Methods for engineering sub-2-cycle mode-locked lasers

We begin by presenting a method to efficiently solve for the steady-state solution of a nonlinear cavity, suitable for simulating a solid-state femtosecond laser. The algorithm directly solves the periodic boundary value problem by using a preconditioned KrylovNewton shooting solver. The method can be applied to the design and study of modelocked lasers, as well as the modeling of field enhancement cavities, such as those used in high harmonic generation. In constrast to the standard approach of dynamic simulation, which converges linearly, our algorithm converges quadratically to the stable solution, typically converging two to three orders of magnitude faster than the standard approach. The second major theme is the control of dispersion in mode-locked lasers. The predominant way to design dispersion compensating optics in the past has been a consideration of the integrated net group delay dispersion (GDD). We propose and implement an alternative spectral quantity based on the energy contained in phase distortions, which we term the Phase Distortion Ratio (PDR). Dispersion compensating mirrors optimized with respect to PDR generally perform significantly better than those where GDD is optimized. We demonstrate this in the design of a dispersion compensating mirror pair capable of compressing single-single pulses. In the final section, we deal with the unique challenges inherent to measuring subtwo-cycle pulses reliably and accurately. We have recently developed a technique, TwoDimensional spectral Shearing Interferometry (2DSI), based on spectral shearing, which requires no calibration and does not disperse the pulse being measured. Our method intuitively encodes spectral group delay in a slowly changing fringe in a two-dimensional interferogram. This maximizes use of spectrometer resolution, allowing for complex phase spectra to be measured with high accuracy over extremely large bandwidths, potentially exceeding an octave. We believe that 2DSI is a uniquely cost effective and efficient method for accurately and reliably measuring fewand even single-cycle pulses. While the method is relatively recent, it is well tested and has been successfully demonstrated on several different lasers in two different groups, including one producing 4.9 fs pulses. Thesis Supervisor: Franz X. Kärtner Title: Professor