Origin of branched wave structures in optical media and long-tail algebraic intensity distribution

Experiments have revealed that branched, fractal-like wave patterns can arise in a variety of physical situations ranging from microwave and optical systems to solid-state devices, and that the wave-intensity statistics are non-Gaussian and typically exhibit a long-tail distribution. The origin of branched wave patterns is currently an issue of active debate. We propose and investigate a "minimal" model of optical wave propagation and scattering with two generic ingredients: 1) a finite-size medium for linear wave propagation and 2) random scatterers characterized by a continuous refractive-index profile. We find that branched waves can emerge as a general phenomenon in a wide parameter regime in between the weak-scattering limit and Anderson localization, and the distribution of high intensities follows an algebraic scaling law. The minimal model can provide insights into the physical origin of branched waves in other physical systems as well.