Femtosecond laser pulses are essential tools in modern science and technology, yet generating pulses that are both extremely short and experimentally accessible remains a persistent challenge. Conventional post-compression methods rely on the Kerr effect, a third-order nonlinear effect, but these approaches often require complex setups and a large laboratory footprint. This thesis explores a fundamentally different route to pulse compression by utilising the coherently driven transversal optical phonon-polariton modes in Potassium Titanyl Phosphate (KTP). Rather than relying on Kerr-based spectral broadening and subsequent dispersive compression, the method exploits strong second-order nonlinearities in KTP to generate polaritons by optical rectification so that their electric fields may be used for efficient Stokes sideband generation by electro-optic interaction. The resulting interplay with normal dispersion in the nonlinear crystal results in an order of magnitude shorter self-compressed pulses generated in a simple setup. Such pulses demand advanced characterisation methods. Building on insights from applied mathematics and optimisation theory, a new retrieval algorithm for Frequency-Resolved Optical Gating (FROG) measurements is introduced, which we call the Line-Search FROG (LSF) algorithm, that decouples the measurement data from the reconstruction process. This greatly improves the performance of the pulse retrieval fidelity in the presence of large amounts of noise. The LSF algorithm is highly versatile and applicable to all FROG geometries, including the so-called double-blind FROG, with which we managed to measure the phase of a mode-locked dark pulse for the first time. Other pulse measurement techniques such as dispersion scan could benefit as well as the underlying optimisation problem is similar. To further improve the performance of pulse characterisation techniques, we also present the Sigma Check, which is a general algorithmic step that aims to reduce the likelihood of stagnating at local minima. This is achieved by performing an image-recognition step that correctly identifies and counteracts local minimums.