Advanced phase retrieval for dispersion scan: a comparative study

Abstract

Dispersion scan is a self-referenced measurement technique for ultrashort pulses. Similar to frequencyresolved optical gating, the dispersion scan technique records the dependence of nonlinearly generated spectra as a function of a parameter. For the two mentioned techniques, these parameters are the delay and the dispersion, respectively. While dispersion scan seems to offer a number of potential advantages over other characterization methods, in particular for measuring few-cycle pulses, retrieval of the spectral phase from the measured traces has so far mostly relied on the Nelder-Mead algorithm, which has a tendency of stagnation in a local minimum and may produce ghost satellites in the retrieval of pulses with complex spectra. We evaluate three different strategies to overcome these retrieval problems, namely regularization, use of a generalized-projections algorithm, and an evolutionary retrieval algorithm. While all these measures are found to improve the precision and convergence of dispersion scan retrieval, differential evolution is found to provide best performance, enabling the near-perfect retrieval of the phase of complex supercontinuum pulses within less than ten seconds, even in the presence of strong detection noise and limited phase-matching bandwidth of the nonlinear process.

Common Pulse Retrieval Algorithm: A Fast and Universal Method to Retrieve Ultrashort Pulses

“…In consequence, they under-perform in the presence of additive Gaussian noise. This fact has been noticed several times in the literature [11,19,25,41], but the relation to the missing least-squares property was not reported so far.…”

“…2 a). Then we retrieved pulses by using four different minimization algorithms: Nelder-Mead (NM) and differential evolution (DE) are scalar, gradient-free minimization methods used to retrieve pulses from d-scan and iFROG measurements [11,15,41]. Broyden-Fletcher-Goldfarb-Shanno (BFGS) is a scalar, gradient-based algorithm, which was used to retrieve pulses from chirp scan and FROG measurements [25].…”

Compact in-line temporal measurement of laser pulses with amplitude swing

“…This kind of problem has already been solved e.g. with d-scan retrievals, using different algorithms, for example non-linear optimization with Nelder-Mead Simplex [13], projections [15], or differential evolution [17]. We choose to perform the phase retrievals with the Levenberg-Marquardt algorithm, which has been previously shown to be robust performing retrievals of d-scan [3,16,26] as well as other techniques [27].…”

“…The unknown pulse group delay dispersion (GDD) can be therefore extracted at a given wavelength by calculating the amount of GDD within the scan range needed to optimize the SHG signal at that wavelength. Later, the d-scan technique [13] used the spectral phase scan concept with some practical modifications and introduced retrieval algorithms [14][15][16][17] to reconstruct the spectral phase of the test pulse. A related technique was proposed in [18], using an acousto-optic programmable dispersive filter (AOPDF) for the known spectral phase scan and an algorithm to reconstruct both the spectral amplitude and phase of the pulse.…”

Linear chirp instability analysis for ultrafast pulse metrology

“…In the past two decades, numerous techniques have been developed for the full characterization of the intensity and phase of ultrashort pulses [1][2][3][4][5][6]. Compared to the more traditional second-order autocorrelation measurement [7], full characterization methods not only deliver precise pulse durations, but they can also resolve the pulse shape, that is, structure in the temporal or spectral intensity and phase of potentially complex pulses [8,9]. However, most such techniques operate multi-shot, so they inherently assume stability of the pulse shape in the pulse train.…”