Laser beam shaping profiles and propagation

Abstract

We consider four families of functions--the super-Gaussian, flattened Gaussian, Fermi-Dirac, and super-Lorentzian--that have been used to describe flattened irradiance profiles. We determine the shape and width parameters of the different distributions, when each flattened profile has the same radius and slope of the irradiance at its half-height point, and then we evaluate the implicit functional relationship between the shape and width parameters for matched profiles, which provides a quantitative way to compare profiles described by different families of functions. We conclude from an analysis of each profile with matched parameters using Kirchhoff-Fresnel diffraction theory and M2 analysis that the diffraction patterns as they propagate differ by small amounts, which may not be distinguished experimentally. Thus, beam shaping optics is designed to produce either of these four flattened output irradiance distributions with matched parameters will yield similar irradiance distributions as the beam propagates.

High cycle thermal fatigue of austenitic stainless steel

“…Then the cyclic thermal loading on the central zone of the surface is modeled by a super Gaussian profile [11] where is the surface absorptivity, 0 the chosen peak power of laser pulse known to be equal to 310W, the Gamma function, p the shape parameter and the reduced cross-sectional distance 2 2…”

Modeling of 3D technological fields and research of principal perspectives and limits in productivity improvement of selective laser melting

“…On the experimental setup three different laser beam power distribution was obtained (Gaussian, Flat-top and Inverse Gaussian) [7][8][9]. For the last 25 years plenty of the authors firstly proved the mathematical possibility of other laser beam power density distributions [14][15][16][17]; next they developed the optical principles and obtained them in their experiments, searched their possible application in the context of technology and machinery [18][19][20][21][22][23][24].…”

Enhanced performance of refractive laser beam shapers through additional phase control at focus

“…The flattop profile at the focal plane is chosen to have roll-off edges rather than perfect steep ones to avoid strong ripples in the far-field diffraction pattern. 18 Shealy and Hoffnagle 26 have summarized for laser beam shaping different flattened profiles, from which we have selected a commonly used one Fermi-Dirac (FD) profile described as E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 2 6 ; 6 3 ; 4 7 3 I FD ðRÞ…”