Femtosecond Pulse Phase Measurement by Spectrally Resolved Up-Conversion: Application To Continuum Compression

We have developed an extension of the usual cross-correlation method in order to get the amplitude and phase of a femtosecond light pulse. This is done by analyzing the spectra of the upconverted pulse obtained by mixing the initial pulse with the reference pulse delayed with different times. the theory is worked out in closed form for Gaussian pulses and then checked with simulations for arbitrary fields. We show that we directly recover the phase derivative of any probed pulse in the limit where the reference is narrowband. We first apply this technique to measure the chirp induced at the output of a femtosecond Ti : sapphire oscillator. This technique is then demonstrated to the determination of the exact pulse shape of a 21 fs compressed continuum at 770 nm using, as a reference, the initial fundamental 65 fs pulse at 620 nm.