Interaction of waveguide and localized modes in a phononic crystal

– The transmission properties of phononic crystal waveguides with grafted stub resonators were measured. The phononic crystal consists of a two-dimensional periodical array of steel rods immersed in water. Waveguides for acoustic waves are created by removing a line defect and stubs are formed by removing rods from the sidewalls of the waveguide. Depending on the stub geometry, definite wavelengths are reflected from the stub creating a one-dimensional bandgap within the waveguide transmission spectrum, the bandwidth of which can be controlled by arranging a proper sequence of stubs. These effects are interpreted as the interaction of propagating waveguide modes with localized stub resonances. A great deal of research effort is currently being devoted to the study of acoustic or elastic waves propagation in periodically structured materials, such as the so-called phononic crystals [1–5]. Phononic crystals are somehow the elastic analogous to photonic crystals. They are made of twoor three dimensional periodical repetitions of different solids or fluids which exhibit absolute stop bands in the transmission spectrum of acoustic waves. The location and width of these band gaps result from a large contrast in the value of elastic constants and/or mass density of the constitutive materials. These structures hence have potential applications as acoustic filters or waveguides, among others. Such materials would be very useful for applications requiring the spatial localization of acoustic waves. Efficient guiding and bending of acoustic and elastic waves have both been studied theoretically [6, 7] and demonstrated experimentally [8–11]. We are here dealing with the possibility of altering the transmission characteristics of an acoustic waveguide managed through a phononic crystal by grafting stub tuners on it. A typical waveguide is formed by removing a line of rods and possesses confined propagation modes within a large frequency range. By grafting an additional defect, or stub, to the sidewall of the waveguide, it was predicted theoretically that the transmission spectrum can be dramatically altered [12, 13]. Indeed, the interaction between the stub and the waveguide can generate spectrally sharp zeros in the transmission spectrum of the waveguide occurring at the resonance modes of the stub. The zeros occur