Page 392 - Phase Space Optics Fundamentals and Applications

Phase Space in Ultrafast Optics 373

isolation of discrete optical frequencies in the pulse under test can
be implemented, provided that a large amount of chirp is added to
the pulse. 73 The phase difference between two adjacent optical fre-
quencies is measured in the time domain by interfering two chirped
replicas of the pulse under test, and the time-frequency dependence in
the chirped pulses naturally links the temporal axis of the measured
intensity to the optical frequency in the pulse under test. This method
can be combined with a Fourier processing algorithm identical to that
74
of spectral shearing interferometry. Another approach to measuring
the spectral phase difference between different optical frequencies re-
lies on a fast electronic detector. The beat note between pairs of ad-
jacent frequencies, instead of the beat note between frequencies, was
75
measured to reduce the bandwidth requirement of the detector. The
overlap of two spectrally dispersed and spatially sheared replicas of
the pulse under test can also be used so that quantity of Eq. (11.81)
can be measured at different spatial locations. 76 Finally, let’s note that
for a periodic source of period T, it suffices to measure the phase dif-
ference between spectral modes separated by 2 /T with a detector of
sufficient resolution. This is of particular interest for optical sources
used in optical telecommunications. 77
A similar interferometric approach has been employed to recon-
struct the electric field amplitude and phase by Rothenberg and
Grischkowsky. 78 In their technique, generically referred to as time-
domain interferometry, a spectral filter is placed in only one arm of
the interferometer. The monochromatic frequency component result-
ing from the spectrally filtered path provides an effective reference
with which to compare the pulse that passes through the unfiltered
arm of the interferometer. Constraints on the available temporal res-
olution limit this method to the measurement of stretched pulses of
relatively long duration.
A complementary approach to the temporally resolved two-pulse
interferometry is spectrally resolved two-pulse interference. This ap-
proach consists of two in-parallel time-nonstationary amplitude-only
filters (time gates), followed by a time-stationary amplitude-only fil-
ter (spectral filter). The two replicas of the pulse are independently
filtered by time gates with variable times of maximum transmission
1 and 2 , before being recombined. The spectral beats, resulting from
the overlap of the two time slices, are resolved by a spectrometer. The
spectrum for each pair of time settings of the time gates is recorded.
The visibility of the spectral fringes, occurring at the spectral period
2 / = 2 /( 1 − 2 ), is a measure of the magnitude of the two-time
correlation function at these two times. The position of the fringes
along the frequency axis is a relative measure of the phase. Thus,
each recorded spectrum returns one point of the two-time correlation
function so that a simple point-by-point reconstruction algorithm is