High-resolution Interferometric Diagnostics for Ultrashort Pulses

3. PHASE RECONSTRUCTION ALGORITHM FOR MULTIPLE SPECTRAL SHEARINGINTERFEROMETRY(a)|E (ω)|Ω 2φ(ω)(b)Γ(ω)Ω 1Γ 2Γ 1ωω(c)φ(ω)ωFigure 3.1: Using multiple shears to cross a spectral null; (a) original (red) and two replicas (green,blue) of a pulse with quadratic spectral phase and a spectral null; the shear Ω 1 of the green replicais less than the width of the null, whilst the shear Ω 2 of the blue replica is greater. The overlapof the blue replica and the original is shown in grey. The pulse has a quadratic spectral phase(not shown). (b) Phase difference between the replicas and original; the phase difference betweenthe lobes is defined for the second replica. (c) Reconstructed phase; the relative phase of the twolobes is constrained by the blue-red overlap, allowing the correct reconstruction (strong red) to bechosen from amongst those consistent with the single shear data (faint red).dynamics of supercontinuum generation in photonic crystal fibre [64]. However a limitation ofthese measurements is their multi-shot nature, necessitated by weak signal levels and the needto angle-dither the nonlinear crystal to obtain sufficient phase-matching bandwidth. Efforts toalleviate these disadvantages have limited sensitivity because of the need to use third order processesto obtain sufficient bandwidth [278]. All spectrographic methods require N well-resolvedsampling points along both the time delay and frequency axes, and the system response must bewell calibrated over both of these domains. This presents an experimental challenge, particularlyto single-shot measurements. The algorithmic complexity of retrieving the pulse from the N 2 datapoints scales as N 2 logN leading to reconstruction times measured in hours.Another concern with spectrographic methods is the possibility of ambiguities pertaining to,or caused by, the temporal structure of the pulse, which do not occur in SSI. For example, aspectrogram only encodes the relative phase of separate temporal components if the gate pulse66