Transmittivity through straight and stublike waveguides in a two-dimensional phononic crystal

We study theoretically the propagation of acoustic waves through a linear waveguide, created inside a two-dimensional phononic crystal, along which a side branch (or stub) is attached. The primary effect of this resonator is to induce zeros of transmission in the transmission spectrum of the perfect waveguide. The transmittivity exhibits very narrow dips whose frequencies depend upon the width and the length of the stub. When a gap exists in the transmittivity of the perfect waveguide, the stub may also permit selective frequency transmission in this gap. We have considered phononic crystals constituted by either fluid or solid constituents. The calculations of the band structure and transmittivity are performed by a combination of finite-difference time domain and plane-wave expansion methods.