Measurement of the Intensity and Phase of Femtosecond Pulses Using Spectrally Resolved Self-Diffraction

Abstract

The technology of ultrashort-pulse measurement has been under development since the advent of ultrashort-pulse lasers over two decades ago. Early methods yielded only the intensity autocorrelation of the pulse.1,2 Later developments have achieved the indirect determination of various phase distortions common to ultrashort pulses.3,4 Unfortunately, these methods do not yield the pulse shape or the phase (or, equivalently, the instantaneous frequency) evolution of the pulse, but instead yield traces that only indirectly indicate each and require an assumed model of the pulse. Some work has been done to extract these quantities,5 but general methods have not yet emerged. Researchers have attempted to implement iterative algorithms to invert these traces to obtain the precise pulse shape and phase.6,7 While such techniques have reconstructed pulses, there remain fundamental inherent ambiguities in any algorithm that uses the above traces. These ambiguities include the direction of time.6 It is therefore not possible to determine, for example, the sign of a chirp. In an important recent development, however, Chilla and Martinez8 have demonstrated a method that directly obtains the pulse shape and phase in the frequency domain. Extending work first performed by Fork, et al., 9 their method involves frequency-filtering the pulse and cross-correlating the filtered pulse with the shorter unfiltered pulse, yielding the time vs. frequency, which is integrated to yield the phase vs. frequency. This result, in conjunction with the spectrum, is the pulse field in the frequency domain, and Fourier transformation then yields the intensity and phase in the time domain. This method is an important development, so it is reasonable that other methods achieving a similar end be considered.