Advanced experimental and computational methods for ultrashort laser pulse characterization

正如最近所展示的，可以使用全光学、全固态、仅基于二次谐波产生（SHG）的色散扫描设备来表征八度跨度超短激光脉冲的完整时间波形。d扫描和类似脉冲表征方法（PC）的精度在非线性光学的许多领域具有实际意义。简单的实验装置（一对玻璃楔，SHG晶体，光谱仪）减少了系统误差，实现了高灵敏度。标准优化求解器用于从d扫描谱图中检索脉冲形状。如果噪声是主要的误差来源，我最近开发的牛顿求解器可以改进任何其他求解器的解。因此，对于具有简单实验设置和较小系统误差的pc来说，它是有益的。因此，本课题的一个重点是将牛顿求解器扩展到敏感PC的d-扫描和a-摆动。求解器随后被gpu加速，并在无需本地软件安装的web服务器上公开可控。第二个重点是开发除SHG晶体外没有光学元件的PC，进一步降低系统误差，并且非常容易实现。围绕光束轴旋转晶体可以调整SH过程本身，并使光谱图参数化。我将扩展牛顿求解器来求解相关的更复杂的积分方程，使其在数值上可访问，并找到合适的材料，切割平面和厚度。最后，测试并应用该技术。第三个重点是开发与FROG、CRAB和d-scan兼容的宽带脉冲的高速PC和求解器。测量两个相似的谱图而不是一个。它们之间的细微差别是求解器的输入。由于要求解的方程得到了显著的简化，因此反演时间仅为几毫秒。在第二次测量中，脉冲在SHG之前穿过色散介质。这种所谓的简化层析方法起源于信号处理。层析成像方法不为人所知和尚未广泛应用的主要原因是，只有当引入的色散可以假定为脉冲带宽上的二次元时，简化才有效。我将消除这一限制，推导广义方程，选择合适的数值方法并应用该技术。在未来，GPU加速求解器可以快速地从一组谱图中检索几个不同的脉冲（混合状态检索）。扩展已开发的PC来表征脉冲序列（单发）中的单个脉冲似乎是可能的。层析成像方法可以在未来实现快速的时空PC（类似于SPIDER）。

As recently shown, it is possible to characterize the complete temporal waveform of octave-spanning ultrashort laser pulses using an all-optical, all-solid-state, dispersion-scan device based only on second-harmonic generation (SHG). The accuracy of d-scan and similar pulse characterization methods (PC) is practically relevant in many areas of nonlinear optics. The simple experimental setup (pair of glass wedges, SHG crystal, spectrometer) reduces systematic errors and enables high sensitivity. Standard optimization solvers are used to retrieve the pulse shape from a d-scan spectrogram. The Newton Solver I recently developed can refine the solution of any other solver if noise is the dominant source of error. Therefore, it is beneficial for PCs with a simple experimental setup and, thus, minor systematic errors.Therefore, one focus of this project is to extend the Newton Solver to the sensitive PC d-scan and a-swing. The solver is then GPU-accelerated and made publicly controllable on a web server without local software installation.The second focus is developing a PC with no optical components other than the SHG crystal, further boiling down systematic errors and very easy to implement. Rotating the crystal around the beam axis tunes the SH process itself and parametrizes the spectrogram. I will extend the Newton Solver to solve the associated more complex integral equation, make it numerically accessible, and find a suitable material, cutting plane, and thickness. Finally, test and apply the technique.The third focus is the development of a high-speed PC and solver for broadband pulses compatible with FROG, CRAB, and d-scan. Two similar spectrograms are measured instead of one. Their slight difference is input for the solver. As the equation to be solved is significantly simplified, the retrieval takes only a few ms. For the second measurement, the pulse passes through a dispersive medium before SHG. This so-called simplified tomographic method originates from signal processing.The main reason tomographic methods are not well-known and not yet widely used is that simplification only works if the dispersion introduced can be assumed to be the quadratic over the pulse bandwidth. I will remove this limitation, derive the generalized equations, select favorable numerical methods and apply the technique.In the future, GPU accelerated solvers can quickly retrieve several different pulses from a sum of spectrograms (mixed-state retrieval). Extending the developed PC to characterize a single pulse of a pulse train (single-shot) seems possible. Tomographic methods could enable fast Spatio-temporal PC in the future (analogous to SPIDER).