm with feedback,” Appl. Phys. B 65(6), 779–782 (1997).
[CrossRef]

Brixner, T.

T. Brixner, N. H. Damrauer, P. Niklaus, and G. Gerber, “Photoselective adaptive femtosecond quantum control in the liquid phase,” Nature 414(6859), 57–60 (2001).
[CrossRef] [PubMed]

T. Brixner and G. Gerber, “Femtosecond polarization pulse shaping,” Opt. Lett. 26(8), 557–559 (2001).
[CrossRef]

T. Baumert, T. Brixner, V. Seyfried, M. Strehle, and G. Gerber, “Femtosecond pulse shaping by an evolutionary algorithm with feedback,” Appl. Phys. B 65(6), 779–782 (1997).
[CrossRef]

Buckup, T.

Cundiff, S. T.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–639 (2000).
[CrossRef] [PubMed]

Damrauer, N. H.

Dantus, M.

Dela Cruz, J. M.

Diddams, S. A.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–639 (2000).
[CrossRef] [PubMed]

Dudovich, N.

N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature 418(6897), 512–514 (2002).
[CrossRef] [PubMed]

Dugan, M. A.

Feurer, T.

Frumker, E.

Galler, A.

A. Galler and T. Feurer, “Pulse shaper assisted short laser pulse characterization,” Appl. Phys. B 90(3-4), 427–430 (2008).
[CrossRef]

Gerber, G.

T. Brixner, N. H. Damrauer, P. Niklaus, and G. Gerber, “Photoselective adaptive femtosecond quantum control in the liquid phase,” Nature 414(6859), 57–60 (2001).
[CrossRef] [PubMed]

T. Brixner and G. Gerber, “Femtosecond polarization pulse shaping,” Opt. Lett. 26(8), 557–559 (2001).
[CrossRef]

T. Baumert, T. Brixner, V. Seyfried, M. Strehle, and G. Gerber, “Femtosecond pulse shaping by an evolutionary algorithm with feedback,” Appl. Phys. B 65(6), 779–782 (1997).
[CrossRef]

Grumstrup, E. M.

Gunn, J. M.

Hall, J. L.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–639 (2000).
[CrossRef] [PubMed]

Hänsch, T. W.

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
[CrossRef] [PubMed]

Holzwarth, R.

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
[CrossRef] [PubMed]

Hornung, T.

Huang, C. B.

V. R. Supradeepa, C. B. Huang, D. E. Leaird, and A. M. Weiner, “Femtosecond pulse shaping in two dimensions: towards higher complexity optical waveforms,” Opt. Express 16(16), 11878–11887 (2008).
[CrossRef] [PubMed]

Z. Jiang, C. B. Huang, D. E. Leaird, and A. M. Weiner, “Optical arbitrary waveform processing of more than 100 spectral comb lines,” Nat. Photonics 1(8), 463–467 (2007).
[CrossRef]

Jiang, Z.

Z. Jiang, C. B. Huang, D. E. Leaird, and A. M. Weiner, “Optical arbitrary waveform processing of more than 100 spectral comb lines,” Nat. Photonics 1(8), 463–467 (2007).
[CrossRef]

Jones, D. J.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–639 (2000).
[CrossRef] [PubMed]

Leaird, D. E.

Lozovoy, V. V.

Meshulach, D.

D. Meshulach and Y. Silberberg, “Coherent quantum control of two-photon transitions by a femtosecond laser pulse,” Nature 396(6708), 239–242 (1998).
[CrossRef]

D. Yelin, D. Meshulach, and Y. Silberberg, “Adaptive femtosecond pulse compression,” Opt. Lett. 22(23), 1793–1795 (1997).
[CrossRef]

Montgomery, M. A.

Motzkus, M.

Nelson, K. A.

Niklaus, P.

T. Brixner, N. H. Damrauer, P. Niklaus, and G. Gerber, “Photoselective adaptive femtosecond quantum control in the liquid phase,” Nature 414(6859), 57–60 (2001).
[CrossRef] [PubMed]

Oron, D.

