Frequency-Multiplexed Transmitted-Wave Manipulation with Multifunctional Acoustic Metasurfaces

Passive metasurfaces are known for their fixed and usually single-wave manipulation functionality, which limits their potential applications for diverse scenarios. To expand the functionality of the passive metasurfaces, frequency-multiplexed technology has been proposed to encode multiple operation frequencies in a single metasurface for function selection and switching. Although this technology has been extensively utilized for electromagnetic waves, there have been few studies on designing frequency-multiplexed metasurfaces for acoustic-wave manipulation. This work applies a topology optimization method based on a multiobjective genetic algorithm (GA) to develop different frequency-encoded multifunctional acoustic metasurfaces to attain acoustic focusing and anomalous wave refraction. The effectiveness of the optimized metasurfaces is validated both numerically and experimentally. Additionally, the underlying physical mechanisms of the designed frequency-multiplexed acoustic metasurfaces are systematically analyzed. This study presents high-performance frequency-multiplexed metasurfaces for acoustic-wave-front modulation and demonstrates the promising potential of the GA-based topology optimization approach in designing integrated, miniaturized multifunctional acoustic devices for real-world applications.

Figure 1

Schematic diagram of frequency-multiplexed metasurfaces: (a) frequency-multiplexed acoustic-wave focusing, and (b) frequency-multiplexed acoustic function switching.

Figure 2

Evolution process of unit cell no. 2 of a two-frequency-multiplexed acoustic focusing metasurface (the insets show the best individual at different generations, $G$).

Figure 3

Schematic diagram of the simulation model for an acoustic wave propagating through a unit cell.

Figure 4

Photographs of the acoustic test rig and the associated measurement equipment.

Figure 5

The unit cells of the optimized metasurface for two-frequency-multiplexed wave focusing and their acoustic characteristics. (a) The cross section of each unit cell (black elements represent the solid materials, white elements are the air domain). (b) The phase shift of each unit cell and the corresponding desired value. (c) The transmission coefficient of each unit cell. (d) The 3D printed test samples (arrange from no. 1 to no. 16 to form the entire metasurface sample).

Figure 6

The transmitted wave fields of normally incident plane waves through the designed metasurface for two-frequency-multiplexed wave focusing. (a) Simulated pressure and normalized intensity fields at 3000 Hz. (b) Simulated pressure and normalized intensity fields at 4000 Hz. (c) Measured sound pressure field at 3000 Hz. (d) Measured sound pressure field at 4000 Hz.

Figure 7

Acoustic performance of the two-frequency-multiplexed focusing metasurface (FWHM and SNR): (a) wave focusing at 3000 Hz; (b) wave focusing at 4000 Hz; (c) measured focusing intensity at 3000 Hz; and (d) measured focusing intensity at 4000 Hz.

Figure 8

The unit cells of the optimized metasurface for two-frequency-multiplexed function switching. (a) The cross section of the unit cells (black elements represent the solid materials, white elements are the air domain). (b) The phase shifts of the unit cells and the corresponding desired values. (c) The transmission coefficients of the unit cells. (d) The 3D printed test samples (arrange from no. 1 to no. 16 to form the entire metasurface sample).

Figure 9

The transmitted wave fields of normally incident plane waves through the designed metasurface for two-frequency-multiplexed function switching. (a) Simulated pressure and intensity fields at 3000 Hz (wave focusing). (b) Simulated pressure field at 4000 Hz (beam steering). (c) Measured sound pressure field of wave focusing at 3000 Hz. (d) Measured sound pressure field of beam steering at 4000 Hz.

Figure 10

Acoustic performance of the designed metasurface for two-frequency multiplexed function switching: (a) simulated FWHM and SNR at 3000 Hz; (b) measured wave focusing intensity at 3000 Hz; and (c) simulated far-field sound directivity at 4000 Hz.

Figure 11

Acoustic characteristics of three representative blocklike unit cells of the two-frequency-multiplexed acoustic focusing metasurface. (a) Normalized sound pressure fields and energy flux of forward (left two panels) and backward (right two panels) wave propagation. (b) Impedance spectra.

Figure 12

Acoustic characteristics of three representative labyrinthlike unit cells of the two-frequency-multiplexed acoustic focusing metasurface. (a) Normalized sound pressure fields and energy flux of forward (left two panels) and backward (right two panels) wave propagation. (b) Impedance spectra.

Figure 13

Acoustic characteristics of three representative blocklike unit cells of the two-frequency-multiplexed function switching metasurface. (a) Normalized sound pressure fields and energy flux of forward (left two panels) and backward (right two panels) wave propagation. (b) Impedance spectra.

Figure 14

Acoustic characteristics of three representative labyrinthlike unit cells of the two-frequency-multiplexed acoustic focusing metasurface. (a) Normalized sound pressure fields and energy flux of forward (left two panels) and backward (left two panels) wave propagation. (b) Impedance spectra.

Figure 15

Acoustic performance of the three-frequency-multiplexed metasurface for off-axis focusing at 2500 Hz: (a) simulated sound pressure and normalized intensity field; and (b) FWHM and SNR.

Figure 16

Acoustic performance of the three-frequency-multiplexed metasurface for off-axis focusing at 3500 Hz: (a) simulated sound pressure and normalized intensity field; and (b) FWHM and SNR.

Figure 17

Acoustic performance of the three-frequency-multiplexed metasurface for off-axis focusing at 4500 Hz: (a) simulated sound pressure and normalized intensity field; and (b) FWHM and SNR.

Figure 18

Acoustic performance of the three-frequency-multiplexed metasurface for in-line focusing at 3000 Hz: (a) simulated sound pressure and normalized intensity field; and (b) FWHM and SNR.

Figure 19

Acoustic performance of the three-frequency-multiplexed metasurface for in-line focusing at 4000 Hz: (a) simulated sound pressure and normalized intensity field; and (b) FWHM and SNR.

Figure 20

Acoustic performance of the three-frequency-multiplexed metasurface for in-line focusing at 4500 Hz: (a) simulated sound pressure and normalized intensity field; and (b) FWHM and SNR.

Figure 21

Acoustic performance of the three-frequency-multiplexed metasurface for function switching at 3000 Hz: (a) simulated sound pressure and normalized intensity field; and (b) FWHM and SNR.

Figure 22

Simulated sound pressure fields of three-frequency-multiplexed metasurface for function switching at 4500 and 6000 Hz.

Figure 23

The unit cells of the optimized metasurface for three-frequency-multiplexed off-axis wave focusing and their acoustic characteristics. (a) The cross section of each unit cell (black elements represent the solid materials, white elements are the air domain). (b) The phase shifts of the unit cells and the corresponding desired values. (c) The transmission coefficients of the unit cells.

Figure 24

The unit cells of the optimized metasurface for three-frequency-multiplexed in-line wave focusing and their acoustic characteristics. (a) The cross section of each unit cell (black elements represent the solid materials, white elements are the air domain). (b) The phase shifts of the unit cells and the corresponding desired values. (c) The transmission coefficients of the unit cells.

Figure 25

The unit cells of the optimized metasurface for three-frequency-multiplexed function switching and their acoustic characteristics. (a) The cross section of each unit cell (black elements represent the solid materials, white elements are the air domain). (b) The phase shifts of the unit cells and the corresponding desired values. (c) The transmission coefficients of the unit cells.