High-resolution Interferometric Diagnostics for Ultrashort Pulses

2.4 Extending ultrashort metrology to the space-time domainmain.As mentioned in the discussion of the purely spatial case (section 2.4.1.2), a well-characterisedspatial reference may be produced by spatial filtering. Applied to a space-time coupled pulse, thisproduces a factorable pulse with well-characterised spatial profile. Temporal characterisation ofthis factorable pulse yields a fully characterised reference, against which the phase of an unknownpulse can be measured using spatio-spectral interferometry [67, 252]. There are however, twocaveats to this approach.• The spectrum of the factorable pulse must contain all the frequencies present in the unknownpulse. Using linear time-stationary optics, it impossible to produce a spatial filteringsystem which satisfies this requirement for all pulses. As a concrete example, first consider abeam with spatial chirp. A pinhole in the collimated beam will block certain frequencies, sothe filtering must be performed in the Fourier domain, using a pinhole placed at the focusof a lens. If the pulse is now changed to exhibit some angular dispersion, then in the focalplane the frequencies will be dispersed and some will be blocked by the pinhole.• The spatial filtering must be more aggressive than in the purely spatial case. In the spatialcase, one requires a beam which approximately resembles a plane wave. However, thewavevector of this plane wave is not important, since in externally referenced interferometryone is almost always unconcerned by the tilt between the beams, or equivalently the linearcomponent of the phase. In the spatio-spectral case, one requires each frequency of the referenceto have the same wavevector, or else erroneous angular dispersion will be diagnosed.Adhering to this requirement reduces the throughput of the spatial filter.There have been two main implementations of spatio-spectral interferometry.Fourier-transform interferometry. Many implementations use some form of two-dimensionalspectrometer, in which frequency is mapped to one axis of a two-dimensional detector array leavingthe other free to resolve one spatial dimension. In this discussion, I shall associate the x-axiswith frequency. A particular example is an imaging spectrometer, which performs re-imaging ofits entrance slit perpendicular to the plane of dispersion. In any case, the signal is proportional to59