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(a) Reduced frequencies for the first (blue) and second (red) super cell bands of the Hermitian system. (b,c) Real and imaginary parts of the frequencies for the first and second super cell bands, respectively. The dark gray regions indicate the merged bands.
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We present a two-dimensional (2D) parity-time-symmetric (PT-symmetry) phononic crystals (PCs) with balanced gain and loss medium. Using the super cell method of rectangular lattice, we exhibit the thresholdless spontaneous PT-symmetry breaking in the band structure. The numerical results show that the asymmetric scattering properties obviously occu...
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... provide a vivid illustration of the degenerate phenomenon, the 3D dispersion surface for the first and second bands are plotted. The band structure for the super cell of the underlying Hermitian acoustic system (α = 0) is shown in Fig. 2(a). We observe a degenerate contour of frequency eigenvalues along the line of k x = 0.5π/a in the band structure because of the fold features in the super cell system. When the gain and loss are added to form a non-Hermitian system with a coefficient α = 0.25, Fig. 2(b) shows that the degenerate contours at the band crossing ...
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... the super cell of the underlying Hermitian acoustic system (α = 0) is shown in Fig. 2(a). We observe a degenerate contour of frequency eigenvalues along the line of k x = 0.5π/a in the band structure because of the fold features in the super cell system. When the gain and loss are added to form a non-Hermitian system with a coefficient α = 0.25, Fig. 2(b) shows that the degenerate contours at the band crossing instantaneously experience thresholdless spontaneous PT-symmetry breaking. A particularly interesting phenomenon occurs, where the folded bands merge together outwards from the primary degenerate contour, and a new contour appears at the boundary between the merged and the ...
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... low-symmetry points. Due to the extra spatial degree of freedom, the degenerate points in the 1D structure evolve into an irregular contour in the 2D system. A comparison of data values also shows that the bands nearly flatten in the x direction perpendicular to the degenerate contour after they merge. The imaginary part, as presented in Fig. 2(c), contains identical degenerate contour and forms complex conjugate pairs of frequencies with the real ...
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We present a tunable phononic crystal which undergoes a phase transition from mechanically insulating to mechanically transmissive (metallic). Specifically, in our simulations for a phononic lattice under biaxial tension (σ_{xx} = σ_{yy} = 0.01 N/m), we find a bandgap in the range of 48.8-56.4 MHz, which we can close by increasing the degree of ten...
Citations
... With the rapid development of acoustic metamaterials [12][13][14][15][16][17][18][19][20] in recent years, it seems possible to solve this problem. Due to their unique microstructure, acoustic metamaterials can realize some interesting unnatural phenomena, such as negative refraction/density [21][22][23][24][25], acoustic invisible [26][27][28], acoustic focusing [29][30][31], and directional sound propagation [32][33][34]. By using thin membranes [35], curled-space channels [36][37][38] and embedded apertures [39][40][41] to control the sound waves, the thin structure can achieve perfect low-frequency sound absorption. ...
... In recent years, non-Hermitian physics has attracted great attention owing to its rich physical significances and various practical applications [1][2][3][4]. Exceptional point (EP) is a unique feature for non-Hermitian systems, which has become a hot topic in photonics [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19], mechanics [20][21][22][23][24][25][26], and acoustics [27][28][29][30][31][32][33][34][35][36][37][38][39] owing to its great potential in energy transport. In acoustics, based on parity-time symmetric systems [27][28][29][30][31][32], researchers have realized EP by introducing balanced gain and loss which can be obtained by a pair of electro-acoustic resonators loaded with specifically tailored circuits [30] and by a composite structure composed of a leaky waveguide and two speaker arrays [31]. ...
... Exceptional point (EP) is a unique feature for non-Hermitian systems, which has become a hot topic in photonics [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19], mechanics [20][21][22][23][24][25][26], and acoustics [27][28][29][30][31][32][33][34][35][36][37][38][39] owing to its great potential in energy transport. In acoustics, based on parity-time symmetric systems [27][28][29][30][31][32], researchers have realized EP by introducing balanced gain and loss which can be obtained by a pair of electro-acoustic resonators loaded with specifically tailored circuits [30] and by a composite structure composed of a leaky waveguide and two speaker arrays [31]. Additionally, by inserting sound-absorbing sponges in surface holes of coupled cavities, EP can also be obtained in non-Hermitian structures with asymmetric losses [33,34]. ...
... Additionally, by inserting sound-absorbing sponges in surface holes of coupled cavities, EP can also be obtained in non-Hermitian structures with asymmetric losses [33,34]. Based on exotic characteristics of EPs [29,31,[35][36][37], several advanced acoustic devices have been proposed, such as sound absorber [27], focusing lens [28,32], invisible acoustic sensor [30], and acoustic mirror [38]. ...
