Reversal of transmission and reflection based on acoustic metagratings with integer parity design

Abstract

Phase gradient metagratings (PGMs) have provided unprecedented opportunities for wavefront manipulation. However, this approach suffers from fundamental limits on conversion efficiency; in some cases, higher order diffraction caused by the periodicity can be observed distinctly, while the working mechanism still is not fully understood, especially in refractive-type metagratings. Here we show, analytically and experimentally, a refractive-type metagrating which can enable anomalous reflection and refraction with almost unity efficiency over a wide incident range. A simple physical picture is presented to reveal the underlying diffraction mechanism. Interestingly, it is found that the anomalous transmission and reflection through higher order diffraction can be completely reversed by changing the integer parity of the PGM design, and such phenomenon is very robust. Two refractive acoustic metagratings are designed and fabricated based on this principle and the experimental results verify the theory.

Fig. 1

Concept of studied metagratings. a Schematic diagram of the proposed PGM consisting of periodically repeated supercells. b Geometric topology of the supercell composed of m groups of unit cells. The regions in gray are sound-hard materials and the regions with blue colors are gradient index materials for generating gradient phase shift along +x-direction. c Trajectories of rays propagating in two adjacent unit cells. d Sketch map of diffraction mechanism and multiple reflections effect in the jth unit cell in (c). Each unit cell can be regarded as a Fabry–Perot (FP) resonator, inside which the wave oscillates back and forth L times before reaching a resonance condition that determines the reflection or transmission. The higher order diffraction depends on the propagation number L and the number m of unit cells in a supercell

Fig. 2

Parity-dependent phenomena. a, b The equifrequency contours of the PGMs (ξ = k₀) with odd unit cells and even unit cells, respectively, where the black circles are the equifrequency contours of incident wave in air, the blue circles are the transmission contours of the n = 1 order and the solid (dashed) red circle is the transmission (reflection) contour of the n = −1 order. c, d The simulated acoustic total field patterns of the PGMs (ξ = k₀) with three cells and four unit cells, respectively. In each case, the upper (lower) plot is the case of θ_in = 30° (θ_in = −30°). All the arrows represent propagation directions. In simulations, p = h = λ₀, a = 0.9w and n_j = ρ_j

Fig. 3

The relationship between transmission/reflection and incident angle of all diffraction orders in the PGMs with ξ = k₀. a, b The PGM with m = 3. c, d The PGM with m = 4. The solid lines are analytical results, and the symbols represent numerical results

Fig. 4

Experimental setup and results. a Photograph of the fabricated samples. b Photograph of experimental setup. c The relationship between transmission/reflection (T₁, T₀ and R₋₁) and the incident angle for the designed PGM with m = 3. d, e The simulated and measured scattered pressure field patterns for incident beam with θ_in = 30° bumping on the designed PGM with m = 3, respectively. f The relationship between transmission/reflection (T₁, T₋₁, and R₀) and the incident angle for the designed PGM with m = 4. g, h The simulated and measured scattering pressure field patterns for incident beam with θ_in = 30° bumping on the designed PGM with m = 4

Fig. 5

Parity-dependent transmission and reflection and robust performance. a, b The phase distributions in the u-complex plane for m = 3 (odd) and m = 4(even), respectively. c, d The reflection (c) and transmission (d) vs. integer m in a PGM with ξ = 1.5k₀ based on coupled mode theory