Self-collimation of Ultrasonic Waves in a Two-dimensional Prism-shaped Phononic Crystal
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Self-collimation of Ultrasonic Waves in a Two-dimensional Prism-shaped Phononic Crystal Hwi Suk Kang and Kang Il Lee∗ Department of Physics, Kangwon National University, Chuncheon 24341, Korea (Received 7 October 2019 ; accepted 15 June 2020) The self-collimation of ultrasonic waves in a two-dimensional prism-shaped phononic crystal (PC) with a square lattice immersed in water was theoretically and experimentally investigated. The acoustic pressure fields at the frequencies of the first and the second pass bands were calculated with and without the PC in the acoustic path by using the finite element method. The normalized pressure distributions of the ultrasonic waves transmitted through water only and through the PC were theoretically and experimentally obtained along the direction perpendicular to the beam axis. We demonstrated self-collimation and directivity enhancement of the ultrasonic waves in the two-dimensional prism-shaped PC. Keywords: Acoustic metamaterial, Phononic crystal, Band structure, Negative refraction, Self-collimation DOI: 10.3938/jkps.77.510
I. INTRODUCTION
All materials present in nature have inherent properties, such as the electrical permittivity, the magnetic permeability, the density, and the bulk modulus, which influence the transmission of electromagnetic and mechanical waves through those materials. Metamaterials are new artificial materials with unusual material properties that are not found in naturally occurring materials [1]. Photonic crystals are a kind of metamaterial composed of periodic structures that control the propagation of electromagnetic waves [2, 3]. Over the past decades, many interesting phenomena, such as band gaps, negative refraction, focusing, and photon tunneling, have been observed in these structures [4–6]. Kushwaha et al. introduced phononic crystals (PCs), which are the acoustical analogs of photonic crystals for optical waves, by using the mathematical analogy between Maxwell’s equations and the equations of linear elasticity [7]. PCs have periodic structures composed of at least two materials with different elastic properties and are classified mainly into three categories according to their dimensional periodicity: one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) PCs. They have been shown to exhibit a number of remarkable properties, such as acoustic diffraction, negative refraction, and band gaps [8,9]. One of the most important properties of PCs is the frequency ranges at which acoustic waves are allowed (pass band) and not allowed (stop band, band gap), respec∗ E-mail:
tively [10]. The mechanism for the formation of band gaps in PCs is known to be Bragg scattering of waves with wavelengths comparable to the lattice constant [11]. Most previous studies have focused on a search for large band gaps in the band structure of PCs, expecting to find applications, such as acoustic filters, sound isolation, and acoustic imaging [12–14]. Recently, attention has turned to another class of applications based on the negative refraction of acoustic wave
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