Dr. Rick Trebino

Georgia Institute of Technology

School of Physics

Atlanta, GA 30332

The Musical Score, the Fundamental Theorem of Algebra, and the Measurement of the Shortest Events Ever Created

Monday, April 16, 2007

4:30 p.m.

Leasure 13

To measure an event in time requires a shorter one. As a result, the development of a technique to measure ultrashort laser pulses has been particularly difficult—these pulses are the shortest events ever created, so the shorter event required for their measurement doesn’t exist. We have, however, developed a simple method for fully characterizing these events, that is, for measuring a pulse's intensity and phase vs. time. It involves making an optical analog of a musical score of the pulse by using nonlinear optics to measure the pulse spectrogram. The mathematics involved is equivalent to the two-dimensional phase-retrieval problem—a problem that’s solvable because the Fundamental Theorem of Algebra fails for polynomials of two variables.  We call the method Frequency-Resolved Optical Gating (FROG), and it’s simple, rigorous, intuitive, and general. FROG has recently been used to measure pulses as short as 4 femtoseconds (4 x 10^-15 sec) and as weak as a few hundred photons. FROG has also recently measured the most complex ultrashort pulse ever generated. And we have recently developed an extremely simple FROG (see below) that never needs alignment and simultaneously measures the elusive spatio-temporal distortions that plague ultrashort pulses.