Regularization strategies for advanced laser pulse shape reconstruction

提出了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。不稳定的脉冲串通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的锁模，例如，半导体激光器这种脉冲源的时间平均自相关测量表现出相干尖峰，这经常被误解为一个稳定的短脉冲序列的签名。在这里，我们提出的方法，允许这两种现象的第一次明确的分离。该方法是基于频率分辨光学门控（FROG）和光谱相位干涉直接电场重建（SPIDER，光谱干涉的自参考变体），但需要进一步发展，不仅在实验方面，而且还涉及从测量数据，我们计划解决的两个功能之间的合作努力光学和应用数学的数学重建。从数学的角度来看，FROG提出了一个不适定的反问题，在其检索。计划中的重建方法基于正则化，我们已经在以前的合作中成功地采用了正则化。该提案的目标包括测量设备的设置，该测量设备能够在幅度和相位上对来自不稳定脉冲串的单个脉冲进行完整测量。然后，我们计划开发的测量方法，使检索的包络函数和相干函数从一个或多个脉冲平均测量。后一个问题的解决方案将需要一个数学公式的检索问题，数值模拟的综合测量，开发一个正则化的检索算法及其实施，以及联合应用这三个开发步骤的真实的测量数据。 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，物理方面也希望从拟议的测量能力中获得对非线性光纤传播和伴随的相干性损失的更深入理解。

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.