Page 389 - Phase Space Optics Fundamentals and Applications

370 Chapter Eleven

kind are known as self-referencing. It is also possible to reconstruct
the electric field of an unknown pulse from the interferogram result-
ing from the overlap of the unknown pulse with a well-characterized
reference. 68–70 Of course, this approach requires one to first character-
ize a reference, which begs the question. We thus confine this discus-
sion to self-referencing techniques.
One significant advantage of direct techniques compared to phase-
space techniques is that the entire space over which the phase-space
or correlation functions are defined need not be explored if the pulse
train is assumed to consist of identical pulses. Only a single section of
one quadrature of the (complex) correlation function is required to ob-
tain the electric field amplitude and phase, and this is precisely what
is recorded by direct techniques. Thus, while phase-space techniques
must explore the entire chronocyclic space even when the electric field,
rather than the correlation function, is the fundamental quantity of
interest, direct techniques need only return a single slice of the cor-
relation function in order to construct the simpler quantity. Roughly
speaking, if one wishes to reconstruct the complex electric field at
N temporal points, at least 2N independent real data points are re-
quired. While direct techniques are capable of reconstructing the field
by recording only the necessary 2N points, phase-space techniques
2
essentially require the measurement of N points. The excess data of
the phase-space methods can be advantageous as a means of refining
the estimate of the pulse shape. Of course, the overcomplete data set
is available from direct measurement of the entire correlation function
as well, or from any extended sampling of it.

11.3.4.1 Two-Pulse Double-Slit Interferometry
This class consists of an in-parallel pair of amplitude-only filters, fol-
lowed by an additional amplitude-only filter, as shown in Fig. 11.7.
The in-parallel amplitude-only filters select either two frequency slices
or two time slices of the pulse which beat together at the output of the
interferometer to provide information for a single point of the respec-
tive correlation function. Thus these two types of direct techniques
are the time-domain analog of Young’s double-slit interferometer. In a
type V apparatus, the in-parallel pair of amplitude-only filters is time-
stationary (spectral filters), and the final filter is a time-nonstationary
amplitude-only filter (time gate) (see Fig. 11.7e). Each pulse in the en-
semble under consideration is split into identical replicas at a beam
splitter, and a single frequency from each replica is selected by the
spectral filters. The center frequencies of the spectral filters C1 and
C2 are independently controllable, and usually the two spectral fil-
ters have the same passband . The selected frequency components
are recombined, and the resulting temporal interferogram is subse-
quently resolved by a time gate. The signal recorded by the square-law