Figure 2. Effective material properties of the helical-structured acoustic metamaterials.

(a) The refractive index n directly got from geometric parameters are calculated by Equation (1) and shown with the red curve versus lead P. The effective refractive index n_eff acquired using the effect medium approach are calculated by Equation (3) and shown with the blue sphere dots versus lead P. (b) The dynamic mass density ρ_eff acquired using effect medium approach are calculated by Equation (3) and shown with the blue sphere dots versus lead P. (c) The effective refractive indices n_eff and dynamic mass densities ρ_eff change with the frequency, calculated by Equation (4). Two different samples were studied. The first one has L=12.15 mm, P=7 mm. (d) The second sample has L=13.49 mm, P=7.8 mm. The flat lines demonstrate the non-dispersive nature of both samples. Notice that the arrows in c and d indicate the correspondences between the data lines and vertical coordinates.