... A parity-time (P T ) symmetric system is a physical system that is invariant under the combined reversal of the space and time coordinates. Having its roots in quantum physics [1], the principle of P T -symmetry has recently found many applications in classical wave propagation and scattering problems in photonic structures [2][3][4], phononic crystals [5][6][7] and acoustic metamaterials [8][9][10]. Motivations for designing P T -symmetric materials are the exotic properties that can be achieved, such as unidirectional optical wave propagation [11], negative refraction [10] and acoustic cloaking [8,9]. ...
... Operator matrix A in Equations (1) and (2) obeys, for all wave phenomena of Table 1, the following symmetry properties A t N = −NA, (7) A † K = −KĀ, (8) A * J = JĀ, (9) with ...
Inspired by recent developments in wave propagation and scattering experiments with parity-time (PT) symmetric materials, we discuss reciprocity and representation theorems for 3D inhomogeneous PT-symmetric materials and indicate some applications. We start with a unified matrix-vector wave equation which accounts for acoustic, quantum-mechanical, electromagnetic, elastodynamic, poroelastodynamic, piezoelectric and seismoelectric waves. Based on the symmetry properties of the operator matrix in this equation, we derive unified reciprocity theorems for wave fields in 3D arbitrary inhomogeneous media and 3D inhomogeneous media with PT-symmetry. These theorems form the basis for deriving unified wave field representations and relations between reflection and transmission responses in such media. Among the potential applications are interferometric Green’s matrix retrieval and Marchenko-type Green’s matrix retrieval in PT-symmetric materials.
... A parity-time (P T ) symmetric system is a physical system that is invariant under the combined reversal of the space and time coordinates. Having its roots in quantum physics [1], the principle of P T -symmetry has recently found many applications in classical wave propagation and scattering problems in photonic structures [2][3][4], phononic crystals [5][6][7] and acoustic metamaterials [8][9][10]. Motivations for designing P T -symmetric materials are the exotic properties that can be achieved, such as unidirectional optical wave propagation [11], negative refraction [10] and acoustic cloaking [8,9]. ...
... Operator matrix A in equations (1) and (2) obeys, for all wave phenomena of Table 1, the following symmetry properties A t N = −NA, (7) A † K = −KĀ, (8) A * J = JĀ, (9) with ...
Inspired by recent developments in wave propagation and scattering experiments with parity-time (PT) symmetric materials, we discuss reciprocity and representation theorems for 3D inhomogeneous PT-symmetric materials and indicate some applications. We start with a unified matrix-vector wave equation which accounts for acoustic, quantum-mechanical, electromagnetic, elastodynamic, poroelastodynamic, piezoelectric and seismoelectric waves. Based on the symmetry properties of the operator matrix in this equation, we derive unified reciprocity theorems for wave fields in 3D arbitrary inhomogeneous media and 3D inhomogeneous media with PT-symmetry. These theorems form the basis for deriving unified wave field representations and relations between reflection and transmission responses in such media. Among the potential applications are interferometric Green’s matrix retrieval and Marchenko-type Green’s matrix retrieval in PT-symmetric materials.
... Generally, the positive imaginary part indicates the loss in material, while the negative imaginary part indicates the gain. [25][26][27][28][29] The most important characteristic of a PT-symmetric system is the PT transition stemming from the complex eigenvalues. A PT-transition refers to a phase transition from a PT-exact phase to a PT-broken phase, and the critical points between these two phases are called the exceptional points (EPs). ...
... 24 In acoustics, Zhu et al. achieved acoustic cloak in the PT-symmetric acoustic system, 25 Liu et al. achieved the second-order topological insulator through a PT-symmetric system, 26 Zhao et al. obtained perfect sensing in the PT-symmetric acoustic lattice, 27 and Yang et al. exploited the PT-symmetry induced self-collimation effect and acoustic flat focusing. 28,29 However, most previous studies were not in the scope of the sub-wavelength range; moreover, there has been less analytical analysis of the dispersion relation caused by PT-symmetry breaking in the subwavelength range. ...
