JuliaCon 2026

Structured light in interaction with matter has been of interest, particularly as it relates to the production of high intensity gamma beams. In our package, ElectronDynamicsModels.jl, we developed a way to efficiently compute the radiated field resulting from the scattering of a Laguerre-Gauss laser beam off a thin sheet of electrons. The electrons are represented as relativistic classical particles whose motion is integrated using DifferentialEquations.jl. ModellingToolkit.jl was used to formulate the model, allowing us to take advantage of its compiler to generate efficient Julia code. Moreover, this also enables an easy scaling to parallel ensemble simulations on the CPU and GPU. Besides performance, this approach is also useful for enabling higher precision computations, which naturally leverage Julia's multiple dispatch. Once the trajectories are known, the far electromagnetic field can be computed over a grid of pixels from the Lienardt-Wiechert potentials, and finally we compute their Fourier transform.

Many modern manufacturing techniques rely heavily on lasers and more often than not, the behavior of heat in these systems plays a key role in determining whether a finished product is of acceptable quality. In this talk, I present how it's possible to construct a bespoke finite-element method solver for the heat equation, starting from first principles and building on the work of Ferrite.jl and DifferentialEquations.jl. The solver is then validated against experimental results and I show how access to the inner workings facilitates the extension of the code base to tackle related problems such as computing surface hardness after laser processing.