Page 388 - Phase Space Optics Fundamentals and Applications

Phase Space in Ultrafast Optics 369

Phase modulator ω
OSA
Phase shifter
φ φ
t
t t
ω
(a) (b) (c)

FIGURE 11.9 (a) Schematics of simplified chronocyclic tomography based
on a temporal phase modulator. Quadratic temporal phase modulations of
opposite signs are provided by a sinusoidally driven phase modulator
synchronized such that the pulse under test coincides with the minimum or
maximum of the phase modulation. (b) The Wigner function of a chirped
pulse is shown in the absence of modulation (upper left plot) and with
quadratic temporal modulations of opposite signs (upper right and lower
left plots). The effect of the shear along the frequency axis can be seen. (c)
The initial spectrum of the pulse (continuous line) and the spectra after the
quadratic temporal phase modulations of opposite signs (continuous lines
with round and square markers) are seen, from which the electric field of the
test pulse can be reconstructed.

the two measured optical spectra. Figure 11.9b represents the Wigner
function of a chirped pulse in the absence of modulation, and after
quadratic temporal phase modulation of opposite signs. The shear
effect due to the modulation can be observed, and it results in a
change of the frequency marginal. The spectral phase can directly be
reconstructed from the corresponding optical spectra represented in
Fig. 11.9c. The combination of a quadratic spectral phase modulation
(i.e., chromatic dispersion) and temporal gating by photodetection has
also been demonstrated based on the same formalism. 66 These one-
dimensional determinations of the electric field are closely related to
phase retrieval using the transport-of-intensity equation in the spatial
domain. 67

11.3.4 Interferometric or Direct Techniques
Direct techniques, as the name indicates, reconstruct the correlation
function in either the time domain or frequency domain directly
(i.e., noniteratively) from the recorded intensity distributions. In such
schemes each pulse in the ensemble is split into two replicas at a
beam splitter, and each replica is independently filtered before be-
ing recombined. The interference of the field from the parallel path-
ways introduces structure on the output intensity distribution, which
then carries information about both the amplitude and the phase of
the correlation function of the input field. Direct techniques of this