Regularization strategies for advanced laser pulse shape reconstruction

提出了一种同时测量非稳定激光脉冲序列的包络函数和相干函数的新方法。不稳定的脉冲串经常出现在激光脉冲压缩中，或者可能源于某些激光材料中的不完美锁模，例如在半导体激光器中。这种脉冲源的时间平均自相关测量显示出相干尖峰，这经常被误解为稳定的短脉冲序列的特征。在这里，我们首次提出了明确区分这两种现象的方法。这些方法基于频率分辨光学门控(FROG)和用于直接电场重建的光谱相位干涉术(SPIDER，光谱干涉术的自参考变体)，但不仅需要在实验方面进一步发展，还需要从测量数据进行数学重建，我们计划在光学和应用数学之间的合作努力中解决这两个函数的重建问题。从数学的角度来看，FROG在检索时提出了一个不适定的反问题。计划中的重建方法是基于正则化的，我们已经在以前的合作中成功地采用了正则化。该方案的目标包括建立测量设备，使得能够完整地测量来自不稳定脉冲序列的单个脉冲的幅度和相位。然后，我们计划开发能够从一个或多个脉冲平均测量中恢复包络函数和相干函数的测量方法。后一个问题的解决将需要建立检索问题的数学公式、合成测量的数值模拟、基于正则化的检索算法的开发及其实现、以及在实际测量数据上联合应用这三个开发步骤。在数学方面，还计划根据具体的物理问题进一步开发正则化策略，物理方面也希望通过提出的测量能力来更深入地了解非线性光纤传输和伴随的相干损失。

Novel methods for simultaneous measurement of the enveloping function and the coherence function of an unstable laser pulse train are proposed. Unstable pulse trains often arise in laser pulse compression or may stem from imperfect mode-locking in certain laser materials, e.g., in semiconductor lasers. Temporally averaged autocorrelation measurements of such pulse sources exhibit a coherence spike, which has frequently been misinterpreted as the signature of a stable train of short pulses. Here we propose methods that allow a clear separation of these two phenomena for the first time. The methods are based on frequency-resolved optical gating (FROG) and spectral phase interferometry for direct electric-field reconstruction (SPIDER, a self-referenced variant of spectral interferometry), but require further development not only on the experimental side, but also concerning the mathematical reconstruction of the two functions from measured data, which we plan to address in a collaborative effort between optics and applied mathematics. From a mathematical point of view, FROG poses an ill-posed inverse problem in its retrieval. The planned reconstruction methods are based on regularization, which we already employed successfully in a previous collaboration. Goals of this proposal include the set-up of measurement devices that enable the complete measurements of single pulses from an unstable pulse train, both in amplitude and phase. We then plan to develop measurement methods that enable retrieval of the enveloping function and the coherence function from one or several pulse averaged measurements. Solution of the latter problem will require a mathematical formulation of the retrieval problem, numerical simulation of synthetic measurements, development of a regularization based retrieval algorithm and its implementation, as well as the joint application of these three development steps on real measured data. On the mathematics side, it is also planned to further develop regularization strategies according to the specific physical problems, and the physics side also hopes to obtain a deeper understanding of nonlinear fiber propagation and the concomitant loss of coherence from the proposed measurement capabilities.