Experimental Demonstration of an Acoustic Asymmetric Diffraction Grating Based on Passive Parity-Time-Symmetric Medium

A passive parity-time (PT) symmetric medium provides a feasible scheme to experimentally investigate non-Hermitian systems. We experimentally demonstrate an acoustic asymmetric diffraction grating based on a designed passive PT-symmetric medium. The proposed passive PT-symmetric medium is composed of additional cavities and leaked holes. By skillfully combining these two unit cells, the composite unit cell can simultaneously modulate the real and imaginary parts of the refractive index. When the modulation amplitudes of the real and imaginary parts are equal, asymmetric diffraction is observed in both simulated and experimental results at an exceptional point. Compared to the previous design method of a passive PT-symmetric medium, the proposed scheme could prevent the influence of interferential diffraction beams and enhance the diffraction ability with more compact modulation. In addition, the designed metamaterial structure provides a practical way to construct passive PT-symmetric acoustic potential and opens alternative possibilities for further investigation of acoustic wave control in non-Hermitian systems.

Figure 1

Schematic diagrams of PT-symmetric potentials and model of the AADG. (a) Evolution of PT-symmetric potential. The red (blue) curves denote the real (imaginary) part of the modulation. The top, middle, and bottom panels schematically illustrate the modulation of the exact PT-symmetric potential, the existing popular passive PT-symmetric potential with doubled period, and the revised passive PT-symmetric potential with unchanged period, respectively. (b) A schematic model of the AADG based on the revised passive PT-symmetric medium. Diffractions of incident wave with negative (positive) incident angle are shown in the upper (lower) panel, whose arrows represent an incident wave and corresponding diffracted waves.

Figure 2

Energy intensities of first-order diffractive beams with oblique incident waves at Bragg angles. (a) Diffraction intensities of the negative first-order and positive first-order diffractions with different modulation ratios. (b) Diffraction intensity ratio between the negative first-order diffraction and positive first-order diffraction with different modulation ratios.

Figure 3

Relationships between the effective refractive indices and the geometry parameters. Insets are the sectional views of three modulators. (a) The real refractive index can be modulated by adjusting the heights of additional cavities. The adopted height is $h_1=9.0\mathrm{mm}$ when the side length of each cavity is fixed as 7.6 mm. (b) The imaginary refractive index can be modulated by adjusting the radii of leaked holes. The adopted radius is $r_1=1.7\mathrm{mm}$. (c) Additional cavities and leaked holes are combined together to modulate the real and imaginary parts simultaneously. The adopted height is $h_2=9.0\mathrm{mm}$ as the side length is fixed as 8.6 mm and the radius is $r_2=1.5\mathrm{mm}$. (d) Experimental setup. Ten sample pieces are mounted on the top plate and the enlarged sectional view of the configuration is shown in the upper right inset. Two sample pieces fabricated by the three-dimensional (3D) printing technique are shown in the lower right inset. Each piece contains three kinds of modulators side by side. Ten periodical units are used in the z direction and the thickness of the grating in the z direction is 10 cm.

Figure 4

Asymmetric diffraction of the revised PT-symmetric acoustic grating at 3.1 kHz. The simulated sound pressure fields in the whole 2D waveguide: (a) The positive first-order diffraction is suppressed completely. (c) The negative first-order diffraction can be obviously observed. Corresponding enlarged views of simulated (S-I and S-II) and experimental (E-I and E-II) sound pressure fields are shown in (b),(d). Remarkable contrast of different incident angles can be observed in both simulated and measured results.

Figure 5

Asymmetric diffraction phenomenon in a wide frequency range. (a) Measured sound pressure fields of diffracted waves at 3.0, 3.2, and 3.3 kHz. The positive first-order diffractions and negative first-order diffractions are shown in the left panel and right panel, respectively. The sound pressure fields are normalized separately in different frequencies. (b) The simulated diffraction intensity contrast under the same conditions as the experimental configuration. (c) Corresponding intensity bars of measured sound fields with different frequencies.