Abstract

We present a remarkably simple technique for measuring the full spatio-temporal electric field of a single ultrashort laser pulse. It involves capturing a large digital hologram containing multiple smaller holograms, each of which characterizes the spatial intensity and phase distributions of an individual frequency component of the pulse. From that single camera frame, we numerically reconstruct the complete electric field, E(x,y,t), using a direct algorithm. While holography requires a well-characterized reference pulse, this pulse can easily be generated from the pulse itself in most cases, so the technique is self-referencing. We experimentally demonstrate this technique using femtosecond pulses from a mode-locked Ti:Sapphire oscillator.

© 2006 Optical Society of America

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    [CrossRef]
  15. P. H. Lissberger, and W. L. Wilcock, "Properties of All-Dielectric Interference Filters. II. Filters in Parallel Beams of Light Incident Obliquely and in Convergent Beams," J. Opt. Soc. Am. 29,126-130 (1959). http://www.opticsinfobase.org/abstract.cfm?URI=josa-49-2-126.
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2004

2002

2001

2000

S. Lai, B. King, and M. A. Neifeld, "Wave front reconstruction by means of phase-shifting digital in-line holography," Opt. Commun. 173,155-160 (2000).
[CrossRef]

1997

1994

1992

1982

1959

P. H. Lissberger, and W. L. Wilcock, "Properties of All-Dielectric Interference Filters. II. Filters in Parallel Beams of Light Incident Obliquely and in Convergent Beams," J. Opt. Soc. Am. 29,126-130 (1959). http://www.opticsinfobase.org/abstract.cfm?URI=josa-49-2-126.
[CrossRef]

Antonetti, A.

Audebert, P.

Bille, J. F.

Centurion, M.

Chen, C.

Chen, Y.

De Nicola, S.

Dilworth, D.

Dorrer, C.

Dos Santos, A.

Falliès, F.

Ferraro, P.

Finizo, A.

Gabolde, P.

Gallmann, L.

Gauthier, J. C.

Geindre, J. P.

Goelz, S.

Grilli, S.

Grimm, B.

Gu, X.

Hamoniaux, G.

Hong, J.

Iaconis, C.

Ina, H.

Kannari, F.

Keller, U.

Kimmel, M.

King, B.

S. Lai, B. King, and M. A. Neifeld, "Wave front reconstruction by means of phase-shifting digital in-line holography," Opt. Commun. 173,155-160 (2000).
[CrossRef]

Kobayashi, S.

Kosik, E. M.

Lai, S.

S. Lai, B. King, and M. A. Neifeld, "Wave front reconstruction by means of phase-shifting digital in-line holography," Opt. Commun. 173,155-160 (2000).
[CrossRef]

Lane, R. G.

Leith, E.

Liang, J.

Lissberger, P. H.

P. H. Lissberger, and W. L. Wilcock, "Properties of All-Dielectric Interference Filters. II. Filters in Parallel Beams of Light Incident Obliquely and in Convergent Beams," J. Opt. Soc. Am. 29,126-130 (1959). http://www.opticsinfobase.org/abstract.cfm?URI=josa-49-2-126.
[CrossRef]

Liu, Z.

Lopez, J.

Meucci, R.

Mysyrowicz, A.

Neifeld, M. A.

S. Lai, B. King, and M. A. Neifeld, "Wave front reconstruction by means of phase-shifting digital in-line holography," Opt. Commun. 173,155-160 (2000).
[CrossRef]

O'Shea, P.

Panotopoulos, G.

Pierattini, G.

Platt, B. C.

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

Psaltis, D.

Rousse, A.

Rudd, J.

Rupp, T.

Shack, R.

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

Steinmeyer, G.

Sun, P. C.

Sutter, D. H.

Takeda, M.

Tallon, M.

Tanabe, H.

Tanabe, T.

Teramura, Y.

Trebino, R.

Valdmanis, J.

Vossler, G.

Walmsley, I. A.

Wilcock, W. L.

