Abstract

We present full vector-field characterization of amplitude, phase, and polarization controlled femtosecond laser pulses in the ultraviolet (UV) with a method termed DFG-XTURTLE. It combines the recently developed technique of tomographic ultrafast retrieval of transverse light E-fields (TURTLE) with the well-established cross-correlation frequency-resolved optical gating (XFROG) amplitude and phase retrieval algorithm. Three individual linear projections at 0°, 45°, and 90° of the vector-shaped field in the UV are frequency mixed with a well-characterized reference field at 800nm and the generated frequency-resolved difference-frequency cross correlations in the visible are analyzed with a standard XFROG algorithm. The TURTLE search algorithm then establishes the full vector field of the UV pulses by finding the correct phase relationship between the 0° and 90° projections to reconstruct the projection at 45°. To retrieve the interpulse phase of temporally well-separated pulses, additional spectra must be taken. The handedness of shaped pulses can also be assigned with additional measurements.

© 2011 Optical Society of America

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  1. R. Selle, P. Nuernberger, F. Langhojer, F. Dimler, S. Fechner, G. Gerber, and T. Brixner, “Generation of polarization-shaped ultraviolet femtosecond pulses,” Opt. Lett. 33, 803–805 (2008).
    [CrossRef] [PubMed]
  2. P. Nuernberger, R. Selle, F. Langhojer, F. Dimler, S. Fechner, G. Gerber, and T. Brixner, “Polarization-shaped femtosecond laser pulses in the ultraviolet,” J. Opt. A 11, 085202 (2009).
    [CrossRef]
  3. M. T. Seidel, Z. Zhang, S. Yan, and H.-S. Tan, “Ultraviolet polarization pulse shaping using sum-frequency generation,” J. Opt. Soc. Am. B 28, 1146–1151 (2011).
    [CrossRef]
  4. W. J. Walecki, D. N. Fittinghoff, A. L. Smirl, and R. Trebino, “Characterization of the polarization state of weak ultrashort coherent signals by dual-channel spectral interferometry,” Opt. Lett. 22, 81–83 (1997).
    [CrossRef] [PubMed]
  5. T. Oksenhendler, S. Coudreau, N. Forget, V. Crozatier, S. Grabielle, R. Herzog, O. Gobert, and D. Kaplan, “Self-referenced spectral interferometry,” Appl. Phys. B 99, 7–12 (2010).
    [CrossRef]
  6. J. Möhring, T. Buckup, and M. Motzkus, “Shaper-assisted full-phase characterization of UV pulses without a spectrometer,” Opt. Lett. 35, 3916–3918 (2010).
    [CrossRef] [PubMed]
  7. J. A. Bolger, A. E. Paul, and A. L. Smirl, “Ultrafast ellipsometry of coherent processes and exciton-exciton interactions in quantum wells at negative delays,” Phys. Rev. B 54, 11666–11671 (1996).
    [CrossRef]
