Improved phase retrieval for dispersion scan

Ultrashort pulse generation has come of age, along with several well established methods that allow characterization of femtosecond pulses in amplitude and phase. While all these methods have been demonstrated to work well for pulses with >10 fs pulse duration, the reliable measurement of few-cycle pulses still poses a challenge that requires sophisticated adaptation of these existing techniques. In the sub-2-cycle regime, the recently devised dispersion-scan (d-scan) technique [1] has recently attracted much interest since it relies on single-beam geometry, is easy to implement, robust against adjustment errors, and can be completely immune against phase-matching limitations [2]. Formally, it is similar to frequency-resolved optical gating (FROG), yet with the noted difference of scanning the added group delay dispersion in the beam path rather than the delay between two replicas of the pulse under test. Spectrally resolving the pulses after nonlinear conversion then gives rise to two-dimensional d-scan traces, from which the pulse shape can be reconstructed by a retrieval algorithm. To this end, the Nelder-Mead (NM) algorithm has been nearly exclusively employed. While NM is a very flexible algorithm and does not require gradients, it turns out to be very slow for complex pulse shapes that require a large number of points, i.e., a large dimension for the retrieval algorithm, for which one often observes local stagnation, slow convergence speed, and the build-up of erroneous spectral phase oscillations. To overcome this limiting problem of the otherwise very promising d-scan technique, we investigated a number of possible solutions, including regularization, generalized projections (GP), and differential evolution (DE), and combinations thereof. Here we demonstrate that the last method can overcome all above-mentioned problems of d-scan retrieval and is remarkably resilient against detection noise. Furthermore, we demonstrate the possibility of retrieving both phase and amplitude of the test pulse.