In this study, a spring–mass physical model is proposed to study the complex band structure of a one-dimensional parity-time (PT)-symmetric local resonant phononic crystal. By solving the kinetic equations, the analytical solutions of the dispersion relation and effective mass are obtained. As is known, the infinite effective mass would appear at the resonant frequency in a Hermitian system without any gain or loss. Once the balanced gain and loss are added to form a PT-symmetric system, the infinite effective mass would become finite, and the exceptional points can be observed in the subwavelength realm. With the increase in gain and loss, exceptional points would coalesce and form a higher order one. The numerical simulations in a practical structure agree well with the analytical analysis. In addition, the simulated transmission/reflection spectrum and field distribution clearly demonstrate the anisotropic transmission resonances. Our investigation enriches the physical connotation of local resonant phononic crystals in non-Hermitian systems.
... Non-Hermitian Hamiltonians with PT symmetry have been stimulated experimentally in open systems with balanced gain and loss [16][17][18][19][20][21]. Representative examples are optical waveguides [22][23][24][25][26], cold-atomic systems [27], coupled resonators [28], acoustic waves [29,30], and circuit quantum electrodynamics (QED) [31]. This progress improves the probability of realization of theoretical proposals and schemes. ...
We theoretically investigate the band structure of the parity-time ( ${\cal P}{\cal T}$ P T )-symmetric non-Hermitian bilayer honeycomb photonic lattice by considering the co-existence of onsite energy detuning and ${\cal P}{\cal T}$ P T -symmetric imaginary potentials. It is found that ${\cal P}{\cal T}$ P T symmetry causes the system’s energy spectra to display salient features, which include various energy-band degeneracies and deformation of the band structure in the vicinity of the Dirac point. Also, the ${\cal P}{\cal T}$ P T -symmetry breaking can be modulated by introducing strain to the system. The findings in this work can help in understanding the band structures of ${\cal P}{\cal T}$ P T -symmetric bilayer honeycomb photonic-lattice systems.
Acoustic metasurfaces are at the frontier of acoustic functional material research owing to their advanced capabilities of wave manipulation at an acoustically vanishing size. Despite significant progress in the last decade, conventional acoustic metasurfaces are still fundamentally limited by their underlying physics and design principles. First, conventional metasurfaces assume that unit cells are decoupled and therefore treat them individually during the design process. Owing to diffraction, however, the non-locality of the wave field could strongly affect the efficiency and even alter the behavior of acoustic metasurfaces. Additionally, conventional acoustic metasurfaces operate by modulating the phase and are typically treated as lossless systems. Due to the narrow regions in acoustic metasurfaces' subwavelength unit cells, however, losses are naturally present and could compromise the performance of acoustic metasurfaces. While the conventional wisdom is to minimize these effects, a counter-intuitive way of thinking has emerged, which is to harness the non-locality as well as loss for enhanced acoustic metasurface functionality. This has led to a new generation of acoustic metasurface design paradigm that is empowered by non-locality and non-Hermicity, providing new routes for controlling sound using the acoustic version of 2D materials.
This review details the progress of non-local and non-Hermitian acoustic metasurfaces, providing an overview of the recent acoustic metasurface designs and discussing the critical role of non-locality and loss in acoustic metasurfaces. We further outline the synergy between non-locality and non-Hermiticity, and delineate the potential of using non-local and non-Hermitian acoustic metasurfaces as a new platform for investigating exceptional points (EPs), the hallmark of non-Hermitian physics. Finally, the current challenges and future outlook for this burgeoning field are discussed.
In this paper, we perform the theoretical investigation of the band structure of the non-Hermitian zigzag-edged ribbon of the bilayer photonic graphene by considering the presence of PT-symmetric imaginary potentials. It is found that such potentials cause the energies of edge states to display prominent features, manifested as their extensive distribution in the parameter region and the modification of topological properties. When interlayer level detuning is incorporated, PT symmetry is destroyed, but two new pairs of edge states have an opportunity to arise that can induce complex Dirac cones. All these results imply that PT-symmetric imaginary potentials are effective mechanisms to modify the band structure properties of the zigzag-edged ribbon of bilayer photonic graphene.
By introducing the \(\mathcal PT\)-symmetric complex potentials, we investigate the properties of the band structure of the bowtie lattice with \(\mathcal PT\) symmetry. It is found that the complex potentials directly lead to the enhancement of the energy-band overlap, including the occurrence of the threefold degeneracy. Meanwhile, the flat band is destroyed gradually and the \(\mathcal PT\)-symmetry breaking occurs. When the two-dimensional lattice is cut into one-dimensional ribbons, the effect of the complex potentials is tightly dependent on the types of the ribbon edges, i.e., zigzag or armchair. For the case of armchair ribbon, the roles of the \(\mathcal PT\)-symmetric potentials are more dependent on its width. We believe that this work is useful for understanding the band structures of the \(\mathcal PT\)-symmetric bowtie-lattice systems.
