Finite-difference Time-domain Method And Application For Two-Dimensional Phononic Crystals

Recently, the study of elastic and acoustic wave propagation in periodic elastic composite materials has attracted much attention. These periodic composite materials, also known as phononic crystals, are constituted of two- or three-dimensional arrays of inclusions embedded in some different host materials. Similar to the photonic band gap materials where the propagation of light is prohibited in some frequency range, phononic crystal can exhibit large acoustic band gaps where the propagation of sound or vibration is strictly forbidden in all directions. The existence of absolute band gaps in phononic crystals has been predicted theoretically and observed experimentally. A phononic crystal may, therefore, have potential applications in transducer technology, guidance of acoustic waves, and filtering. By breaking the periodicity of the phononic crystal, it is possible to create highly localized defect or guided modes within the acoustic band gap. This makes these systems potential candidates for the design of elastic or acoustic waveguides or filters.Manipulating the propagation of light through waveguides created inside photonic crystal can have interesting engineering applications such as low loss transmission through sharp bends, channel drop filtering, and wavelength division multiplexing. The transmission spectrum can be altered drastically by the coupling of a waveguide with resonant cavities, and this may be found useful applications. In analogy to photonic crystal, several works have been devoted to study the acoustic behavior of linear and point defects in phononic crystal, wave bending and splitting, transmission through perfect or defect-containing waveguides, tunable filtering and demultiplexing.In this paper, we propose a design of a multiport filter in a two dimensional phononic crystal of a triangular lattice, formed by two separate straight waveguides. By introducing appropriate cavities in between the waveguides, optional resonant tunneling processes can occur between the two waveguides through the coupling of guiding modes with cavity modes. We illustrate the results by performing computational simulations on the acoustic wave propagation in a two-dimensional solid/fluid phononic crystal. The calculations performed in this work are based on the finite difference time domain (FDTD) method which has been widely used in the simulations of wave motions in phononic crystal.