Temperature distributions due to annular laser beam heating

Optical trepanning is a new laser drilling method using an annular beam. Since laser heating of the substrate occurs first due to heat conduction, this article investigates the temperature distribution in the workpiece due to pulsed annular laser beams by solving an axisymmetric transient heat conduction equation. The annular beams allow numerous irradiance profiles to supply laser energy to the workpiece and thus provide more flexibility in affecting the hole quality than a traditional circular laser beam. Such profiles include half Gaussian with maximum intensities at the inner and outer radii of the annulus, respectively, and full Gaussian with maximum intensity within the annulus. In addition to this spatial beam shaping, the temporal profile of the laser pulse can be shaped to improve the hole quality. The Hankel and Laplace transforms have been used to obtain an analytic solution for the temperature distribution in a semi-infinite workpiece. The effects of the temperature distribution on laser drilling are analyzed to understand the influence of different laser parameters on the drilling process.