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Phase Space in Ultrafast Optics 355
Phase
modulator
φ
t
(a) (c)
ω ω
t t
(b) (d)
FIGURE 11.5 Representations of the effect of (a) dispersive propagation in a
two-grating compressor and (c) propagation in a quadratic temporal phase
modulator. (b) Dispersive propagation leads to a shear of the chronocyclic
representation along the time axis. (d) The quadratic temporal phase
modulator leads to a shear of the chronocyclic representation along the
frequency axis.
belonging to the transfer matrix
1 0
T modulator = (11.51)
− 1
t
This adds a time-dependent instantaneous frequency − t to the
t
pulse, as is observed in Fig. 11.5d. Analogy to the combined action
of free-space propagation followed by a lens suggests that prop-
agation in a time-stationary dispersive element (such as a grating
pair compressor) and passage through a time-nonstationary phase
modulator (such as an electrooptic crystal driven by a temporal
parabolic voltage) will cause a rotation of the phase-space distri-
bution of the temporal ray bundle in the chronocyclic phase space.
The combination of dispersive propagation ,1 followed by a tem-
poral lens , again followed by dispersive propagation ,2 , leads
t