Numerical and Experimental Investigation of Beam Shaping in Unstable Resonators Using a Bandlimited Hybrid Angular Spectrum–Fourier Method

We investigate beam shaping and field evolution in unstable optical resonators using a hybrid numerical scheme that combines the Split-Step Fourier Method (SSFM) with the Angular Spectrum Method (ASM) and preliminary experiments. The propagation dynamics in open resonator cavities include realistic gain profiles and boundary effects. A bandlimited ASM with zero-padding, suitable frequency cutoffs, and Matsushima-based sampling enhances accuracy and numerical stability. Runtime and resolution are optimized to reduce aliasing and axis-dependent artefacts. Simulations predict hollow, annular beams with improved phase coherence and a beam quality factorM2≈2.12. Preliminary experiments confirm key spatial features, although deviations in beam radius and symmetry highlight the need for better alignment and multi-pass validation. For high-power systems using media such as Yb: YAG or Nd: YAG, the approach enables accurate modelling of unstable cavity dynamics and structured beam design.