High-resolution Interferometric Diagnostics for Ultrashort Pulses

2.3 Introduction to ultrashort pulse metrology|E (ω)|Ωφ(ω)(a)ωΓ(ω)(b)ωφ(ω)(c)ωFigure 2.10: The relative phase ambiguity in spectral shearing interferometry; (a) original (red)and sheared replica (green) of a pulse with quadratic spectral phase and a spectral null; the shearΩ is less than the width of the null. (b) Phase difference between the replicas and original, blankedout where there is zero overlap and phase difference is undefined. (c) Reconstructed phase; thephase of the low-frequency lobe has been set to an arbitrary value but the relative phase of thehigh-frequency lobe is unconstrained by the data.Another ambiguity in shearing interferometry occurs when the spectrum has two or more disjointcomponents, separated by a spectral null region wider than the shear. In this case, the phasedifferences are undefined at one or more points between the components, and will take a completelyrandom value in an actual reconstruction. The concatenation algorithm will “blindly” addthis random value as it steps across the spectrum. Whilst the individual components are still reconstructedcorrectly, their relative phase is not determined. More generally, if the spectrum iswritten as the sum of two components E (ω)=E 1 (ω)+E 2 (ω), and the two components are separatedby more than the spectral shear, then the measured interferometric product E (ω+Ω)E ∗ (ω) iscompletely independent of the relative phase of the components. Simply increasing the shear maynot be an option because this decreases the spectral resolution, or equivalently the time windowof the reconstructed pulse; indeed setting the shear to be larger than a spectral null is somewhatcontradictory since the shear should in principle be fine enough to resolve all spectral features.One of the results of this thesis is a means of alleviating this ambiguity — a reconstructionalgorithm which permits shears of different sizes to be combined. It is presented, along with some43