Davies B, Herren L. Robustness of subwavelength devices: a case study of cochlea-inspired rainbow sensors.
Proc Math Phys Eng Sci 2022;
478:20210765. [PMID:
35702593 PMCID:
PMC9185833 DOI:
10.1098/rspa.2021.0765]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/01/2021] [Accepted: 04/29/2022] [Indexed: 11/25/2022] Open
Abstract
We derive asymptotic formulae describing how the properties of subwavelength devices are changed by the introduction of errors and imperfections. As a demonstrative example, we study a class of cochlea-inspired rainbow sensors. These are graded metamaterials which have been designed to mimic the frequency separation performed by the cochlea. The device considered here has similar dimensions to the cochlea and has a resonant spectrum that falls within the range of audible frequencies. We show that the device’s properties (including its role as a signal filtering device) are stable with respect to small imperfections in the positions and sizes of the resonators. Additionally, under suitable assumptions, if the number of resonators is sufficiently large, then the device’s properties are stable under the removal of a resonator.
Collapse