Bragg Reflection of Walking Droplets

In Bragg diffraction, a subatomic particle may become stalled or reflected upon encountering a periodic array of potential barriers with spacing equal to an integer multiple of half its de Broglie wavelength, due to the interference between wavefunction components reflected by each barrier. Here, we demonstrate a classical, particle-based analog of Bragg diffraction by examining the motion of a walking droplet over a periodic array of submerged pillars. These droplets, which exhibit a macroscopic form of wave–particle duality, interact with the underlying topography through wave-mediated forces that impose effective potentials on their dynamics. Through experiments and simulations, we show that a walking droplet traversing a one-dimensional submerged lattice undergoes dramatic deceleration and reflection when the pillars spacing is, as in Bragg diffraction, an integer multiple of half the wavelength of the droplet’s self-generated waves. By analyzing the topography-induced wavefield, we discover that Bragg lattice configurations support standing waves due to matching periodicity between pillars and the droplet’s wavefield. Droplets riding such standing waves experience a net force opposing their motion, while the travelling waves induced by non-Bragg lattices exert no net force.