The vanishing distance: a practical range boundary for dynamic wavefront shaping
Wavefront shaping (WFS) is a powerful modern method to control light propagation through scattering media, with applications ranging from biomedical imaging via cryptography to free-space optical communication. While WFS has been highly successful in static or slowly evolving media, its practical relevance in dynamic and extended scattering environments remains difficult to assess. In particular, no simple criterion currently identifies the propagation distance beyond which the residual ballistic component is no longer distinguishable from the scattered background. Here, we introduce the vanishing distance, defined as the propagation length where the ballistic power equals that carried by a single diffuse mode. Unlike the transport mean free path, which characterizes angular randomization of the scattered field, the vanishing distance identifies the loss of the ballistic channel on a modal-power basis. Beyond this distance, transmission or imaging can no longer rely on the ballistic component and must instead exploit the scattered field. We present a simple semi-analytical model, validated against Monte Carlo simulations and experiments in both monodisperse and heterogeneous scattering media, allowing the vanishing distance and the associated minimum source power to be estimated. Across representative scattering environments, the transition is found to occur typically after about 30-40 scattering mean free paths. These results provide a simple guideline for assessing the practical relevance of dynamic wavefront shaping.