Approximation of the time form of a laser pulse using finite functions

Abstract

The influence of the time form of a surface heat source on the distribution of the temperature field in a homogeneous half-space is investigated.Introduction. The intensity of laser radiation is either constant (continuous operation) or a function of time (pulsed operation) [1]. Most gas lasers, in particular, CO 2 and He-Ne ones, can operate in both continuous and pulsed lasing regimes. Solid-state lasers (ruby, neodymium glass, and Nd:YAG ones) are used in a pulsed regime, although the latter can operate continuously, too. The function describing the time variation in the specific laser-radiation power is called the time form (structure) of a laser beam. The time structure of a pulse of modern lasers can vary with operating conditions (e.g., ruby and neodymium lasers).We have a millisecond (normal) lasing regime when the laser is pumped using a flash lamp. The pulse duration typical of this operating regime of the laser takes on values in the interval 0.1-1 msec. Usually, such a pulse consists, in turn, of a series of randomly occurring flashes with a duration of about a few microseconds. The amplitude and time intervals between them are different. Ruby and neodymium glass lasers frequently operate in such a regime. In a millisecond regime of laser operation, we can also have the generation of a quasistationary pulse, when microflashes are absent. A typical oscillogram of variation in the specific power of a neodymium glass laser operating in a millisecond regime is shown in Fig. 1 [2].Heat-Conduction Problem. The depth of penetration of laser light into the irradiated material is much smaller than the thickness of a layer heated by heat conduction. It is well known that if the thickness of the heated layer is much smaller than the radius of the laser beam, the process of heating of a body can be modeled using a surface heat source [1]. In selecting laser-radiation parameters necessary for forming the temperature field of a certain (for this depth) level in a material with prescribed thermophysical properties, one uses, as a rule, the solution of a one-dimensional (in space coordinate) linear heat-conduction equation for a semiinfinite body z ≥ 0 [3]: