Defect modes for a promising acoustic wave-guide in two-dimensional sonic/phononic crystals

Abstract

Defect modes, which propagate along a line of periodic defects of scatterers in a periodic array of scatterers, have been found to be well guided in a frequency range within the full band-gap of such sonic/phononic crystals as arrays of methacrylic resin cylinders in air, steel cylinders in air or in water, and aluminum cylinders in air. For example, the defect mode along a periodic lacking of every second scatterers in the central line of a periodic array of methacrylic resin cylinders in air has a perfect pass-band with a 0 dB transmission between 0.54 and 0.59 in the normalized frequency, which is defined by the lattice constant divided by the free-space wavelength. This defect-mode pass-band locates itself within a full band-gap of the original sonic/phononic crystal of methacrylic resin cylinders in air, whose frequency is between 0.47 and 0.63 in the normalized frequency. The level of the acoustic leakage just outside one of the rear side corners of 11 times 11 size of crystal was calculated as �21 to �28 dB. Also a wave-guide with a bend made of a periodic lacking of every second scatterers in the same sonic crystal has a good transmittance and an impedance matching at the inlet and the outlet just as the straight wave-guide has. Consequently, the defect modes are promising for effectively well-confined and guided modes in contrast to the conventionally investigated modes along a hollow wave-guide in a sonic/phononic crystals. For these theoretical investigations of defect modes in sonic/ phononic crystals, we have developed an impulse response elastic FDTD method to obtain precise frequency response of a finite size of periodic structures of acoustic scatterers placed in liquid or gas. The frequency responses of such typical sonic/phononic crystals have been numerically investigated as those composed of a two-dimensional array of methacrylic-resin cylinders in air, aluminum cylinders in air, and steel cylinders in water. We have found that the former two crystals may be numerically investigated by our conventional sonic FDTD method with a small normalized frequency difference of 0.01 to 0.02 compared with those obtained by our new elastic FDTD analysis. On the other hand, it has been found that the latter crystal should be investigated by the elastic FDTD method, because of a large frequency difference of 0.06 to 0.08 compared with the conventional sonic FDTD method. All results shown in this report have been calculated by means of the elastic FDTD method developed by us.