Regularization strategies for advanced laser pulse shape reconstruction

• Applicants: Professor Dr. Bernd Hofmann; Professor Dr. Günter Steinmeyer
• Subject Area: Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas ; Mathematics
• Term: from 2016 to 2019
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 282462670

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.

• DFG Programme: Research Grants
• International Connection: Finland, USA
• Cooperation Partners: Professor Dr. Goery Genty; Privatdozent Dr. Peter Mathé; Professor Dr. Rick Trebino