Abstract
Abstract The mechanism of the perfect anti-reflection of acoustic waves, regardless of frequency and incident angle, is presented. We show that reflections at a planar interface between two different acoustic media can be removed by adding a nonlocal metamaterial that compensates for the impedance mismatch. The properties required of a nonlocal metamaterial are explicitly specified through spatio-temporally dispersive mass density and bulk modulus. We analyze the characteristics of spatio-temporal dispersion according to the thickness of the matching layer. We discuss the issue of the total internal reflection caused by conventional matching layers and explain how our nonlocal matching layer avoids this. The practical design of our nonlocal layer using metamaterials is explained. The omni-directional frequency-independent behavior of the proposed anti-reflection matching layer is confirmed through explicit numerical calculation using the finite element method, and comparisons made to the conventional quarter-wave matching layer approach.
Highlights
Acoustic waves reflect at the interface between two different media, due to the discontinuity of acoustic impedance
To understand the dispersive behavior, we consider the example of a constant universal acoustic impedance matching (UAIM) layer between the PZT4 ceramic ( ρ1 = 7500 kg/m−3, K1 = 120 GPa), which is a typical material for the ultrasound probe, and water (ρ2 = 998 kg/m−3, K2 = 2.20 GPa)
We established a theory of universal acoustic impedance matching and provide an example of a constant UAIM layer that enables the perfect transmission of acoustic waves independent of frequency and incident angle
Summary
Acoustic waves reflect at the interface between two different media, due to the discontinuity of acoustic impedance. The Mason’s equivalent circuit model [18] and the Krimholtz, Leedom, and Matthaei transmission line method [19] have been utilized to develop anti-reflection matching layers for broader frequency band operations [20]. This bandwidth broadening was achieved at the cost of unnecessary acoustic wave absorption inside the matching layer, which reduced the efficiency of energy transfer [4]. We derive the material condition for universal acoustic impedance matching (UAIM) from acoustic wave equations, allowing us to remove unwanted reflection regardless of frequencies and incident angles. We demonstrate the perfect anti-reflective performance of the UAIM layer both analytically and numerically
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