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Self-referenced measurement of the complete electric field of ultrashort pulses

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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

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Directly measuring the spatio-temporal electric field of focusing ultrashort pulses

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Supplementary Material (1)

Media 1: AVI (3125 KB)     

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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)

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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 .
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