## 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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### Equations (5)

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(1)
$$E\left(x.y,t\right)=\frac{1}{2\pi}\underset{-\infty}{\overset{+\infty}{\int}}\mathrm{exp}\left(\text{}+i\omega t\right)\stackrel{\u0342}{E}(x,y,\omega )d\omega \simeq \frac{1}{2\pi}\sum _{k}\mathrm{exp}\left(+i{\omega}_{k}t\right)\stackrel{\u0342}{E}\left(x,y;{\omega}_{k}\right)\mathrm{\delta \omega}.$$
(2)
$$H\left(x,y\right)\equiv {\u3008{\mid {E}_{r}+{E}_{o}\mid}^{2}\u3009}_{t}$$
(3)
$$\text{}=R+\sum _{k}S\left(x,y;{\omega}_{k}\right)$$
(4)
$$\text{}+\left[\sqrt{R}\mathrm{exp}\left(\mathit{ix}\left(\frac{{\omega}_{r}}{c}\right)\mathrm{sin}\phantom{\rule{.2em}{0ex}}\alpha \right)\sqrt{S\left(x,y;{\omega}_{r}\right)}\mathrm{exp}\left(-i\phi \left(x,y;{\omega}_{r}\right)\right)\text{}+c.c.\right]$$
(5)
$$\sum _{k}S\left(x,y;{\omega}_{k}\right)\delta \omega \simeq \underset{-\infty}{\overset{+\infty}{\int}}I\left(x,y,t\right)dt\propto {\u3008I\left(x,y,t\right)\u3009}_{t}.$$