Date of Award

Fall 2008

Document Type


Degree Name

Doctor of Philosophy (PhD)


Computational Analysis and Modeling

First Advisor

Weizhong Dai


Ultrashort-pulsed lasers with pulse durations of the order of sub-picoseconds to femtoseconds possess the capabilities in limiting the undesirable spread of the thermal process zone in a heated sample. Because of this, ultrashort-pulsed lasers have been attracting worldwide interest in science and engineering. The 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 induced 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 lasers, laser damage is caused by melting temperature, resulting from continuous pulse of energy. Therefore, in order to apply ultrashort-pulsed lasers successfully, one must study the thermal deformation to prevent the thermal damage.

In the previous research, the parabolic two-step micro heat transport equations have been widely applied in microscale heat transfer. However, when the laser pulse duration is much shorter than the electron thermal relaxation time for the activation of ballistic behavior in the electron gas, the parabolic two-step model may be inadequate to describe the continuous energy flow from hot electrons to lattices during non-equilibrium heating, as pointed out in the literature.

To our knowledge, it has not been seen in the literature that the hyperbolic two-step model is used for studying thermal deformation in micro spheres exposed to ultrashort-pulsed lasers. Micro spheres are considered because they are of interest related to micro resonators in optical applicants, such as ultra-low-threshold lasing, sensing, optoelectronic microdevices, cavity quantum electrodynamics, and their potential in quantum information processing. Hence, the purpose of this dissertation is to employ the hyperbolic two-step model with temperature-dependent thermal properties for obtaining temperature distribution in micro spheres induced by ultrashort-pulsed lasers. This model is coupled with the dynamic equations of motions for studying thermal deformation in micro spheres. To achieve this goal, we first employ an implicit finite difference scheme for solving the hyperbolic two-step model with temperature-dependent thermal properties. We then apply it to studying thermal deformations in Three-Dimensional (3D) micro spheres exposed to ultrashort-pulsed lasers. For this method, staggered grids are designed, and the coupling effect between lattice temperature and strain rate, as well as the hot electron blast effect in momentum transfer, are considered. As such, this obtained method allows us to avoid non-physical oscillations in the solution.

To demonstrate the applicability of the method, we test two physical cases, (1) 3D micro sphere irradiated by ultrashort-pulsed lasers, and (2) 3D double-layered micro sphere with perfectly thermal contacted interface irradiated by ultrashort-pulsed lasers. Results show that the micro spheres expand, and there are some differences between the hyperbolic two-step model and the parabolic two-step model. Particularly, one may see the differences between these two models in the change in electron temperature (Δ Te/(ΔTe)max).

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