Boundaryless finite-difference method for three-dimensional beam propagation
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Updated: Aug 9, 2026

Automatic Laser-based Geometry Capture for Finite Element Analysis of Weld Beads
Published on: July 25, 2025
Manuel Guizar-Sicairos1, Julio C Gutiérrez-Vega
1Photonics and Mathematical Optics Group, Tecnológico de Monterrey, México.
Abstract:
A two-dimensional optical field paraxial propagation scheme, in Cartesian and cylindrical coordinate systems, is proposed. This is achieved by extending the method originally proposed by Ladouceur [Opt. Lett. 21, 4 (1996)] for boundaryless beam propagation to two-dimensional optical wave fields. With this formulation the arbitrary choice of physical window size is avoided by mapping the infinite transverse dimensions into a finite-size domain with an appropriate change of variables, thus avoiding the energy loss through the artificial physical boundary that is usually required for the absorbing or the transparent boundary approach.
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