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Friday, November 10, 2000
Physics Building, Room 204
Note special time.
[Host: Louis Bloomfield]
"The Musical Score, the Fundamental Theorem of Algebra, and the Measurement"
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.
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