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

Rick Trebino*
Department of Physics
Georgia Institute of Technology

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 multishot basis.

For additional information, contact:

Daniel Mittleman at (daniel@rice.edu)

* Biography:

Rick Trebino was born in Boston, Massachusetts on January 18, 1954. He received his B.A. from Harvard University in 1977 and his Ph.D. degree from Stanford University in 1983. His dissertation research involved the development of a technique for the measurement of ultrafast events in the frequency domain using long-pulse lasers and by creating moving gratings.

He continued this research during a three-year term as a physical sciences research associate at Stanford. In 1986, he went to Sandia National Laboratories in Livermore, California, where he studied higher-order wave-mixing effects, nonlinear-optical perturbation theory using Feynman diagrams, and ultrashort-laser-pulse techniques with application to chemical dynamics measurements and combustion diagnostics. He has recently moved to the Physics Department at the Georgia Institute of Technology, where he holds the Georgia Research Alliance-Eminent Scholar Chair in Ultrafast Optical Physics. His latest work has been the development of techniques for the measurement of the intensity and phase of ultrashort laser pulses, for which he has received numerous awards, including the SPIE's Edgerton Prize. He has also developed devices for optical communications and biotechnology and has been involved in several start-up companies. He has been a consultant in laser technology, biotechnology, and communications. Prof. Trebino is currently the IEEE LEOS Distinguished Lecturer and a Fellow of the Optical Society of America. His interests include adventure travel, humorous travel writing, archaeology, and primitive art.

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