N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature 418(6897), 512–514 (2002).
[CrossRef] [PubMed]

Oudin, S.

Pastirk, I.

Ranka, J. K.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–639 (2000).
[CrossRef] [PubMed]

Reitze, D. H.

Schlup, P.

Seyfried, V.

T. Baumert, T. Brixner, V. Seyfried, M. Strehle, and G. Gerber, “Femtosecond pulse shaping by an evolutionary algorithm with feedback,” Appl. Phys. B 65(6), 779–782 (1997).
[CrossRef]

Shim, S. H.

Silberberg, Y.

E. Frumker and Y. Silberberg, “Phase and amplitude pulse shaping with two-dimensional phase-only spatial light modulators,” J. Opt. Soc. Am. B 24(12), 2940–2947 (2007).
[CrossRef]

N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature 418(6897), 512–514 (2002).
[CrossRef] [PubMed]

D. Meshulach and Y. Silberberg, “Coherent quantum control of two-photon transitions by a femtosecond laser pulse,” Nature 396(6708), 239–242 (1998).
[CrossRef]

D. Yelin, D. Meshulach, and Y. Silberberg, “Adaptive femtosecond pulse compression,” Opt. Lett. 22(23), 1793–1795 (1997).
[CrossRef]

Stentz, A.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–639 (2000).
[CrossRef] [PubMed]

Strehle, M.

T. Baumert, T. Brixner, V. Seyfried, M. Strehle, and G. Gerber, “Femtosecond pulse shaping by an evolutionary algorithm with feedback,” Appl. Phys. B 65(6), 779–782 (1997).
[CrossRef]

Supradeepa, V. R.

Tull, J. X.

Udem, T.

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
[CrossRef] [PubMed]

Vaughan, J. C.

von Vacano, B.

Warren, W. S.

Wefers, M. M.

Weiner, A. M.

Wilson, J. W.

Windeler, R. S.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–639 (2000).
[CrossRef] [PubMed]

Xu, B. W.

Yelin, D.

Zanni, M. T.

Appl. Phys. B (2)

T. Baumert, T. Brixner, V. Seyfried, M. Strehle, and G. Gerber, “Femtosecond pulse shaping by an evolutionary algorithm with feedback,” Appl. Phys. B 65(6), 779–782 (1997).
[CrossRef]

A. Galler and T. Feurer, “Pulse shaper assisted short laser pulse characterization,” Appl. Phys. B 90(3-4), 427–430 (2008).
[CrossRef]

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

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

Nat. Photonics (1)

Z. Jiang, C. B. Huang, D. E. Leaird, and A. M. Weiner, “Optical arbitrary waveform processing of more than 100 spectral comb lines,” Nat. Photonics 1(8), 463–467 (2007).
[CrossRef]

Nature (4)

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
[CrossRef] [PubMed]

D. Meshulach and Y. Silberberg, “Coherent quantum control of two-photon transitions by a femtosecond laser pulse,” Nature 396(6708), 239–242 (1998).
[CrossRef]

T. Brixner, N. H. Damrauer, P. Niklaus, and G. Gerber, “Photoselective adaptive femtosecond quantum control in the liquid phase,” Nature 414(6859), 57–60 (2001).
[CrossRef] [PubMed]

N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature 418(6897), 512–514 (2002).
[CrossRef] [PubMed]

Opt. Express (3)

Opt. Lett. (9)

D. Yelin, D. Meshulach, and Y. Silberberg, “Adaptive femtosecond pulse compression,” Opt. Lett. 22(23), 1793–1795 (1997).
[CrossRef]

T. Brixner and G. Gerber, “Femtosecond polarization pulse shaping,” Opt. Lett. 26(8), 557–559 (2001).
[CrossRef]

V. V. Lozovoy, I. Pastirk, and M. Dantus, “Multiphoton intrapulse interference. IV. Ultrashort laser pulse spectral phase characterization and compensation,” Opt. Lett. 29(7), 775–777 (2004).
[CrossRef] [PubMed]