P. H. Lissberger, and W. L. Wilcock, "Properties of All-Dielectric Interference Filters. II. Filters in Parallel Beams of Light Incident Obliquely and in Convergent Beams," J. Opt. Soc. Am. 29,126-130 (1959). http://www.opticsinfobase.org/abstract.cfm?URI=josa-49-2-126.
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am.

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]

P. H. Lissberger, and W. L. Wilcock, "Properties of All-Dielectric Interference Filters. II. Filters in Parallel Beams of Light Incident Obliquely and in Convergent Beams," J. Opt. Soc. Am. 29,126-130 (1959). http://www.opticsinfobase.org/abstract.cfm?URI=josa-49-2-126.
[CrossRef]

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. Commun.

S. Lai, B. King, and M. A. Neifeld, "Wave front reconstruction by means of phase-shifting digital in-line holography," Opt. Commun. 173,155-160 (2000).
[CrossRef]

Opt. Express

Opt. Lett.

Other

M. Bass, "Handbook of Optics, 2nd ed.," 42.89-42.90 (1995).

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).

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Figures (5)

Fig. 1.
Fig. 1.

Principle of operation of STRIPED FISH to measure E(x,y,t). (a) View in the x-y-z space. (D): diffractive element; (F): band-pass interference filter; (C): digital camera. The signal and reference pulses are crossed at a small vertical angle α. The diffractive element (D) is rotated by an angle φ about the z-axis, and the filter (F) is rotated by an angle β about the y-axis. The inset shows one of the spatial interferograms (“digital holograms”) captured by the digital camera. (b) Side view (y-z plane) showing the signal and reference beams crossing at an angle. (c) Top view (x-z plane) showing how the frequencies transmitted by the band-pass filter increase with position x.

Fig. 2.
Fig. 2.

Algorithm used to reconstruct the 3D electric field from a single camera frame. A 2D fast Fourier transform is applied to a simulated STRIPED FISH trace (a). The interferometric terms are selected in the Fourier plane (b), and transformed back to the original x-y plane (c). The resulting image contains both the spatial amplitude and phase, at the expense of a loss of vertical spatial resolution. A registration step is applied to center all the spatial distributions, and to assign the calibrated wavelengths, in order to obtain the multi-spectral complex data E(x,y,ω)(d).

Fig. 3.
Fig. 3.

(a) Mach-Zehnder interferometer used to implement our STRIPED FISH device, drawn in the x-z plane. (BS1,2): beam-splitters. (D, F, C): same as in Fig. 1. The optical paths of both arms are matched using the delay stage, and a small vertical angle is introduced between the signal and reference pulses so that horizontal fringes are obtained on the digital camera. (b) Typical experimental STRIPED FISH trace (2208×3000 pixels) obtained with a 5-megapixel CMOS camera. Because of the limited dynamic range of the digital camera, the central interferogram is saturated so we discarded the corresponding data, leaving over 20 digital holograms for the data analysis.

Fig. 4.
Fig. 4.

(a) Fringe shift in each digital hologram as a function of frequency, showing a linear phase due to group delay. Open circles: measurement; dotted line: linear fit. (b) Fringe shift in each digital hologram as a function of frequency, showing a quadratic phase due to group-delay dispersion. Open circles: measurement; dotted line: quadratic fit.

Fig. 5.
Fig. 5.

(a) x-t slice of the measured electric field E(x,y,t) of a pulse with spatial chirp. The vertical axis shows the electric field intensity |E(x,t)|2 and the color shows the instantaneous wavelength derived from the phase ψ(x,t). The spatial gradient of color shows the spatial chirp along the x direction. (b) y-t slice of the same measured electric field. No spatial chirp is present along the y direction, as expected.

Equations (2)

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I ( x , y ) = E s ( x , y ) 2 + E r ( x , y ) 2 + E s ( x , y ) * E r ( x , y ) e iky sin α + E s ( x , y ) E r ( x , y ) * e iky sin α
E ( x , y , t ) = 1 2 π E ( x , y , ω ) e i ω t d ω 1 2 π k E ( x , y ) ω k e i ω k t δ ω

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