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/ηmax 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.
Supplementary Materials
Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/6/10/eaay8507/DC1
Section S1. Calculation of the transmission efficiency
Section S2. Rayleigh correction for the resonant frequency of the nanowire
Section S3. Q factor of the nanowire
Section S4. Geometry optimization
Section S5. Acoustic energy densification in the nanowire
Section S6. Temporal variation of the dilatation
Fig. S1. Rayleigh end correction for a tungsten nanowire.
Fig. S2. Influence of groove pitch and position on the normalized transmission efficiency.
Fig. S3. Influence of groove height and width on the normalized transmission efficiency.
Fig. S4. Influence of groove number on the transmission efficiency.
Fig. S5. Fourier amplitudes of the dilatation along the central axis.
Fig. S6. Time domain data for the dilatation.
Movie S1. Animations of the EAT at the first resonance.
Movie S2. Animations of the EAT in the time domain.
Additional Files
Supplementary Materials
The PDF file includes:
- Section S1. Calculation of the transmission efficiency
- Section S2. Rayleigh correction for the resonant frequency of the nanowire
- Section S3. Q factor of the nanowire
- Section S4. Geometry optimization
- Section S5. Acoustic energy densification in the nanowire
- Section S6. Temporal variation of the dilatation
- Fig. S1. Rayleigh end correction for a tungsten nanowire.
- Fig. S2. Influence of groove pitch and position on the normalized transmission efficiency.
- Fig. S3. Influence of groove height and width on the normalized transmission efficiency.
- Fig. S4. Influence of groove number on the transmission efficiency.
- Fig. S5. Fourier amplitudes of the dilatation along the central axis.
- Fig. S6. Time domain data for the dilatation.
Other Supplementary Material for this manuscript includes the following:
Files in this Data Supplement:
