Tailoring k-Space Functionalities by Design in Phononic Crystals

Abstract

K-space functionalities in 2-D phononic crystals (PCs) were studied through the use of the finite difference time domain method (FDTD) as well as the plane wave expansion method (PWE) to solve for the propagation behavior of acoustic waves in these periodic structures. Each of these methods are fully explained in sections 2 and 3 in Appendix A. Characteristics of the various structures were found which aid in the design of the PC to obtain very specific and controlled propagation behavior.Various refractive behaviors were studied which included positive, negative, or zero-angle refraction depending on the angle of the incident wave. For all three cases of refraction, the transmitted beam underwent splitting upon exiting the crystal. These properties are analyzed theoretically as well as demonstrated experimentally. Band structures and equifrequency surfaces (EFSs) show that the observed properties result from the unique geometry of the PC's EFSs as compared to that of the incident media. These properties were extended to the applications of multiplexing and demultiplexing in which the separation of information carried by acoustic waves was attributed entirely to their differences in wave vector. To the best of our knowledge, this is the first report of a k-space multiplexing/demultiplexing device.Subwavelength resolution imaging capabilities of a flat lens composed of a phononic crystal (PC) were also studied. It was found that the image resolution of the PC flat lens beats the Rayleigh diffraction limit because bound modes in the lens can be excited by evanescent waves emitted by the source. These are modes that propagate only in the direction parallel to the lens surface. These modes resonantly amplify evanescent waves that contribute to the reconstruction of an image. The effect on the image resolution and focal point on various structural and operational parameters were studied. These parameters included source frequency, geometry of the lens, source position, and time. The mechanisms by which these factors affect resolution are discussed in terms of the competition between the contribution of propagative modes to focusing and the ability of the source to excite bound modes of the PC lens.