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It is known that the transmission spectrum of the so-called locally resonant phononic crystal can exhibit absolute sharp dips in the sonic frequency range due to the resonance scattering of elastic waves. In this paper, we study theoretically, using a finite difference time domain method, the propagation of acoustic waves through a two-dimensional locally resonant crystal in which the matrix is a fluid (such as water) instead of being a solid as in most of the previous papers. The transmission is shown to be dependent upon the fluid or solid nature of the matrix as well as upon the nature of the coating material in contact with the matrix. The other main purpose of this paper is to consider inclusions constituted by coaxial cylindrical multilayers consisting of several alternate shells of a soft material (such as a soft rubber) and a hard material (such as steel). With respect to the usual case of a hard core coated with a soft rubber, the transmission spectrum can exhibit in the same frequency range several peaks instead of one. If two or more phononic crystals are associated together, we find that the structure displays all the zeros of transmission resulting from each individual crystal. Moreover, we show that it is possible to overlap the dips by an appropriate combination of phononic crystals and create a larger acoustic stop band.

Acoustic band gap (ABG) materials constituted of steel hollow cylinders immersed in water can exhibit a tunable narrow pass band (NPB) located inside their gap. We theoretically investigate, using the finite difference time domain (FDTD) method, the properties of waveguides composed of a row of hollow cylinders in a two-dimensional (2D) phononic crystal made of filled steel cylinders. These waveguides exhibit NPB's at frequencies slightly higher than their infinite periodic ABG counterpart. The frequency of the waveguide's NPB can be selected by adjusting the inner radius of the hollow cylinders or by changing the nature of the fluid that fills them. We show that a waveguide constituted of a row of hollow cylinders with different inner radii can transport waves at two different frequencies. By selectively filling the cylinders with water or mercury we have created an active device that permits the transmission of waves at one, both, or neither of these frequencies. Finally, we examine the multiplexing and demultiplexing capabilities of Y shaped waveguides constituted of hollow cylinders.

We present a simple multiplexing structure made of two discrete plasmon wires coupled by two metal nanoclusters. We show that this simple nanosystem can transfer one plasmon wavelength from one wire to the other. Closed-form relations between the transmission coefficients and the nanocluster distances are given to optimize the desired directional plasmon ejection.

The directional transfer of a single photon from one wire to another, leaving all other neighbor states unaffected, is of great importance. We present a simple coupling structure that makes such transfer possible, for any given photon wavelength and linewidth. We give closed-form expressions for the parameters necessary to build such a structure. An illustration of our analytic study is given for the directional transmission of a telecommunication signal between two lines.

The propagation of acoustic waves in a two-dimensional composite medium constituted of a square array of parallel copper cylinders in air is investigated both theoretically and experimentally. The band structure is calculated with the plane wave expansion (PWE) method by imposing the condition of elastic rigidity to the solid inclusions. The PWE results are then compared to the transmission coefficients computed with the finite difference time domain (FDTD) method for finite thickness composite samples. In the low frequency regime, the band structure calculations agree with the FDTD results indicating that the assumption of infinitely rigid inclusion retains the validity of the PWE results to this frequency domain. These calculations predict that this composite material possesses a large absolute forbidden band in the domain of the audible frequencies. The FDTD spectra reveal also that hollow and filled cylinders produce very similar sound transmission suggesting the possibility of realizing light, effective sonic insulators. Experimental measurements show that the transmission through an array of hollow Cu cylinders drops to noise level throughout frequency interval in good agreement with the calculated forbidden band.

We combine a general Green's function formalism and an approach due to Nyborg [W. L. Nyborg, in Acoustic Streaming, Physical Acoustics, edited by W. P. Mason (Academic, London, 1965), Vol. II B, Chap. 11] to calculate the first-order pressure and second-order pressure gradient fields in the vicinity of solid inhomogeneities at a solid/liquid interface. We treat the problem of scattering of an incident acoustic plane wave by a single ridge and two parallel ridges separated by a trench on a planar substrate. The calculated vibrational density of states shows the existence of resonances at low frequencies, especially in the case of a trench. Excitation of a trench resonant vibrational mode enhances the magnitude of the first-order pressure and of the second-order pressure gradient. The resonant frequencies of a trench decrease and the pressure enhancement increases with increasing aspect ratio of the ridges (height to width).

A two-dimensional periodic array of air cylinders in water is known to have giant acoustic stop bands [M.S. Kushwaha and B. Djafari-Rouhani, J. Appl. Phys. 84 (1998) 4677]. It is shown in the present paper that hollow cylinders made of an elastically-soft polymer containing air inside and arranged on a square lattice in water can still give rise to large acoustic band gaps. Similar properties can also be obtained with a close-packed array of tubes containing water when arranged on a honeycomb lattice in air. The transmission coefficient of films made of such polymer-fluid composites has been calculated by finite difference time domain method. With film thickness not exceeding 75 mm, a deep sonic attenuation band was found with, in the best cases, a lower limit below 1 kHz and an upper limit above 10 kHz.