Mathematical Model of the Distribution of Laser Pulse Energy

Abstract

Method allows for modelling of the complex process of laser pulse energy distribution over flat work surface. The process of calculating the correct result does not use common lasing formulas but instead employs the mathematical model of matrix multiplication of three input matrices representing a pulse model, a line model, and a plane model. The pulse model represents the distribution of planar energy densities within the laser pulse. The line model represents the distribution of pulses within the line. The plane model represents the distribution of lines within the plane. Because mathematical model is implemented within a spreadsheet processor, its size can be adjusted as needed and it can be instantiated multiple times for simultaneous modelling of different input parameters.

Study of Laser Source Output Characteristics

“…Therefore additional mathematical simulation was carried out for distributing energy EP of a single laser pulse over some scanned distance s (Fig. 10) [5]. Based on the results of a simulation it can be seen that pulse was scanned over a distance s ≤ 20 μm, which corresponds to pulse duration τ ≤ 200 ns.…”

“…This way pulse energy EP, which is moving at the speed of light c in certain direction, can cross imaginary plane that is perpendicular to this direction in the amount of time equal to pulse duration τ. In other words, total amount of laser pulse energy EP that can be delivered in continuous way to a plane perpendicular to direction of its propagation in the amount of time equal to pulse duration τ defines pulse peak power PP as shown in formula (5).…”