A new method is developed for treating atoms and molecules in a magnetic field in a gauge-invariant way using the Rayleigh-Ritz energy variational principle. The energy operator depends on the vector potential which must be chosen in some gauge. In order to adapt the trial wave function to the gauge of the vector potential, the trial wave function can be multiplied by a phase factor which depends on the spatial coordinates. When the energy expectation value is minimized with respect to the phase function, the equation for charge conservation for stationary states is obtained. This equation can be solved for the phase function, and the solution used in the energy expectation value to obtain a gauge-invariant energy. The method is applicable to all quantum mechanical systems for which the variational principle can be applied. It ensures satisfaction of the charge conservation condition, a gauge-invariant energy, and the best upper bound to the ground-state energy which can be obtained for the form of trial wave function chosen.

The picosecond optical response of germanium is investigated by performing excitation-probe experiments on a thin, intrinsic-germanium wafer maintained at 135 K. The results of three distinct experiments are reported: (1) the transmission of a single pulse is measured as a function of irradiance, (2) the probe transmission is measured at a fixed time after excitation as a function of the excitation energy, and (3) the transmission of a probe pulse is monitored as a function of time after excitation. These experiments employ 10-picosecond laser pulses at 1.06 um and Stokes-shifted pulses at 1.55-um.

This thesis relates a technique for increasing the optical strength of NaCl and KCl single-crystal samples. The 1.06-μm pulsed laser damage thresholds were increased by factors as large as 4.6 for a bulk NaCl single-crystal sample. The bulk laser damage breakdown threshold (LDBT) of the crystal was measured prior to and after heat treatment at 800*C using a Nd:YAG laser operating at 1.06 μm. Bulk and surface LDBTs were also studied on samples annealed at 400° C. These samples showed differences in damage morphology on both cleaved and polished surfaces, and the cleaved surfaces had improved damage thresholds. However, neither the polished surfaces nor the bulk showed improved threshold at the lower annealing temperature.