A finite difference method for studying thermal deformation in a three-dimensional microsphere exposed to ultrashort-pulsed lasers.

摘要

Ultrashort-pulsed lasers with pulse durations on the order of sub-picoseconds to femtoseconds possess the capabilities in limiting the undesirable spread of the thermal process zone in a heated sample which have been attracting worldwide interest in science and engineering. Success of ultrashort-pulsed lasers in real application relies on: (1) well characterized pulse width, intensity and experimental techniques; (2) reliable microscale heat transfer models; and (3) prevention of thermal damage. Laser damage by ultrashort-pulsed lasers occurs after the heating pulse is over since the pulse duration time is extremely short and the heat flux is essentially limited to the region within the electron thermal diffusion length. In contrast with long-pulse laser, laser damage is caused by melting temperature resulting from continuous pulse of energy. This dissertation investigates the mathematical model of heat transport phenomenon in a 3D micro-sphere exposed to ultrashort-pulsed lasers and presents a numerical method for studying thermal deformations. The method is obtained based on the parabolic two-step model and implicit finite difference schemes on a staggered grid. It accounts for the coupling effect between lattice temperature and strain rate, as well as for the hot electron blast effect in momentum transfer. In particular, a fourth-order compact scheme is developed for evaluating those stress derivatives in the dynamic equations of motion. It should be pointed out that micro-spheres are considered because they are of interest related to micro resonators in optical applications, such as ultra-low-threshold lasing, sensing, optoelectronic microdevices, cavity quantum electrodynamics and their potential in quantum information processing.; The numerical method is tested for its applicability by investigating the temperature rise and deformation in five examples, which are (1) a portion of the upper hemisphere is irradiated by a single-pulse laser, (2) portions of both the upper hemisphere and the lower hemisphere are irradiated by a single-pulse laser, (3) the upper hemisphere is irradiated by a single-pulse laser, (4) a portion of the upper hemisphere is irradiated by a double-pulse laser, and (5) portions of both the upper hemisphere and the lower hemisphere are irradiated by a double-pulse laser. Results show that no non-physical oscillations appear in the solutions and the micro-sphere expands when it is irradiated by ultrashort-pulsed lasers.