  8. B. Haase, “Determination of weak optical pulses in amplitude and phase by measurement of the transient polarization state,” Opt. Lett. 24, 543–545 (1999).
    [CrossRef]
  9. M. Plewicki, F. Weise, S. M. Weber, and A. Lindinger, “Phase, amplitude, and polarization shaping with a pulse shaper in a Mach–Zehnder interferometer,” Appl. Opt. 45, 8354–8359 (2006).
    [CrossRef] [PubMed]
  10. J. J. Ferreiro, R. de la Fuente, and E. López-Lago, “Characterization of arbitrarily polarized ultrashort laser pulses by cross-phase modulation,” Opt. Lett. 26, 1025–1027 (2001).
    [CrossRef]
  11. P. Schlup, O. Masihzadeh, L. Xu, R. Trebino, and R. A. Bartels, “Tomographic retrieval of the polarization state of an ultrafast laser pulse,” Opt. Lett. 33, 267–269 (2008).
    [CrossRef] [PubMed]
  12. P. Schlup and R. A. Bartels, “Impact of measurement noise in tomographic ultrafast retrieval of transverse light E-fields (TURTLE) ultrashort polarization characterization,” IEEE Photon. J. 1, 163–171 (2009).
    [CrossRef]
  13. L. Xu, P. Schlup, O. Masihzadeh, R. A. Bartels, and R. Trebino, “Analysis of the measurement of polarization-shaped ultrashort laser pulses by tomographic ultrafast retrieval of transverse light E fields,” J. Opt. Soc. Am. B 26, 2363–2369 (2009).
    [CrossRef]
  14. P. Lu, J. Liu, H. Li, H. Pan, J. Wu, and H. Zeng, “Cross-correlation frequency-resolved optical gating by molecular alignment for ultraviolet femtosecond pulse measurement,” Appl. Phys. Lett. 97, 061101 (2010).
    [CrossRef]
  15. S. Linden, J. Kuhl, and H. Giessen, “Amplitude and phase characterization of weak blue ultrashort pulses by downconversion,” Opt. Lett. 24, 569–571 (1999).
    [CrossRef]
  16. D. T. Reid, P. Loza-Alvarez, C. T. A. Brown, T. Beddard, and W. Sibbett, “Amplitude and phase measurement of mid-infrared femtosecond pulses by using cross-correlation frequency-resolved optical gating,” Opt. Lett. 25, 1478–1480(2000).
    [CrossRef]
  17. 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. Am. B 11, 2206 (1994).
    [CrossRef]
  18. P. O’Shea, M. Kimmel, X. Gu, and R. Trebino, “Highly simplified device for ultrashort-pulse measurement,” Opt. Lett. 26, 932–934 (2001).
    [CrossRef]
  19. C. T. Middleton, D. B. Strasfeld, and M. T. Zanni, “Polarization shaping in the mid-IR and polarization-based balanced heterodyne detection with application to 2D IR spectroscopy,” Opt. Express 17, 14526–14533 (2009).
    [CrossRef] [PubMed]
  20. S. Yan and H.-S. Tan, “Phase cycling schemes for two-dimensional optical spectroscopy with a pump-probe geometry,” Chem. Phys. 360, 110–115 (2009).
    [CrossRef]
  21. M. T. Seidel, S. Yan, and H.-S. Tan, “Mid-infrared polarization pulse shaping by parametric transfer,” Opt. Lett. 35, 478–480(2010).
    [CrossRef] [PubMed]

