Page 391 - Phase Space Optics Fundamentals and Applications

372 Chapter Eleven

2π/Δω

Frequency Time

ω C1 ω C2
(a) (b)

FIGURE 11.10 (a) Schematics of a double-slit experiment in the spectral
domain and (b) resulting experimental trace for one particular setting of the
central frequencies of the two filters. The gray regions in part a depict the
filtering of two narrowband spectral slices at the center frequencies C1
and C2 .

In many implementations, especially for femtosecond duration
pulses, the time gate consists of a nonlinear optical mixing process,
such as up-conversion with a portion of the pulse being characterized,
which sets the temporal resolution −1 to be close to the duration of
the input pulses. Consequently, the narrow time-gate assumption of
Eq. (11.80) is not valid for frequency separations greater than a
small fraction of the pulse bandwidth, since the temporal beat note is
too fast to resolve.
The narrow time-gate approximation does hold for small frequency
separations so that slices of the two-frequency correlation function
near = 0 can be recorded. If the pulses in the train are assumed to
be identical, a sampling of one such slice is sufficient for reconstruct-
ing the pulse electric field. When coherence is assumed, the phase
of the two-frequency correlation function is no more than the phase
difference between the selected spectral components. Coupled with
knowledge of the pulse spectrum, the spectral phase differences for
a set of frequencies separated by provide ample information for
reconstructing the pulse electric field. This is precisely the approach of
direct optical spectral phase measurement (DOSPM). 71 DOSPM uses
an apparatus in which a pair of adjustable slits is placed in the Fourier
transform plane of a zero-dispersion line. This spectral filter with dual
passbands of adjustable center frequencies is equivalent to a pair of
in-parallel single-frequency spectral filters. The beating with pairs of
optical frequencies was recorded by nonlinear interaction with the
pulse under test. This work was extended to the measurement of the
spectral phase difference between a reference optical frequency and a
set of other frequencies in the pulse, these frequencies being filtered
by a mask with multiple slits placed at the Fourier plane of a zero-
dispersion line. 72 A version of the DOSPM that does not require the