T. Hornung, J. C. Vaughan, T. Feurer, and K. A. Nelson, “Degenerate four-wave mixing spectroscopy based on two-dimensional femtosecond pulse shaping,” Opt. Lett. 29(17), 2052–2054 (2004).
[CrossRef] [PubMed]

J. C. Vaughan, T. Hornung, T. Feurer, and K. A. Nelson, “Diffraction-based femtosecond pulse shaping with a two-dimensional spatial light modulator,” Opt. Lett. 30(3), 323–325 (2005).
[CrossRef] [PubMed]

B. von Vacano, T. Buckup, and M. Motzkus, “In situ broadband pulse compression for multiphoton microscopy using a shaper-assisted collinear SPIDER,” Opt. Lett. 31(8), 1154–1156 (2006).
[CrossRef] [PubMed]

A. M. Weiner and D. E. Leaird, “Generation of Terahertz-Rate Trains of Femtosecond Pulses by Phase-Only Filtering,” Opt. Lett. 15(1), 51–53 (1990).
[CrossRef] [PubMed]

M. M. Wefers and K. A. Nelson, “Programmable Phase and Amplitude Femtosecond Pulse Shaping,” Opt. Lett. 18(23), 2032–2034 (1993).
[CrossRef] [PubMed]

M. M. Wefers and K. A. Nelson, “Generation of High-Fidelity Programmable Ultrafast Optical Wave-Forms,” Opt. Lett. 20(9), 1047–1049 (1995).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71(5), 1929–1960 (2000).
[CrossRef]

Science (1)

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–639 (2000).
[CrossRef] [PubMed]

Other (2)

A typical ultrafast Ti:Sapphire laser oscillator, operating at 80 MHz and having 100-nm bandwidth, features about 106 comb lines within its spectrum. At the same time, the number of addressable pixels in a dispersive 4f pulse shaper with a linear SLM in its Fourier plane ranges from 100 to ~1,000.

The experimental data reported in this work were partially presented at SPIE Photonics West 2009 (San Jose, CA - January 24–29, 2009)

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1.
Fig. 1.

The concept of multiple independent comb shaping (MICS). The sequence of two shaped pulses (e.g., a delayed TL pulse and a pulse with the third-order dispersion) is created by encoding a piecewise phase mask across the spectrum of an original TL laser pulse. This piecewise phase can be viewed as an alternating superposition of continuous phase functions applied to two independent subsets (combs) of the available spectrum.

Fig. 2.
Fig. 2.

(a) Layout of the experimental setup. G, plane-ruled grating (600/mm, Newport); SM, a 3-inch silver-coated spherical mirror (f = 500 mm, Thorlabs); SLM, spatial light modulator; NDF, neutral density filter; FM, focusing mirror (f = 250 mm); NL, nonlinear crystal; F, filter (BG39 glass); Spec., Ocean Optics S-2000 or USB4000 spectrometer. (b) Typical laser spectrum after the shaper (solid line) and MIIPS phase compensation mask (dashed line).

Fig. 3.
Fig. 3.

Single-beam auto- and cross-correlation of optical waveforms via MICS. (a) Nonbackground-free and interferometric autocorrelation spectrograms (MICA and i-MICA, respectively) obtained experimentally for a TL 15-fs pulse. (b) Integrated SHG signal as a function of time delay between two pulse replicas. (c) Non-background-free and interferometric cross-correlation traces, x-MICA and xi-MICA, between a TL pulse and: (topleft) a pulse with the programmed second-order dispersion of + 300 fs2; (top-right) a pulse with the programmed third-order dispersion of + 10,000 fs3; (bottom) an original pulse right after the pulse shaper, with zero phase mask on the SLM. To obtain the TL pulse, MIIPS compensation mask is used.

Fig. 4.
Fig. 4.