2011 (1)

2010 (4)

M. T. Seidel, S. Yan, and H.-S. Tan, “Mid-infrared polarization pulse shaping by parametric transfer,” Opt. Lett. 35, 478–480(2010).
[CrossRef] [PubMed]

J. Möhring, T. Buckup, and M. Motzkus, “Shaper-assisted full-phase characterization of UV pulses without a spectrometer,” Opt. Lett. 35, 3916–3918 (2010).
[CrossRef] [PubMed]

T. Oksenhendler, S. Coudreau, N. Forget, V. Crozatier, S. Grabielle, R. Herzog, O. Gobert, and D. Kaplan, “Self-referenced spectral interferometry,” Appl. Phys. B 99, 7–12 (2010).
[CrossRef]

P. Lu, J. Liu, H. Li, H. Pan, J. Wu, and H. Zeng, “Cross-correlation frequency-resolved optical gating by molecular alignment for ultraviolet femtosecond pulse measurement,” Appl. Phys. Lett. 97, 061101 (2010).
[CrossRef]

2009 (5)

S. Yan and H.-S. Tan, “Phase cycling schemes for two-dimensional optical spectroscopy with a pump-probe geometry,” Chem. Phys. 360, 110–115 (2009).
[CrossRef]

P. Nuernberger, R. Selle, F. Langhojer, F. Dimler, S. Fechner, G. Gerber, and T. Brixner, “Polarization-shaped femtosecond laser pulses in the ultraviolet,” J. Opt. A 11, 085202 (2009).
[CrossRef]

P. Schlup and R. A. Bartels, “Impact of measurement noise in tomographic ultrafast retrieval of transverse light E-fields (TURTLE) ultrashort polarization characterization,” IEEE Photon. J. 1, 163–171 (2009).
[CrossRef]

C. T. Middleton, D. B. Strasfeld, and M. T. Zanni, “Polarization shaping in the mid-IR and polarization-based balanced heterodyne detection with application to 2D IR spectroscopy,” Opt. Express 17, 14526–14533 (2009).
[CrossRef] [PubMed]

L. Xu, P. Schlup, O. Masihzadeh, R. A. Bartels, and R. Trebino, “Analysis of the measurement of polarization-shaped ultrashort laser pulses by tomographic ultrafast retrieval of transverse light E fields,” J. Opt. Soc. Am. B 26, 2363–2369 (2009).
[CrossRef]

2008 (2)

2006 (1)

2001 (2)

2000 (1)

1999 (2)

1997 (1)

1996 (1)

J. A. Bolger, A. E. Paul, and A. L. Smirl, “Ultrafast ellipsometry of coherent processes and exciton-exciton interactions in quantum wells at negative delays,” Phys. Rev. B 54, 11666–11671 (1996).
[CrossRef]

1994 (1)

Bartels, R. A.

Beddard, T.

Bolger, J. A.

J. A. Bolger, A. E. Paul, and A. L. Smirl, “Ultrafast ellipsometry of coherent processes and exciton-exciton interactions in quantum wells at negative delays,” Phys. Rev. B 54, 11666–11671 (1996).
[CrossRef]

Brixner, T.

P. Nuernberger, R. Selle, F. Langhojer, F. Dimler, S. Fechner, G. Gerber, and T. Brixner, “Polarization-shaped femtosecond laser pulses in the ultraviolet,” J. Opt. A 11, 085202 (2009).
[CrossRef]

R. Selle, P. Nuernberger, F. Langhojer, F. Dimler, S. Fechner, G. Gerber, and T. Brixner, “Generation of polarization-shaped ultraviolet femtosecond pulses,” Opt. Lett. 33, 803–805 (2008).
[CrossRef] [PubMed]

Brown, C. T. A.

Buckup, T.

Coudreau, S.

T. Oksenhendler, S. Coudreau, N. Forget, V. Crozatier, S. Grabielle, R. Herzog, O. Gobert, and D. Kaplan, “Self-referenced spectral interferometry,” Appl. Phys. B 99, 7–12 (2010).
[CrossRef]

Crozatier, V.

T. Oksenhendler, S. Coudreau, N. Forget, V. Crozatier, S. Grabielle, R. Herzog, O. Gobert, and D. Kaplan, “Self-referenced spectral interferometry,” Appl. Phys. B 99, 7–12 (2010).
[CrossRef]

de la Fuente, R.

DeLong, K. W.

Dimler, F.

P. Nuernberger, R. Selle, F. Langhojer, F. Dimler, S. Fechner, G. Gerber, and T. Brixner, “Polarization-shaped femtosecond laser pulses in the ultraviolet,” J. Opt. A 11, 085202 (2009).
[CrossRef]

R. Selle, P. Nuernberger, F. Langhojer, F. Dimler, S. Fechner, G. Gerber, and T. Brixner, “Generation of polarization-shaped ultraviolet femtosecond pulses,” Opt. Lett. 33, 803–805 (2008).
[CrossRef] [PubMed]

Fechner, S.

