SPIDER Concepts
Different approaches have been followed for the characterization of ultrashort optical pulses. Although the number of elements experimentally available for the implementation of successful techniques is limited (and thus some of these techniques look alike), the order in which the components act on the measured pulse determines the principle of the measurement and the algorithm needed to reconstruct the electric field from the experimental trace.
One requirement for a successful short pulse characterization technique is the presence of a non-stationnary filter, i.e. an element acting on the pulse with a time response of the order of the duration of the pulse. This element is there to ensure that the diagnostic is sensitive to the temporal variations of the field. Without such filter, the results are only sensitive to the spectral density of the pulse, a quantity which is identical for an ultrashort optical pulse and an incoherent white light which happens to have the same spectrum. For the ultrashort optical pulses with durations in the femtosecond range no electronic device usually has a fast enough temporal response and non-linear interactions provide the necessary filtering.
Whereas the analytic signal corresponding to the electric field of an ultrashort optical pulse is a mono dimensional complex function (a function of time or frequency), some techniques need to construct a two dimensional experimental trace, which requires scanning of two parameters thus making single-shot measurement of the experimental trace more complex. Obtaining the pulse shape from the measured experimental trace sometimes require minimization of the difference between the measured trace and the calculated trace using an iterative algorithm. This can be a difficult problem, causing stagnation of the algorithm in local minima, slow convergence or high sensitivity to noise. Algebraic inversion algorithms are based on a finite predefined number of algebraic operations, and thus provide most of the time an error-free reconstruction as soon as the measured experimental trace is error-free. Three classes of techniques have been identified :
- spectrographic techniques aim at measuring a time-frequency representation of the pulse, from which an attempt to reconstruct the analytic signal of the pulse is made. A blurred or modified Wigner function is measured, as a function of two parameters (a time delay and an optical frequency) which need to be scanned. Although the shape of this experimental trace can in some cases be interpreted to give an overview of the shape of the pulse, complete reconstruction of the analytic signal can only be obtained with an iterative algorithm. The sonogram and FROG spectrogram belong to this class.
- tomographic techniques are an application of tomography to the reconstruction of the Wigner representation of the pulse, i.e. the reconstruction of this surface using a finite number of its projections along different directions. The experimental trace is most of the time two-dimensional, but sometimes allows an algebraic reconstruction to get the pulse shape. The chronocyclic tomography, the time-to-frequency converter and the Cross Phase Modulation (XPM) technique belong to this class.
- interferometric techniques are based on the measurement of interferences between different frequencies of the spectrum of the pulse. The experimental trace is monodimensional, and the inversion is algebraic. Spectral Phase Interferometry for Direct Electric-field Reconstruction (SPIDER) and Direct Optical Spectral Phase Measurement (DOSPM) belong to this class of techniques.