Colloquia

To measure an event in time requires a shorter one. As a result, the development of a technique to measure ultrashort laser pulses--less than 10^-12 seconds long and the shortest events ever created--has been particularly difficult. We have, however, recently developed a simple method for fully characterizing these events, that is, for measuring a pulse's intensity and phase vs. time. This method relies on two seemingly unrelated ideas: the concept of the musical score and the fact that the Fundamental Theorem of Algebra fails in two dimensions. Specifically, an optical analog of a musical score of the pulse is produced by measuring its spectrogram. And the mathematics involved is equivalent to the two-dimensional phase-retrieval problem--a problem that is solvable only because the Fundamental Theorem of Algebra fails in two dimensions. We call the method Frequency-Resolved Optical Gating (FROG), and it is simple, rigorous, intuitive, and general. It can measure pulses in all spectral ranges, on a single-shot basis, and over a wide range of energies. FROG has been used to measure pulses as short as 4.5 femtoseconds (4.5 x 10^-15 sec), and it can measure two pulses simultaneously. More recently, we have shown that FROG can be used in conjunction with spectral interferometry to measure essentially arbitrary pulses with as little as zeptojoules of energy (less than one photon!) on a multi-shot basis.