P. Nuernberger, R. Selle, F. Langhojer, F. Dimler, S. Fechner, G. Gerber, and T. Brixner, “Polarization-shaped femtosecond laser pulses in the ultraviolet,” J. Opt. A 11, 085202 (2009).
[CrossRef]

R. Selle, P. Nuernberger, F. Langhojer, F. Dimler, S. Fechner, G. Gerber, and T. Brixner, “Generation of polarization-shaped ultraviolet femtosecond pulses,” Opt. Lett. 33, 803–805 (2008).
[CrossRef] [PubMed]

Ferreiro, J. J.

Fittinghoff, D. N.

Forget, N.

T. Oksenhendler, S. Coudreau, N. Forget, V. Crozatier, S. Grabielle, R. Herzog, O. Gobert, and D. Kaplan, “Self-referenced spectral interferometry,” Appl. Phys. B 99, 7–12 (2010).
[CrossRef]

Gerber, G.

P. Nuernberger, R. Selle, F. Langhojer, F. Dimler, S. Fechner, G. Gerber, and T. Brixner, “Polarization-shaped femtosecond laser pulses in the ultraviolet,” J. Opt. A 11, 085202 (2009).
[CrossRef]

R. Selle, P. Nuernberger, F. Langhojer, F. Dimler, S. Fechner, G. Gerber, and T. Brixner, “Generation of polarization-shaped ultraviolet femtosecond pulses,” Opt. Lett. 33, 803–805 (2008).
[CrossRef] [PubMed]

Giessen, H.

Gobert, O.

T. Oksenhendler, S. Coudreau, N. Forget, V. Crozatier, S. Grabielle, R. Herzog, O. Gobert, and D. Kaplan, “Self-referenced spectral interferometry,” Appl. Phys. B 99, 7–12 (2010).
[CrossRef]

Grabielle, S.

T. Oksenhendler, S. Coudreau, N. Forget, V. Crozatier, S. Grabielle, R. Herzog, O. Gobert, and D. Kaplan, “Self-referenced spectral interferometry,” Appl. Phys. B 99, 7–12 (2010).
[CrossRef]

Gu, X.

Haase, B.

Herzog, R.

T. Oksenhendler, S. Coudreau, N. Forget, V. Crozatier, S. Grabielle, R. Herzog, O. Gobert, and D. Kaplan, “Self-referenced spectral interferometry,” Appl. Phys. B 99, 7–12 (2010).
[CrossRef]

Hunter, J.

Kaplan, D.

T. Oksenhendler, S. Coudreau, N. Forget, V. Crozatier, S. Grabielle, R. Herzog, O. Gobert, and D. Kaplan, “Self-referenced spectral interferometry,” Appl. Phys. B 99, 7–12 (2010).
[CrossRef]

Kimmel, M.

Kuhl, J.

Langhojer, F.

P. Nuernberger, R. Selle, F. Langhojer, F. Dimler, S. Fechner, G. Gerber, and T. Brixner, “Polarization-shaped femtosecond laser pulses in the ultraviolet,” J. Opt. A 11, 085202 (2009).
[CrossRef]

R. Selle, P. Nuernberger, F. Langhojer, F. Dimler, S. Fechner, G. Gerber, and T. Brixner, “Generation of polarization-shaped ultraviolet femtosecond pulses,” Opt. Lett. 33, 803–805 (2008).
[CrossRef] [PubMed]

Li, H.

P. Lu, J. Liu, H. Li, H. Pan, J. Wu, and H. Zeng, “Cross-correlation frequency-resolved optical gating by molecular alignment for ultraviolet femtosecond pulse measurement,” Appl. Phys. Lett. 97, 061101 (2010).
[CrossRef]

Linden, S.

Lindinger, A.

Liu, J.

P. Lu, J. Liu, H. Li, H. Pan, J. Wu, and H. Zeng, “Cross-correlation frequency-resolved optical gating by molecular alignment for ultraviolet femtosecond pulse measurement,” Appl. Phys. Lett. 97, 061101 (2010).
[CrossRef]

López-Lago, E.

Loza-Alvarez, P.

Lu, P.

