**
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.