Abstract

A self-referenced technique based on digital holography and frequency-resolved optical gating is proposed in order to characterize the complete complex electric field E(x,y,z,t) of a train of ultrashort laser pulses. We apply this technique to pulses generated by a mode-locked Ti:Sapphire oscillator and demonstrate that our device reveals and measures common linear spatio-temporal couplings such as spatial chirp and pulse-front tilt.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. S. Akturk, M. Kimmel, P. O'Shea, and R. Trebino, "Measuring spatial chirp in ultrashort pulses using single-shot Frequency-Resolved Optical Gating," Opt. Express 11, 68-78 (2003), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-1-68">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-1-68</a>.
    [CrossRef] [PubMed]
  2. S. Akturk, M. Kimmel, P. O'Shea, and R. Trebino, "Measuring pulse-front tilt in ultrashort pulses using GRENOUILLE," Opt. Express 11, 491-501 (2003), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-5-491">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-5-491</a>.
    [CrossRef] [PubMed]
  3. J. P. Geindre, P. Audebert, A. Rousse, F. Falliès, J. C. Gauthier, A. Mysyrowicz, A. Dos Santos, G. Hamoniaux, and A. Antonetti, "Frequency-domain interferometer for measuring the phase and amplitude of a femtosecond pulse probing a laser-produced plasma," Opt. Lett. 19, 1997-1999 (1997).
    [CrossRef]
  4. T. Tanabe, H. Tanabe, Y. Teramura, and F. Kannari, "Spatiotemporal measurements based on spatial spectral interferometry for ultrashort optical pulses shaped by a Fourier pulse shaper," J. Opt. Soc. Am. B 19, 2795- 2802 (2002).
    [CrossRef]
  5. C. Dorrer and I. A. Walmsley, "Simple linear technique for the measurement of space-time coupling in ultrashort optical pulses," Opt. Lett. 27, (2002).
    [CrossRef]
  6. L. Gallmann, G. Steinmeyer, D. H. Sutter, T. Rupp, C. Iaconis, I. A. Walmsley, and U. Keller, "Spatially resolved amplitude and phase characterization of femtosecond optical pulses," Opt. Lett. 26, 96-98 (2001).
    [CrossRef]
  7. C. Dorrer, E. M. Kosik, and I. A. Walmsley, "Spatio-temporal characterization of the electric field of ultrashort pulses using two-dimensional shearing interferometry," Applied Physics B (Lasers and Optics) 74 [Suppl.], S209-S217 (2002).
    [CrossRef]
  8. S. A. Diddams, H. K. Eaton, A. A. Zozulya, and T. S. Clement, "Full-field characterization of femtosecond pulses after nonlinear propagation," Conference on Lasers and Electro-Optics Paper CFF3 (1998).
  9. B. C. Platt and R. Shack, "History and Principles of Shack-Hartmann Wavefront Sensing," J. Refractive Surg 17, S573-S577 (2001).
  10. C. Elster and I. Weingartner, "Solution to the shearing problem," Appl. Opt. 38, 5024-5031 (1999).
    [CrossRef]
  11. E. Arons, D. Dilworth, M. Shih, and P. C. Sun, "Use of Fourier synthesis holography to image through inhomogeneities," Opt. Lett. 18, 1852-1854 (1993).
    [CrossRef] [PubMed]
  12. P. Almoro, M. Cadatal, W. Garcia, and C. Saloma, "Pulsed full-color digital holography with a hydrogen Raman shifter," Appl. Opt. 43, 2267-2271 (2004).
    [CrossRef] [PubMed]
  13. I. Yamaguchi, T. Matsumura, and J.-i. Kato, "Phase-shifting color digital holography," Opt. Lett. 27, 1108- 1110 (2002).
    [CrossRef]
  14. Z. Liu, M. Centurion, G. Panotopoulos, J. Hong, and D. Psaltis, "Holographic recording of fast events on a CCD camera," Opt. Lett. 27, 22-24 (2002).
    [CrossRef]
  15. E. Leith, C. Chen, Y. Chen, D. Dilworth, J. Lopez, J. Rudd, P. C. Sun, J. Valdmanis, and G. Vossler, "Imaging through scattering media with holography," J. Opt. Soc. Am. A 9, 1148-1153 (1992).
    [CrossRef]
  16. M. Takeda, H. Ina, and S. Kobayashi, "Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry," J. Opt. Soc. Am. 72, 156-160 (1982).
    [CrossRef]
  17. S. Rivet, L. Canioni, R. Barille, and L. Sarger, "Multidimensional Shearing for Linear and Nonlinear Propagation Analysis.," Ultrafast Optics Conference Paper M20 (2001).
  18. P. O'Shea, M. Kimmel, X. Gu, and R. Trebino, "Highly simplified device for ultra-short measurement," Opt. Lett. 26, 932-934 (2001)
    [CrossRef]
  19. D. Malacara, Optical Shop Testing (John Wiley & Sons, 1992).
  20. J. Liang, B. Grimm, S. Goelz, and J. F. Bille, "Objective measurement of wave aberrations of the human eye with the use of a Hartmann-Shack sensor," J. Opt. Soc. Am. A 11, 1949-1957 (1994).
    [CrossRef]

