Simulation of ultrashort pulse propagation using geometrical optics

A geometrical-optics-based approach for simulating ultrashort pulse propagation is presented. The method extends the geometrical optics analysis tool (GOAT) library to include the temporal and spectral properties of femtosecond pulses by incorporating phase information and a Fourier decomposition of the electromagnetic field. Each frequency component is treated individually, allowing for the evaluation of dispersive effects and interference phenomena in complex optical systems. The influence of spatial resolution, spectral sampling, and material dispersion on the temporal pulse shape is analyzed to assess numerical accuracy. Representative examples, including an optical stretcher, a focusing lens, and a vortex phase plate, demonstrate the flexibility of the method. The approach bridges the gap between purely wave-based solvers and conventional ray optics, providing an efficient tool for studying the propagation and transformation of ultrashort laser pulses in dispersive and structured media.