Huygens-Fresnel principle for active collectives

Groups of actively-moving particles, ranging from swimming microorganisms to synthetic self-propelled colloids, often exhibit collective chemotaxis—directed motion along a chemical gradient that the constituent particles can generate themselves. This process enables active collectives to migrate as coherent fronts that travel at a constant speed over large distances. Here, we use experiments and theory to demonstrate that such traveling fronts of chemically-driven active systems can, over sufficiently large length scales, be described by the Huygens-Fresnel principle of wave propagation. In particular, we examine the canonical example of single-slit diffraction in which an initially-flat front of width ℓ passes through a slit of width w, and show that when ℓ/w ≫ 1, this front indeed emerges from the slit as a cylindrical wave of uniform intensity, just as predicted by the Huygens-Fresnel principle. We also extend our results to the case of multi-slit interference. Altogether, our work bridges classical wave optics principles with active matter biophysics, thereby helping to establish a framework for predicting an controlling collective behavior in chemically-driven active systems in heterogeneous chemical landscapes.