P. Lu, J. Liu, H. Li, H. Pan, J. Wu, and H. Zeng, “Cross-correlation frequency-resolved optical gating by molecular alignment for ultraviolet femtosecond pulse measurement,” Appl. Phys. Lett. 97, 061101 (2010).
[CrossRef]

Masihzadeh, O.

Middleton, C. T.

Möhring, J.

Motzkus, M.

Nuernberger, P.

P. Nuernberger, R. Selle, F. Langhojer, F. Dimler, S. Fechner, G. Gerber, and T. Brixner, “Polarization-shaped femtosecond laser pulses in the ultraviolet,” J. Opt. A 11, 085202 (2009).
[CrossRef]

R. Selle, P. Nuernberger, F. Langhojer, F. Dimler, S. Fechner, G. Gerber, and T. Brixner, “Generation of polarization-shaped ultraviolet femtosecond pulses,” Opt. Lett. 33, 803–805 (2008).
[CrossRef] [PubMed]

O’Shea, P.

Oksenhendler, T.

T. Oksenhendler, S. Coudreau, N. Forget, V. Crozatier, S. Grabielle, R. Herzog, O. Gobert, and D. Kaplan, “Self-referenced spectral interferometry,” Appl. Phys. B 99, 7–12 (2010).
[CrossRef]

Pan, H.

P. Lu, J. Liu, H. Li, H. Pan, J. Wu, and H. Zeng, “Cross-correlation frequency-resolved optical gating by molecular alignment for ultraviolet femtosecond pulse measurement,” Appl. Phys. Lett. 97, 061101 (2010).
[CrossRef]

Paul, A. E.

J. A. Bolger, A. E. Paul, and A. L. Smirl, “Ultrafast ellipsometry of coherent processes and exciton-exciton interactions in quantum wells at negative delays,” Phys. Rev. B 54, 11666–11671 (1996).
[CrossRef]

Plewicki, M.

Reid, D. T.

Schlup, P.

Seidel, M. T.

Selle, R.

P. Nuernberger, R. Selle, F. Langhojer, F. Dimler, S. Fechner, G. Gerber, and T. Brixner, “Polarization-shaped femtosecond laser pulses in the ultraviolet,” J. Opt. A 11, 085202 (2009).
[CrossRef]

R. Selle, P. Nuernberger, F. Langhojer, F. Dimler, S. Fechner, G. Gerber, and T. Brixner, “Generation of polarization-shaped ultraviolet femtosecond pulses,” Opt. Lett. 33, 803–805 (2008).
[CrossRef] [PubMed]

Sibbett, W.

Smirl, A. L.

W. J. Walecki, D. N. Fittinghoff, A. L. Smirl, and R. Trebino, “Characterization of the polarization state of weak ultrashort coherent signals by dual-channel spectral interferometry,” Opt. Lett. 22, 81–83 (1997).
[CrossRef] [PubMed]

J. A. Bolger, A. E. Paul, and A. L. Smirl, “Ultrafast ellipsometry of coherent processes and exciton-exciton interactions in quantum wells at negative delays,” Phys. Rev. B 54, 11666–11671 (1996).
[CrossRef]

Strasfeld, D. B.

Tan, H.-S.

Trebino, R.

Walecki, W. J.

Weber, S. M.

Weise, F.

White, W. E.

Wu, J.

P. Lu, J. Liu, H. Li, H. Pan, J. Wu, and H. Zeng, “Cross-correlation frequency-resolved optical gating by molecular alignment for ultraviolet femtosecond pulse measurement,” Appl. Phys. Lett. 97, 061101 (2010).
[CrossRef]

Xu, L.

Yan, S.

Zanni, M. T.

Zeng, H.

P. Lu, J. Liu, H. Li, H. Pan, J. Wu, and H. Zeng, “Cross-correlation frequency-resolved optical gating by molecular alignment for ultraviolet femtosecond pulse measurement,” Appl. Phys. Lett. 97, 061101 (2010).
[CrossRef]

Zhang, Z.