MICS for generation and coding of multi-pulse sequences. (a) One of the unwrapped piecewise phase masks used to generate the x-MICA spectrogram, shown in the inset of Fig. 4(b). Pixel phase values that belong to the four combs are highlighted by different symbols. For the instance shown, the mapping pulse is delayed by -300 fs. (b) A 3 + 1 pulse sequence, with the first pulse having third-order dispersion of -5000 fs3 (at -150 fs), the second pulse having the second-order dispersion of + 200 fs2 (at 0 fs), and the third pulse being TL (at + 150 fs). The fourth pulse, also TL, is scanned from -300 fs to 300 fs to generate an interferometric cross-correlation trace. Two SLM pixels per peak are assigned for every comb. Inset: Nonbackground-free cross-correlation spectrogram of a similar pulse train but with the locked carrier frequency phase, when only pulse envelopes are shifted in time. (c) Multi-pulse generation and coding: the original 6 + 1 pulse sequence of 70-fs period, which corresponds to 14 THz rep. rate, is coded with π phase shifts that eliminate contributions of various pulses within the sequence. Two SLM pixels per tooth are assigned for every comb. For the pulse to be removed, the phase of one of the two pixels for every tooth in the corresponding comb is shifted by π.

Fig. 5.
Fig. 5.

(a) Spectral comb (top) and corresponding time domain structure (bottom) if the comb teeth are equidistantly spaced in the frequency domain. (b) Experimental xi-MICA profile between two unequal combs for Δ/δ = 10. Tooth width for the first comb is 1 pixel; the other has the tooth width of 9 SLM pixels.

Fig. 6.
Fig. 6.

(a) x-MICA and xi-MICA traces obtained for various-length pulse sequences, from 1 + 1 to 5 + 1, under fixed acquisition conditions. Two pixels per comb tooth are used for every pulse train. (b) Dependence of the acquired SHG intensity on the number of spectral combs in Fig. 6(a). When the scanned pulse does not overlap with any of the pulses in a sequence, collected SHG signal is referred to as background. The increase in the signal intensity due to the constructive interference of overlapped pulses is taken as peak amplitude. The experimental points are fitted with functions of the form ISHG = α·Nβ , where α and β are fitting parameters, and N is the number of combs.

Fig. A1.
Fig. A1.

Pulse shaper range. (a) Effect of shaper resolution on shaper-assisted time delay tuning: (top) single transmitting SLM pixel and corresponding optical waveform; (center) several transmitting SLM pixels and corresponding optical waveform at the shaper output. For simplicity, assume that the pixels are illuminated with equal intensity; (bottom) linear phase mask and its effect on the out-going laser pulse. (b) Pulse shaper range. Black line represents the total SHG signal as a function of time delay of a single TL pulse. The set of enclosed peaks (gray lines) are short-range MICA traces of the pulse for various time delays. (c) Total SHG signal as a function of the programmed time delay for different numbers of binned pixels. Binning is applied only to the linear phase function, not the phase distortion compensation mask.

Fig. A2.
Fig. A2.

Pulse self-characterization via MICS. (a) Pulse shaping for intensity-like multiple-independent-comb assisted autocorrelation (MICA). (b) Pulse shaping for interferometric multiple-independent-comb assisted autocorrelation (i-MICA).

Fig. A3.
Fig. A3.

Pulse characterization at the output of an amplified laser system. (a) Schematic diagram of the setup. NL, nonlinear crystal; F, color filter (BG39). (b) Output laser spectrum. (c) Experimental MICA and i-MICA traces. The autocorrelation FWHM corresponds to pulse duration of 34.2 fs.

Fig. A4.
Fig. A4.

Pulse sequence coding via binary shaping. (a) π-step is programmed on every 2-pixel comb tooth of the corresponding pulse. (b) π-shift is added to the phase of every other tooth in the comb.

Equations (1)

Equations on this page are rendered with MathJax. Learn more.

I=I0×[sin(Δωt/2)ωt/2]2 ,

Metrics