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

Guancong Ma*, Xiying Fan, Fuyin Ma, Julien De Rosny, Ping Sheng, Mathias Fink

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

50 Citations (Scopus)
21 Downloads (Pure)


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.

Original languageEnglish
Pages (from-to)608-612
Number of pages5
JournalNature Physics
Issue number6
Publication statusPublished - 1 Jun 2018

Scopus Subject Areas

  • Physics and Astronomy(all)


Dive into the research topics of 'Towards anti-causal Green's function for three-dimensional sub-diffraction focusing'. Together they form a unique fingerprint.

Cite this