Giant extraordinary transmission of acoustic waves through a nanowire

Abstract

Wave concentration beyond the diffraction limit by transmission through subwavelength structures has proved to be a milestone in high-resolution imaging. Here, we show that a sound wave incident inside a solid over a diameter of 110 nm can be squeezed through a resonant meta-atom consisting of a nanowire with a diameter of 5 nm equal to λ/23, where λ is the incident acoustic wavelength, corresponding to a transmission efficiency of 500 or an energy densification of ~14,000. This remarkable level of extraordinary acoustic transmission is achieved in the absence of ultrasonic attenuation by connecting a tungsten nanowire between two tungsten blocks, the block on the input side being furnished with concentric grooves. We also demonstrate that these "solid organ pipes" exhibit Rayleigh end corrections to their effective longitudinal resonant lengths notably larger than their in-air analogs. Grooves on the output side lead to in-solid directed acoustic beams, important for nanosensing.

Fig. 1. EAT architectures containing a nanowire with or without additional concentric grooves.

(A) Schematic diagram of the EAT geometry, showing a section through a subwavelength-diameter tungsten nanowire connecting two tungsten half-spaces. Three different cases are considered: (B) case of no grooves, (C) case of grooves on the input side, and (D) case of grooves on both input and output sides. (E) Cross section for grooves on the input side with dimensions in nanometers. The acoustic source and analysis regions are also shown.

Fig. 2. Simulated spectra of the transmission efficiency 𝛈(f).

The nanowire length is L = 40 nm and the radius is a = 2.5 nm. (A) η(f) for the case of no grooves, corresponding to Fig. 1B. Vertical dashed lines denote calculated FP resonances of the nanowire from Eq. 2 with end correction ∆L = 1.26a applied. (B to D) Associated x-y plane dilatation fields in the nanowire at the first three resonances together with dilatation-amplitude line plots sampled in the x direction averaged over the nanowire in the area delimited by the black dashed lines. (E) η(f) for the case of N = 8 grooves on the input side, corresponding to Fig. 1C. The groove dimensions are optimized. Vertical dotted lines denote calculated Rayleigh wave resonance frequencies from Eq. 4. (F and G) Associated x-y plane dilatation fields at the first two resonances together with dilatation-amplitude line plots sampled in the y direction averaged over the interface of the input block in the area delimited by the black dashed lines (ignoring the protrusions). All dimensions are in nanometers. The color scales for each image are the same in (B) to (D) and in (F) and (G).

Fig. 3. Comparison of the acoustic output fields for three geometries.

Dilatation fields at the first resonance on the nanowire output side. (A) Case of no grooves. (B) With N = 8 grooves on the input side. The groove dimensions are optimized to enhance the transmission efficiency of the first resonance. (C) For N = 8 grooves on both sides, with groove dimensions unchanged. The color scale of (C) is the same as that for (B). (D) Fourier modulus of the dilatation. The corresponding structure is shown to scale beneath each plot; the insets show three-dimensional views.

Fig. 4. Effect of ultrasonic attenuation on the transmission efficiency.

Plots of the normalized efficiency η/η_max as a function of the normalized attenuation αL, where L is the length of the nanowire. Cases of no grooves and with N = 8 grooves on the input side are shown. The groove dimensions are optimized to enhance the transmission efficiency of the first resonance.