Advanced experimental and computational methods for ultrashort laser pulse characterization

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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).