Two-dimensional phononic crystals: Examples and applications

Phononic crystals are composite materials made of periodic distributions of inclusions embedded in a matrix. Due to their periodic structure, these materials may exhibit under certain conditions, absolute acoustic band gaps i.e. forbidden bands that are independent of the direction of propagation of the incident elastic wave. In the first part of this review paper, we present some examples of two-dimensional bulk phononic crystals i.e. two-dimensional arrays of inclusions assumed of infinite extent along the three spatial directions. We show that the bandwidth of the forbidden band depends strongly on the nature of the constituent materials (solid or fluid), as well as the contrast between the physical characteristics (density and elastic moduli) of the inclusions and of the matrix, the geometry of the array of inclusions, the inclusion shape and the filling factor of inclusions. The second part of this review paper is devoted to some possible applications of these composite materials. In particular, we show that defect modes (cavities, waveguides, stubs, etc.) inserted inside the two-dimensional periodic structure may lead to very selective frequency filters and efficient devices for the wavelength demultiplexing. We present also the possibility of sonic insulators for frequencies of the order of kHz with relatively small thicknesses of phononic crystal samples. Finally we report on the vibration modes of a two-dimensional phononic crystal plate i.e. a phononic crystal of finite thickness along the axis of the inclusions. We discuss guided modes which may occur in the band structure of the plate. Surface acoustic waves propagating in two-dimensional phononic crystals should open new perspectives in high-frequency radio-frequency devices. Throughout the paper, the methods of calculation are presented with some details and some experimental results complete the numerical predictions.