Appl. Opt.

Applied Physics B

C. Dorrer, E. M. Kosik, and I. A. Walmsley, "Spatio-temporal characterization of the electric field of ultrashort pulses using two-dimensional shearing interferometry," Applied Physics B (Lasers and Optics) 74 [Suppl.], S209-S217 (2002).
[CrossRef]

CLEO 1998

S. A. Diddams, H. K. Eaton, A. A. Zozulya, and T. S. Clement, "Full-field characterization of femtosecond pulses after nonlinear propagation," Conference on Lasers and Electro-Optics Paper CFF3 (1998).

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

J. Refractive Surg.

B. C. Platt and R. Shack, "History and Principles of Shack-Hartmann Wavefront Sensing," J. Refractive Surg 17, S573-S577 (2001).

Opt. Express

Opt. Lett.

Ultrafast Optics (20010

S. Rivet, L. Canioni, R. Barille, and L. Sarger, "Multidimensional Shearing for Linear and Nonlinear Propagation Analysis.," Ultrafast Optics Conference Paper M20 (2001).

Other

D. Malacara, Optical Shop Testing (John Wiley & Sons, 1992).

Supplementary Material (1)

» Media 1: AVI (3125 KB)     

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 (4)

Fig. 1.
Fig. 1.

Schematic of the experiment: (a) 4-prism second-order spectral phase (φ 2) control; (b) 2-prism spatial chirp (∂x 0/∂λ) control; M, mirror; BS, beam-splitter; TF, narrow band-pass filter tuned to frequency ωr ; P, pinhole; FM, flip-mirror to perform the FROG measurement.

Fig. 2.
Fig. 2.

Plots of the intensity S(x,y;ωk ) of three spectral components, for ωk corresponding to 782 nm, 806 nm and 830. The color scales represent the normalized intensities, and the dotted white lines are contour plots of the entire pulse intensity. This pulse exhibits a clear spatial chirp (∂x 0/∂λ).

Fig. 3.
Fig. 3.

Profiles in the (x,t) domain of two ultrashort pulses. Both the vertical axis and brightness represent the intensity I(x,t), while colors represent the temporal derivative of the phase ∂ϕ(x,t) / ∂t, converted to instantaneous wavelength. The solid gray lines that are projected onto the top of each cube correspond to the pulse front t 0(x). The angle of these lines with respect to a reference pulse-front (black dotted line) is a direct measurement of pulse-front tilt, measured in space (left: 4.5 mrad, right: 11.3 mrad).

Fig. 4.
Fig. 4.

(3.1 MB) Time-resolved intensity-and-phase measurement of the electric field of an ultrashort pulse. Brightness represents the intensity (dark is zero), and color the instantaneous wavelength (blue is 775 nm, red is 797 nm). To help visualize pulse-front tilt, a contour plot of the intensity has been superimposed (dotted white lines). Note also the presence of spatial chirp and temporal chirp.

Equations (5)

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

E ( x . y , t ) = 1 2 π + exp ( + i ω t ) E ͂ ( x , y , ω ) d ω 1 2 π k exp ( + i ω k t ) E ͂ ( x , y ; ω k ) δω .
H ( x , y ) E r + E o 2 t
= R + k S ( x , y ; ω k )
+ [ R exp ( ix ( ω r c ) sin α ) S ( x , y ; ω r ) exp ( i φ ( x , y ; ω r ) ) + c . c . ]
k S ( x , y ; ω k ) δ ω + I ( x , y , t ) d t I ( x , y , t ) t .

Metrics