Ultrashort pulse chirp parameter determination by interferometric methods

For pulses shorter than 1 ps, only indirect methods can be used. Besides conventional second-order autocorrelations and the detection of the pulse-bandwidth product, two interferometric techniques have been proposed: fringe resolved second-order autocorrelation (FRACF) and linear autocorrelation (LA), i.e., the Fourier spectrum of the pulse. Especially interesting is the measurement of the phase dependence on the length of the pulse duration, the so-called chirp. We have performed calculations of the FRACF and the LA with a fast Fourier transform algorithm for different pulse shapes and chirp functions. The results show for both the FRACF and the LA the typical narrowing of the main peak when the chirp increases. It was already known that FRACF shows side maxima in the presence of chirp, but we have shown that such side maxima also occur in the case of LA if the chirp is nonlinear. Because of the simpler mathematical expression, the LA is easier to interpret. We compare the results of both methods for two different pulses: a hyperbolic secant pulse with a chirp function which is typical of colliding pulse-mode locking of dye lasers and a Gaussian pulse shape where the time dependence of the phase is caused by self-phase modulation.