Broadband Green's Function-KKR-Multiple Scattering Method for the Calculations of Band Structures in Topological Acoustics

Abstract

Topological states in photonics were initially proposed by Haldane in analogy to the quantum Hall (QH) effect in electronic system. Topological acoustics has also been demonstrated recently. In this paper, we apply the Broadband Green's function-KKR-Multiple Scattering Theory (BBGF-KKR-MST) to calculate band eigenvalues and band field solutions in topological acoustics. The advantage of the method is that low order cylindrical waves are used to derive the matrix eigenvalue equations for the bands. For the first two bands, the dimension of the matrix equation is only 7 by 7. Using the eigenvalue and the eigenvector, the band field solutions and the normalization are calculated with higher order cylindrical waves. The CPU time requirements, including setup, is 0.006 seconds for a band eigenvalue. The band field solution requires only 15 coefficients of higher order cylindrical waves for the entire hexagonal cell.