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1. Non-Hermitian skin effect in two dimensional continuous systems

   https://doi.org/10.1088/1402-4896/aca43b  

   Yuce, C; Ramezani, H (December 2022, Physica Scripta)

   Abstract An extensive number of the eigenstates can become exponentially localized at one boundary of nonreciprocal non-Hermitian systems. This effect is known as the non-Hermitian skin effect and has been studied mostly in tight-binding lattices. To extend the skin effect to continues systems beyond 1D, we introduce a quadratic imaginary vector potential in the continuous two dimensional Schrödinger equation. We find that inseparable eigenfunctions for separable nonreciprocal Hamiltonians appear under infinite boundary conditions. Introducing boundaries destroy them and hence they can only be used as quasi-stationary states in practice. We show that all eigenstates can be clustered at the point where the imaginary vector potential is minimum in a confined system. 

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2. Non-reciprocal acoustic transmission through a dissipative phononic crystal with asymmetric scatterers (Conference Presentation)

   https://doi.org/10.1117/12.2295997  

   Krokhin, Arkadii; Neogi, Arup; Walker, Ezekiel; Bozhko, Andrey; Kundu, Tribikram (April 2018, Proceedings Volume 10600, Health Monitoring of Structural and Biological Systems XII; 1060026 (2018) https://doi.org/10.1117/12.2295997)

   The existing concepts of non-reciprocity in propagation of acoustic or elastic waves are based either on nonlinear effects, or on local circulation of linear elastic fluid that leads to red or blue Doppler shift, depending on the direction of sound wave. The same concepts exist for electromagnetic non-reciprocity, where external magnetic field may produce the effect similar to local rotation of the medium. These two concepts originate from two known methods of breaking a time-reversal symmetry (T-symmetry), that is necessary for observation of nonreciprocal wave propagation. Both concepts require additional electrical or mechanical devices to be installed with their own power sources. Here we propose to explore viscosity of fluid as a natural factor of the T-symmetry breaking through energy dissipation. We report experimental observation of the nonreciprocal transmission of ultrasound through a water-submerged phononic crystals consisting of several layers of aluminum rods arranged in a square lattice. While viscous losses break the T-symmetry, making the wave propagation thermodynamically irreversible, the transmission remains reciprocal if the scatterers are symmetrical. To generate different energy losses for opposite directions of propagation, the P-symmetry of the crystal is broken by using asymmetric scatterers. Due to asymmetry, two sound waves propagating in the opposite directions produce different distributions of velocity and pressure that leads to different local absorption. Dissipation of acoustic energy occurs mostly near the surface of the scatterers and it strongly depends on surface roughnesses. Using two phononic crystal with smooth and rough aluminum rods we demonstrate low (2-5 dB) and high (10-15 dB) level of non-reciprocity within a wide range of frequencies, 300-600 kHz. Experimental results are in agreement with numerical simulations based on the Navier-Stokes equation. This nonreciprocal linear device is very cheap, robust and does not require energy source. 

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3. A class of stable nonlinear non-Hermitian skin modes

   https://doi.org/10.1088/1402-4896/ad91f0  

   Ghaemi-Dizicheh, Hamed (November 2024, Physica Scripta)

   The non-Hermitian skin effect (NHSE) is a well-known phenomenon in open topological systems that causes a large number of eigenstates to become localized at the boundary. Although many aspects of its theory have been investigated in linear systems, this phenomenon remains novel in nonlinear models. In the first step of this paper, we look at the conditions for the presence of quasi-skin modes in a semi-infinite, one-dimensional, nonlinear, nonreciprocal lattice. In the following phase, we explore the survival time of the quasi-skin mode in a finite nonlinear lattice with open edges. We study the dependency of the survival time on the system’s parameters and demonstrate how the nonreciprocity of the system affects the survival time. This study introduces a method for achieving a stable localized state in a nonlinear finite lattice. 

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4. Acoustic resonances in non-Hermitian open systems

   https://doi.org/10.1038/s42254-023-00659-z  

   Huang, Lujun; Huang, Sibo; Shen, Chen; Yves, Simon; Pilipchuk, Artem S.; Ni, Xiang; Kim, Seunghwi; Chiang, Yan Kei; Powell, David A.; Zhu, Jie; et al (January 2024, Nature Reviews Physics)

   Acoustic resonances in open systems, which are usually associated with resonant modes characterized by complex eigenfrequencies, play a fundamental role in manipulating acoustic wave radiation and propagation. Notably, they are accompanied by considerable field enhancement, boosting interactions between waves and matter, and leading to various exciting applications. In the past two decades, acoustic metamaterials have enabled a high degree of control over tailoring acoustic resonances over a range of frequencies. Here, we provide an overview of recent advances in the area of acoustic resonances in non-Hermitian open systems, including Helmholtz resonators, metamaterials and metasurfaces, and discuss their applications in various acoustic devices, including sound absorbers, acoustic sources, vortex beam generation and imaging. We also discuss bound states in the continuum and their applications in boosting acoustic wave–matter interactions, active phononics and non-Hermitian acoustic resonances, including phononic topological insulators and the acoustic skin effect. 

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5. Wave redirection, localization, and non-reciprocity in a dissipative nonlinear lattice by macroscopic Landau–Zener tunneling: Experimental results

   https://doi.org/10.1063/5.0047806  

   Kanj, A.; Wang, C.; Mojahed, A.; Vakakis, A.; Tawfick, S. (June 2021, AIP Advances)

   Nonlinear lattices and the nonlinear acoustics they support have a broad impact on shock and vibration mitigation, sound isolation, and acoustic logic devices. In this work, we experimentally study wave redirection, localization, and non-reciprocity in an asymmetric network of two nonlinear lattices with weak linear inter-lattice coupling. We report on the design, fabrication, and system identification of coupled lattices with essentially nonlinear next-neighbor intra-lattice coupling and on their unusual nonlinear acoustics. By weakly coupling the lattices and introducing structural disorder in one of them, we experimentally prove the realization of irreversible breather redirection between lattices governed by a macroscopic analog of the quantum Landau–Zener tunneling effect. In the experiments performed, the input energy is applied by impulse (broadband) excitation, and the resulting acoustical mechanism for wave redirection is in the form of propagating breathers, that is, localized oscillating wave packets formed by the synergy of nonlinearity and dispersion. Moreover, we study the non-reciprocal acoustics of the experimental lattice system by applying separate impulses at each of its four terminals and investigate the tunability with the energy of the resulting acoustic non-reciprocity by systematically varying the impulse intensity. The reported experimental results show that the weakly coupled, disordered, and nonlinear lattice system has wave tailoring properties that are tunable with energy. Altogether, the experimental results agree well with theoretical predictions reported in a companion work based on reduced-order numerical models and prove the efficacy of the system for applications, providing a path for applying these advanced concepts in future structures and devices. 

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