title: Fractional-order Fourier analysis for ultrashort pulse characterization.
abstract: We report what we believe to be the first experimental demonstration of ultrashort pulse characterization using fractional-order Fourier analysis. The analysis is applied to the interpretation of spectral interferometry resolved in time (SPIRIT) traces [which are spectral phase interferometry for direct electric field reconstruction (SPIDER)-like interferograms]. First, the fractional-order Fourier transformation is shown to naturally allow the determination of the cubic spectral phase coefficient of pulses to be analyzed. A simultaneous determination of both cubic and quadratic spectral phase coefficients of the pulses using the fractional-order Fourier series expansion is further demonstrated. This latter technique consists of localizing relative maxima in a 2D cartography representing decomposition coefficients. It is further used to reconstruct or filter SPIRIT traces.
authors.affiliation: CORIA UMR 6614, Université de Rouen, Saint Etienne du Rouvray Cedex, France. marc.brunel@coria.fr
authors.forename: Marc
authors.initials: M
authors.lastname: Brunel
authors.forename: Sébastien
authors.initials: S
authors.lastname: Coetmellec
authors.forename: Mickael
authors.initials: M
authors.lastname: Lelek
authors.forename: Frédéric
authors.initials: F
authors.lastname: Louradour