Discrete dispersion scan setup for measuring few-cycle laser pulses in the mid-infrared

Abstract

In this work, we demonstrate a discrete dispersion scan scheme using a low number of flat windows to vary the dispersion of laser pulses in discrete steps. Monte Carlo simulations indicate that the pulse duration can be retrieved accurately with less than 10 dispersion steps, which we verify experimentally by measuring few-cycle pulses and material dispersion curves at 3 and 10 µm wavelength. This minimal measuring scheme using only five optical components without the need for linear positioners and interferometric alignment can be readily implemented in many wavelength ranges and situations.

Characterizing ultrashort laser pulses with second harmonic dispersion scans

“…In recent years, there has been a great deal of progress in the development of light sources providing ultrashort pulses in the short-, mid-, and long-wave infrared spectral regions as well as the deep UV [76][77][78][79][80][81]. Expanding the d-scan technique to different carrier wavelengths is a subject of ongoing research (see, e.g., [60] for the UV and [50] for the mid-infrared spectral ranges), and, without a doubt, we will see more work in this direction in the future.…”

“…However, the speed-up often comes with the price of reduced robustness, especially when dealing with traces contaminated by noise. This was recently attributed to the fact that these algorithms do not converge to the least-squares solution in the presence of Gaussian noise [49,50]. Thus, it might be preferable to choose general least-squares solvers, which were shown to be more reliable in these conditions [33].…”

“…Generally speaking, the task of designing fast, robust, and efficient retrieval algorithms is an active field of research, and a significant amount of effort is devoted to the development of routines that are optimized for pulse characterization problems. The recently proposed common pulse retrieval algorithm (COPRA) [49,50], for example, is a general algorithm that not only works with d-scan, but with several other methods as well, like FROG or MIIPS. While being inspired by constraint-based methods, COPRA elegantly avoids the aforementioned problem of not reaching the least-squares solution by replacing a data constraint step with a gradient descent in the final stages of the algorithm run.…”

“…These lead to difficulties in retrieving the spectral phase in the low-intensity areas of the trace, which subsequently affect the agreement of certain lowintensity temporal structures outside of the main peak. In this respect, it should be noted that the RMS error G intrinsically reflects both the noise level of the experimental trace and the retrieval uncertainty [50].…”

Solving non-linear integral equations for laser pulse retrieval with Newton's method

“…The most natural choice to test and fine tune the amount of regularisation for optimality in the presents of additive noise would be a chi-square test while varying λ because the pulse error is not available a priori. Considering modern measurement devices and pulse retrieval setups, see for example [33], for the problem at hand, where (difficult to quantify) systematical errors and multiplicative noise are the most relevant sources of error, a goodness of fit test of this type does not seem applicable yet to a measured trace. A popular practical solution that we recommend in this case, is the so-called L-curve method [25] until more sophisticated techniques are asked for.…”