High-resolution Interferometric Diagnostics for Ultrashort Pulses

2.3 Introduction to ultrashort pulse metrologypersed in the plane perpendicular to the crossing angle. This can be achieved by re-imaging theplane of the nonlinear medium onto the entrance slit of an imaging spectrometer [181], or usingthe angular dispersion produced by phase-matching in a thick nonlinear crystal [182, 183]. Eitherway, time delay and frequency are mapped to two dimensions of a detector array, and a single-shotFROG trace acquired.2.3.5.3 Summary — time-frequency distributionsThe measurement and inversion of time-frequency distributions is a general approach to the completecharacterisation of ultrashort pulses. FROG and its variants are particularly widespread. Thedataset is inherently two-dimensional and its inversion requires an iterative algorithm.2.3.6 Self-referenced interferometrySelf referencing is achieved in spectral interferometry when the two pulses have some relation toone another so that knowledge of their spectral phase difference permits unique determination oftheir spectral phase.By far the most common approach is spectral shearing interferometry (SSI), in which thepulses being interfered are related by a translation, or shear, along the frequency axis. This underliesa broad category of ultrashort pulse characterisation devices, the most longstanding andwell known of which is SPIDER. The spatial analogue, lateral shearing interferometry (LSI) has along history. Besides wavefront characterisation it is extensively used in the testing and characterisationof optical components. It plays a fundamental role in this dissertation and is discussed insection 2.4.4.2. However, most of its features are completely analogous to the spectral case.Several important features of shearing interferometry deserve emphasis up-front. It is a phaseonlymeasurement — the intensity must be acquired separately, although in many cases this isconveniently accomplished using only a minor adjustment to the apparatus. There is a computationallyefficient and algebraically simple mapping between the phase and the data, which simplifiesprocessing and error analysis. Finally, an n-dimensional field can be reconstructed 1 usingnn-dimensional datasets. Applying this rule to the most common case, a one dimensional phase1except for ambiguities which I shall discuss in a subsequent section41