Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Physics, 2009.Cataloged from PDF version of thesis.Includes bibliographical references (p. 101-109).In this thesis, we present simulations, using Finite Element Method (FEM), of phonon-polariton generation and coherent control in ferroelectric crystals LiNbO₃ and LiTaO₃ through nonlinear electro-optic interactions with ultrashort laser pulses. This direct space-time monitoring platform is used to investigate the nature of the excitation mechanism, the science of propagation in patterned structure, and the waveform control via multi-dimensional pulse shaping. Compared with previous simulation methods, this platform demonstrates considerable improvement in complex domain by achieving varied accuracy over space based on the level of interest of the region, which may facilitate scientific exploration in high power terahertz generation and polaritonic signal processing.by Zhao Chen.S.M