Appl. Opt. (1)

Appl. Phys. B (1)

T. Oksenhendler, S. Coudreau, N. Forget, V. Crozatier, S. Grabielle, R. Herzog, O. Gobert, and D. Kaplan, “Self-referenced spectral interferometry,” Appl. Phys. B 99, 7–12 (2010).
[CrossRef]

Appl. Phys. Lett. (1)

P. Lu, J. Liu, H. Li, H. Pan, J. Wu, and H. Zeng, “Cross-correlation frequency-resolved optical gating by molecular alignment for ultraviolet femtosecond pulse measurement,” Appl. Phys. Lett. 97, 061101 (2010).
[CrossRef]

Chem. Phys. (1)

S. Yan and H.-S. Tan, “Phase cycling schemes for two-dimensional optical spectroscopy with a pump-probe geometry,” Chem. Phys. 360, 110–115 (2009).
[CrossRef]

IEEE Photon. J. (1)

P. Schlup and R. A. Bartels, “Impact of measurement noise in tomographic ultrafast retrieval of transverse light E-fields (TURTLE) ultrashort polarization characterization,” IEEE Photon. J. 1, 163–171 (2009).
[CrossRef]

J. Opt. A (1)

P. Nuernberger, R. Selle, F. Langhojer, F. Dimler, S. Fechner, G. Gerber, and T. Brixner, “Polarization-shaped femtosecond laser pulses in the ultraviolet,” J. Opt. A 11, 085202 (2009).
[CrossRef]

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

Opt. Express (1)

Opt. Lett. (10)

W. J. Walecki, D. N. Fittinghoff, A. L. Smirl, and R. Trebino, “Characterization of the polarization state of weak ultrashort coherent signals by dual-channel spectral interferometry,” Opt. Lett. 22, 81–83 (1997).
[CrossRef] [PubMed]

B. Haase, “Determination of weak optical pulses in amplitude and phase by measurement of the transient polarization state,” Opt. Lett. 24, 543–545 (1999).
[CrossRef]

S. Linden, J. Kuhl, and H. Giessen, “Amplitude and phase characterization of weak blue ultrashort pulses by downconversion,” Opt. Lett. 24, 569–571 (1999).
[CrossRef]

D. T. Reid, P. Loza-Alvarez, C. T. A. Brown, T. Beddard, and W. Sibbett, “Amplitude and phase measurement of mid-infrared femtosecond pulses by using cross-correlation frequency-resolved optical gating,” Opt. Lett. 25, 1478–1480(2000).
[CrossRef]

P. O’Shea, M. Kimmel, X. Gu, and R. Trebino, “Highly simplified device for ultrashort-pulse measurement,” Opt. Lett. 26, 932–934 (2001).
[CrossRef]

J. J. Ferreiro, R. de la Fuente, and E. López-Lago, “Characterization of arbitrarily polarized ultrashort laser pulses by cross-phase modulation,” Opt. Lett. 26, 1025–1027 (2001).
[CrossRef]

M. T. Seidel, S. Yan, and H.-S. Tan, “Mid-infrared polarization pulse shaping by parametric transfer,” Opt. Lett. 35, 478–480(2010).
[CrossRef] [PubMed]

J. Möhring, T. Buckup, and M. Motzkus, “Shaper-assisted full-phase characterization of UV pulses without a spectrometer,” Opt. Lett. 35, 3916–3918 (2010).
[CrossRef] [PubMed]

P. Schlup, O. Masihzadeh, L. Xu, R. Trebino, and R. A. Bartels, “Tomographic retrieval of the polarization state of an ultrafast laser pulse,” Opt. Lett. 33, 267–269 (2008).
[CrossRef] [PubMed]

