A transfer matrix method for calculating the transmission and reflection coefficient of labyrinthine metamaterials

Abstract

Labyrinthine unit cells have existed for many years and have been central to the design of numerous metamaterial solutions. However, the literature does not present a reproducible analytical model to predict their behaviour both in transmission and reflection, thus limiting design optimization in terms of bandwidth of operation and space occupied. In this work, we present an analytical model based on the transfer matrix method for phase shift and intensity of transmission/reflection-based labyrinthine unit cells. We benchmark our analytical model by finding agreement with finite element method simulations – using commercial software – within 1 dB in amplitude and a 1° in phase. Finally, we compare our predictions with measurements on transmissive/reflective units with 4 and 6 horizontal baffles (“bars”), using different experimental methods. We found that some of the measurement methods lead to an agreement within 2 dB, while others are completely out of range, thus pointing out the challenges in characterizing this type of acoustic metamaterial.

Going round the bend: reflection and transmission of long waves by waveguide corners and labyrinths

“…One reason for our interest in hairpin bends is because they have been the focus of recent work on 'labyrinthine metamaterials', in which a sequence of hairpin bends are joined together [17][18][19][20][21][22]. For analysis of such structures, finite elements have been used [17][18][19], as have matched eigenfunction expansions [20] and homogenization theory [21,22]. We regard these labyrinthine problems as examples of multiple scattering, with each bend considered to be a scatterer.…”