ACOUSTIC METAMATERIALS: TUNABLE GRADIENT-INDEX PHONONIC CRYSTALS FOR ACOUSTIC WAVE MANIPULATION

Open Access
Author:
Lin, Sz-Chin Steven
Graduate Program:
Engineering Science and Mechanics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
August 31, 2011
Committee Members:
  • Jun Huang, Dissertation Advisor
  • Jun Huang, Committee Chair
  • Bernhard R Tittmann, Committee Member
  • Corina Stefania Drapaca, Committee Member
  • Stephen A Hambric, Committee Member
Keywords:
  • phononic crystal
  • metamaterial
  • acoustic
  • tunable
  • gradient-index
Abstract:
Acoustic metamaterials are of growing interest due to their ability to manipulate the propagation of acoustic waves in an extraordinary manner to benefit various applications, such as communications, biosensing, and medical diagnosis and therapy. Among various construction methods of acoustic metamaterials, artificially engineered elastic periodic structures, known as phononic crystals (PCs), are the strongest candidates since they exhibit complete phononic band gaps and negative refractions due to the periodicity of the structure. Perfect acoustic mirrors, high-efficiency waveguides, and frequency-selective filters have been demonstrated based on the strong localization of acoustic waves in phononic band gaps. PC-based flat acoustic lenses that break the diffraction limit of waves and achieve sub-wavelength focusing are also obtained, which is considered as a breakthrough in the development of the ultra-high-resolution imaging systems. In this dissertation, a new class of acoustic metamaterials---gradient-index phononic crystal (GRIN PC)---is introduced to overcome the limitations of regular PCs and further enrich the control over acoustic waves. GRIN PCs with a linear gradient profile are first introduced. The band structure for the propagating wave mode of the structure is calculated by a two-dimensional plane wave expansive (PWE) method without considering the temperature and piezoelectric effects. We show that continuous bending of acoustic waves can be obtained by consecutively modulating the filling fraction of the structure along the wave propagation direction. Wide-band acoustic self-collimation and wavelength-scale acoustic mirage effects are numerically demonstrated by simulating shear vertical-mode bulk acoustic wave propagation in such linear GRIN PCs by a finite-difference time-domain (FDTD) methods. Later, GRIN PCs with a hyperbolic secant gradient profile are presented. Through modulating the elastic properties of the cylinders or periodicity of the structure, a hyperbolic secant gradient distribution along the direction transverse to the acoustic wave propagation can be formed to induce converging of acoustic energy to a focal spot smaller than wavelength over a wide range of working frequencies. Therefore, hyperbolic-secant GRIN PCs are suitable for applications such as flat acoustic lenses and couplers. A high-efficiency acoustic beamwidth compressor is then constructed to couple acoustic waves into a PC waveguide with a beam-size conversion ratio of 6.5:1 and a transmission efficiency of up to 90%. An acoustic beam aperture modifier is invented to decrease or increase the beam aperture of a planar acoustic beam with minimum energy loss and wave form distortion. Finally, the tunability of phononic band gaps in two-dimensional PCs consisting of various anisotropic cylinders in an isotropic host is theoretically investigated. By reorienting the anisotropic cylinders, we show that phononic band gaps for bulk acoustic waves propagating in the PC can be opened, modulated, and closed. The anisotropic materials used in this study include cubic, hexagonal, trigonal, and tetragonal crystal systems, hence the study is comprehensive. Compare to other tuning methods, this technique is more practical and can be applied to all two-dimensional PCs, including GRIN PCs, to establish tunable acoustic metamaterials that have enhanced control over acoustic wave propagation. To sum up, two-dimensional GRIN PCs with different gradient profiles are designed to guide acoustic waves in extraordinary manners that are not shown in nature or regular PCs. A practical method for tuning the phononic band gaps of a PC is investigated. The concepts presented in this dissertation serve as important foundations for the future development of acoustic devices.