Observation of a half-illuminated mode in an open Penrose cavity

The illumination problem in mathematics questions the existence of a bounded region in which light rays from a point light source do not illuminate the whole region. Since Penrose disproved the illumination problem with elliptical reflective boundaries, the interest has mostly remained in ray optics mainly because there can be no completely dark region for light waves due to diffraction. Here, in a two-dimensional Penrose cavity with elliptical boundaries, we report experimental observation of a symmetry-broken mode in the long-wavelength regime with the half of the cavity region with reflection symmetry almost unilluminated in the steady state. The half-illuminated mode (HIM) was observed in an acoustic cavity by using the schlieren method. The HIM originated from the coherent superposition of near-degenerate modes, among which two scarred modes with opposite parities played a major role. The illuminated part of the HIM could be even flipped by choosing different coefficients in the coherent superposition of the participating modes. The HIM of the Penrose cavity provides new perspective to the illumination problem in an open system.