Achromatic Needle Focusing with Superresolution Enabled by a Ring-Shaped Acoustic Metalens

Lijuan Fan and Jun Mei

Phys. Rev. Applied 20, 054053 – Published 27 November 2023

Abstract

Superresolution metalenses that can realize a far-field needle focusing effect are highly desired in various applications, such as medical diagnosing, ultrasonic detection, and underwater communication. Here, we propose a design paradigm of a metalens with superresolution for waterborne sound, which is based on metagrating and has a compact and simple configuration. The central region of the metalens is open, surrounded by a metagrating-based peripheral region. In the radial cross section, each meta-atom contains two elliptical iron cylinders that are intelligently designed to deflect the impinging wave along the desired direction towards the intended focal spot. In this way, a needle focusing effect with high intensity and superresolution is achieved in the far-field region, where the conventional Rayleigh-Abbe diffraction limit is broken due to the coherent interference of the ±1 order diffraction channels. Since the design principle does not rely on sharp resonances, the foci of waves carrying different frequencies partially overlap so that an achromatic focusing functionality is realized where incident waves in a continuous frequency range can be simultaneously focused around the same spots. The compact, planar, and center-open configuration of the metalens not only provides a flexible and practical solution to acoustic needle focusing functionality, but also has potential applications as a powerful planar component that can be easily integrated.

Received 26 September 2023
Revised 11 November 2023
Accepted 15 November 2023

DOI:https://doi.org/10.1103/PhysRevApplied.20.054053

Physics Subject Headings (PhySH)

Acoustic metamaterials Acoustic modeling Acoustic wave phenomena Acoustics

Atomic, Molecular & Optical

Authors & Affiliations

Lijuan Fan and Jun Mei ^*

School of Physics, South China University of Technology, Guangzhou 510640, China

^*phjunmei@scut.edu.cn

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Issue

Vol. 20, Iss. 5 — November 2023

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Images

Figure 1
The needle-focusing effect enabled by a metagrating-based metalens. (a) Schematic of the metalens and it needle-focusing effect. (b) A 2D cross section of the metalens, where the 3D lens can be obtained by rotating its 2D cross section around the x axis. A metagrating composed of 50 meta-atoms is surrounding the central axis, where each meta-atom contains two elliptical iron cylinders. The Lth $(L = 1, 2, \dots, 50)$ meta-atom is intelligently designed to deflect a normally incident plane wave $(p_{inc})$ along the diffraction angle $θ_{L}$ towards the Lth focal spot on the x axis. Different meta-atoms focus the wave energy into different focal spots, as indicated by red arrows, with a distance $0.5 λ$ between neighboring spots. In this way, all focal spots form a quasicontinuous needle pattern on the x axis.
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Figure 2
Design of each meta-atom. (a) Numerical simulation setup in comsol Multiphysics. (b) Shows the wave deflection abilities of the first and 50th meta-atoms, respectively. White arrows represent the directions of incident and transmitted waves. Strong coupling between the incident acoustic wave and the elastic vibration modes in solid cylinders can be seen. (c) The $n = - 1$ channel transmission efficiency $T_{- 1}$ and periodicity $d_{L}$ of the Lth meta-atom as a function of the refraction angle $| θ_{L} |$ .
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Figure 3
The acoustic needle-focusing effect for a metalens consisting of 50 meta-atoms. (a) Shows the logarithm of normalized pressure intensity $(lo g_{10} I_{norm})$ within the x-y plane, where a needle pattern with a propagation length approximately 25λ can be seen. (b) Shows the logarithm of pressure-intensity profile along the x axis (blue line) and the transverse FWHM of each focal spot (red stars). Orange dot-dashed line and green dotted line represent the Rayleigh-Abbe diffraction limit (0.5λ/NA = 0.664λ) and superoscillation criterion (0.38λ/NA = 0.505λ), respectively. (c) Shows the pressure-intensity profiles along the y axis for the second, 20th, and 35th focal spots, respectively, with the corresponding FWHMs explicitly marked.
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Figure 4
The needle-focusing patterns with three larger metalenses consisting of 80, 90, and 180 meta-atoms, respectively. (a) Shows the logarithm of normalized pressure intensity within the x-y plane, where the propagation lengths of 40λ, 45λ, and 90λ can be observed, respectively. (b) Shows the logarithm of pressure-intensity profile along the x axis for three metalenses, where the colored parts of the intensity curves show the high-intensity focusing regions predicted by the initial design targets.
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Figure 5
The focusing performance at different frequencies. (a) Shows the logarithm of normalized pressure intensity within the x-y plane at frequencies 0.95f₀, $f_{0}$ , and 1.05f₀, respectively. (b) Shows the logarithm of pressure-intensity profiles along the x axis at 0.95f₀, $f_{0}$ , and 1.05f₀, where the gray background marks the overlapped needle focusing region valid for a continuum of frequency, i.e., $0.95 f_{0} < f < 1.05 f_{0}$ .
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Figure 6
The configurations of the first–fifth meta-atoms in the metalens.
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