Beyond Gaussians-diffraction of complex light: tutorial

Complex light can evolve radically as a function of propagation simply as a consequence of linear diffraction. Here, we characterize beam profiles in terms of their Dirichlet energy U~_D, which scales with the asymptotic rate of diffraction, i.e., the rate of expansion of the beam mode field radius. This metric is translation-invariant, structure-informed, and constant as a beam propagates through vacuum. The diffraction length of structured light scales as L_df∝β_s=U~_D. We provide examples with Laguerre-Gaussian vortex beams and fractal multi-beams using non-dimensional units, which are vital for self-consistent analyses of complex light.