Towards anti-causal Green’s function for three-dimensional sub-diffraction focusing

• DOI: 10.1038/s41567-018-0082-3
• Publication Date: 2018-04-04T03:15:23Z
• Authors: Guancong Ma; Xiying Fan; Fuyin Ma; Julien de Rosny; Ping Sheng; Mathias Fink
• Keywords: Free space

In causal physics, the causal Green’s function describes the radiation of a point source. Its counterpart, the anti-causal Green’s function, depicts a spherically converging wave. However, in free space, any converging wave must be followed by a diverging one. Their interference gives rise to the diffraction limit that constrains the smallest possible dimension of a wave’s focal spot in free space, which is half the wavelength. Here, we show with three-dimensional acoustic experiments that we can realize a stand-alone anti-causal Green’s function in a large portion of space up to a subwavelength distance from the focus point by introducing a near-perfect absorber for spherical waves at the focus. We build this subwavelength absorber based on membrane-type acoustic metamaterial, and experimentally demonstrate focusing of spherical waves beyond the diffraction limit. A metamaterial-based acoustic sink has been designed to serve the purpose of absorbing the diverging waves and demonstrating three-dimensional sub-diffraction spherical sound wave focusing.