Page 396 - Phase Space Optics Fundamentals and Applications

Phase Space in Ultrafast Optics 377

Phase
Interferometer modulator
DDL χ (2) OSA
OSA
τ
φ

t
(a) (b)

FIGURE 11.12 Schematics of spectral shearing interferometry based on (a)a
linear temporal phase modulator and (b) a nonlinear interaction with a
chirped pulse. In part a, two replicas of the pulse under test are spectrally
sheared in opposite direction by a temporal phase modulator driven by a
sinusoidal drive. In part b, a chirped pulse is generated by a dispersive delay
line (DLL), and nonlinear interaction of two relatively delayed replicas of the
test pulse with the chirped pulse induces a relative shear between the two
resulting pulses.

where is the shear induced on one of the replicas, which can be
as high as several hundreds of gigahertz. Since the relative shear 2
must be of the order of a few percents of the bandwidth of the pulse
under test to provide adequate sampling in the frequency domain and
maintain a measurable finite difference ( + ) − ( − ), EOSI
mostlikelycanbeimplementedforpulseswithdurationdownto50fs.
Advantageously, the signal intensity does not depend significantly on
the amount of chirp present on the pulse, and the technique is accurate
as long as one can maintain a linear phase ramp over the temporal
support of the pulse under test. Other related techniques measuring
the phase difference between the spectral modes of a periodic source
have been demonstrated. 84–86
The nonlinear implementation of spectral shearing interferometry,
also known as spectral phase interferometry for direct electric-field
reconstruction (SPIDER), can provide large shears by nonlinear inter-
action of two replicas of the pulse under test with a highly chirped
pulse. 87,88 For such a pulse, the instantaneous frequency is a linear
function of time and the frequency content in a short time interval is
quasi-monochromatic. As seen in Fig. 11.12b, part of the input pulse
is used to generate a chirped pulse, and two delayed replicas of the
input pulse are generated by an interferometer. Nonlinear interaction
of one replica of the pulse under test with the chirped pulse leads to
a spectral shift given by the instantaneous optical frequency of the
chirped pulse during the interaction. The other replica, delayed by
, interacts with another optical frequency of the chirped pulse. The
two converted replicas are relatively sheared by = / 2 , where