Hyperbolic heat conduction due to a mode locked laser pulse train

Abstract

In situations which involve repetitive pulsing of a material with a mode locked Nd:YAG laser, the pulse duration can be sufficiently small (i.e. in the picosecond range) that the classical parabolic heat conduction equation fails to adequately predict the resulting temperature distribution in the material. In such cases, the hyperbolic heat conduction equation, which accounts for the finite time to the commencement of heat flow, is appropriate. In the present work, the hyperbolic heat conduction equation is used to predict the temperature distributions in both semi-infinite and finite isotropic media due to a train of temporally rectangular pulses which approximate the Gaussian temporal profile of mode locked laser pulses. The energy carried in the pulses is assumed to be absorbed in the surface plane of the material. The spatial profile of the pulses can be either Gaussian, doughnut or a combination of the two. The parabolic and hyperbolic models are examined for selected pulse frequencies.