Acoustic Fano resonators

Summary form only given. The resonances with asymmetric Fano line-shapes were originally discovered in the context of quantum mechanics (U. Fano, Phys. Rev., 124, 1866-1878, 1961). Quantum Fano resonances were generated from destructive interference of a discrete state with a continuum one. During the last decade this concept has been applied in plasmonics where the interference between a narrowband polariton and a broader one has been used to generate electromagnetically induced transparency (EIT) (M. Rahmani, et al., Laser Photon. Rev., 7, 329-349, 2013). In this work, an acoustic device, which supports a Fano-like resonance in its response to an incident sound wave, is designed. The design consists of a 2D array of sub-wavelength unit cells, each of which involves a pair of concentric stopped pipes made of rigid acoustic material. The (longitudinal) acoustic resonance frequency of a pipe depends on its length and the way it is closed. The frequencies of the fundamental resonance in a uniform and canonical pipe of length L are approximately c / (4L) and c / (2L) , respectively. Here, c is the speed of sound. The asymmetric Fano line-shape originates from the interference of two such fundamental modes associated with two pipes with different lengths. In the design proposed here this is achieved by locating a small pipe inside a wider/longer one. Acoustically induced transparency (AIT) is achieved from the destructive interference of two closely spaced (detuned) fundamental modes that decay to the same continuum. Numerical characterization of acoustic pressure wave interactions on the proposed design demonstrates that it can be used to generate novel ultrasonic functionalities such as filters, collimators, and imaging via slow sound. Additionally, the design is flexible enough to allow for generation of multi-AIT effects by using more than two pipes within th unit celll