Figure 2: Interface states and their mode characteristics.

(a) Transmission coefficients of heterostructure waveguides, with the NB connected after the Bragg ones. Two peaks appear in the former band gap for each connection. Only one peak at 2349 Hz for the connection of B1-NB is in the centre of the band gap; the others are all near the band edges. (b) Transmission coefficients of heterostructure waveguides, with the Bragg waveguides connected after the non-Bragg one. One peak appears in the centre of the gap for each connection, but the transmission coefficients are all smaller than −15 dB. (c) Sound pressure for the heterostructure waveguides, with B1-NB at 2349 Hz, B2-NB at 2266 Hz, B3-NB at 2562 Hz, and NB-B1 at 2396 Hz. The maximum magnitudes of the interface states appear at different locations with substantially different mode structures for the four heterostructure waveguides. (d) Absolute value of sound pressure along the symmetry axis of the heterostructure waveguides. The red solid, blue dashed, black dotted, and green dash-dot lines represent the four heterostructure waveguides in c, respectively. (e) Normalized sound pressure with its best fit along the radius at the location of the interface states. The mode structures can be identified by the mean square fit method; the single fundamental and first modes can be achieved in heterostructure B2-NB and others.