R. Selle, P. Nuernberger, F. Langhojer, F. Dimler, S. Fechner, G. Gerber, and T. Brixner, “Generation of polarization-shaped ultraviolet femtosecond pulses,” Opt. Lett. 33, 803–805 (2008).
[CrossRef] [PubMed]

Phys. Rev. B (1)

J. A. Bolger, A. E. Paul, and A. L. Smirl, “Ultrafast ellipsometry of coherent processes and exciton-exciton interactions in quantum wells at negative delays,” Phys. Rev. B 54, 11666–11671 (1996).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Schematic experimental setup for the characterization of polarized UV pulse shapes. SHG-FROG/GRENOUILLE is used for reference pulse characterization. The UV pulse shaper provides amplitude, phase, and polarization shaped test pulses E UV . Scheme 1 consists of a Glan–Taylor polarizer at different settings to select various projections (Pol 1), a fixed Glan–Taylor polarizer at 45 ° (Pol 2), and an optional half-wave retardation plate ( λ / 2 ). Scheme 2 consists of a half-wave retardation plate at different settings to select various projections ( λ / 2 ), a BBO crystal, and a bandpass filter to select the DFG signal (Filter).

Fig. 2
Fig. 2

Linear polarized light at 45 ° : (a) DFG-XFROG traces for projections at 0 ° , 45 ° , and 90 ° ; (b) intensity and phase of E UV , 0 x ( t ) and E UV , 0 y ( t ) as retrieved by an XFROG retrieval algorithm; (c) error of the XTURTLE phase retrieval algorithm; (d) reconstructed vector field.

Fig. 3
Fig. 3

Circular polarized light: (a) DFG-XFROG traces for projections at 0 ° , 45 ° , and 90 ° ; (b) amplitude and phase of E UV , 0 x ( t ) and E UV , 0 y ( t ) as retrieved by an XFROG retrieval algorithm; (c) error of XTURTLE phase retrieval algorithm; (d) reconstructed vector field.

Fig. 4
Fig. 4

Changing polarization: (a) DFG-XFROG traces for projections at 0 ° , 45 ° , and 90 ° ; (b) amplitude and phase of E UV , 0 x ( t ) and E UV , 0 y ( t ) as retrieved by an XFROG retrieval algorithm; (c) reconstructed vector field.

Fig. 5
Fig. 5

Double pulse train: (a) DFG-XFROG traces for projections at 0 ° , 45 ° , and 90 ° ; (b) amplitude and phase E UV , 0 x ( t ) and E UV , 0 y ( t ) as retrieved by an XFROG retrieval algorithm; (c) UV spectrum at a projection of 45 ° ; (d) reconstructed vector field.

Fig. 6
Fig. 6

Determination of handedness: (a) DFG-XFROG traces for projections at 0 ° , 45 ° , and 90 ° ; (b) DFG-XFROG traces for projections at 0 ° , 45 ° , and 90 ° with an additional quarter-wave retardation plate.

Equations (6)

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E UV ( t ) = E UV , x ( t ) + E UV , y ( t ) = x ^ · E UV , 0 x ( t ) · e i ω UV t + y ^ · E UV , 0 y ( t ) · e i ( ω UV t + φ ) ,
E DFG , η E UV , η ( t ) E Ref * ( t τ ) ,
I DFG XFROG , η ( ω , t ) = | E UV , η ( t ) E Ref * ( t τ ) e i ω UV t d t | 2 .
E UV , η ( t ) = cos η · E UV , 0 x ( t ) + r · sin η · E UV , 0 y ( t ) · e i φ ,
E UV , 45 ° ( t ) = 1 / 2 · E UV , 0 x ( t ) + r · 1 / 2 · E UV , 0 y ( t ) · e i φ .
error ( φ ) = i , j = 1 N [ I 45 ° meas ( i , j ) I 45 ° calc ( i , j ) ] 2 i , j = 1 N [ I 45 ° meas ( i , j ) ] 2 .

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