Related papers: Edge modes in subwavelength resonators in one dime…
We study the skin effect in a one-dimensional system of finitely many subwavelength resonators with a non-Hermitian imaginary gauge potential. Using Toeplitz matrix theory, we prove the condensation of bulk eigenmodes at one of the edges of…
Topological phonon polaritons (TPhPs) are highly protected and localized edge modes that are capable of achieving a strong confinement of electromagnetic waves and immune to impurities and disorder. Here we realize TPhPs by constructing…
The interplay between topological localization and non-Hermiticity localization in non-Hermitian crystal systems results in a diversity of shapes of topological edge modes (EMs), offering opportunities to manipulate these modes for…
We survey functional analytic methods for studying subwavelength resonator systems. In particular, rigorous discrete approximations of Helmholtz scattering problems are derived in an asymptotic subwavelength regime. This is achieved by…
Resonant electromagnetic modes are analyzed inside a dielectric cavity of equilateral triangular cross section and refractive index n, surrounded by a uniform medium of refractive index n'. The field confinement is determined only under the…
In the presence of loss and gain, the coupled mode equation on describing the mode hybridization of various waveguides or cavities, or cavities coupled to waveguides becomes intrinsically non-Hermitian. In such non-Hermitian waveguides, the…
We develop the effective non-Hermitian Hamiltonian approach for open systems with Neumann boundary conditions. The approach can be used for calculating the scattering matrix and the scattering function in open resonator-waveguide systems.…
One-dimensional structures of non-Hermitian plasmonic metallic nanospheres are studied in this paper. For a single sphere, solving Maxwell's equations results in quasi-stationary eigenmodes with complex quantized frequencies. Coupled mode…
The bulk-boundary correspondence predicts the existence of boundary modes localized at the edges of topologically nontrivial systems. The wavefunctions of hermitian boundary modes can be obtained as the eigenmodes of a modified Jackiw-Rebbi…
We prove the possibility of achieving unidirectional edge modes in time-modulated supercell structures. Such finite structures consist of two trimers repeated periodically. Because of their symmetry, they admit degenerate edge eigenspaces.…
We study the asymptotic distribution of the eigenvalues of random Hermitian periodic band matrices, focusing on the spectral edges. The eigenvalues close to the edges converge in distribution to the Airy point process if (and only if) the…
The eigenvector-eigenvalue identity relates the eigenvectors of a Hermitian matrix to its eigenvalues and the eigenvalues of its principal submatrices in which the jth row and column have been removed. We show that one-dimensional arrays of…
In a lossless periodic structure, a bound state in the continuum (BIC) is characterized by a real frequency and a real Bloch wavevector for which there exist waves propagating to or from infinity in the surrounding media. For applications,…
We use multi-band SSH models to demonstrate a prescription for calculating the correct Zak phase and winding number of multi-band systems. We verify our prescription by comparing the resultant winding number of a four-band SSH model with…
As energy dissipation and gain are ubiquitous in the real world, such phenomena demand the generalization of Hermitian methods such as the analysis of topological properties for non-Hermitian systems. However, as non-Hermitian systems…
We present a systematic micromagnetic study of standing spin-wave modes in infinitely long Permalloy strips with rectangular cross-section. Using a finite-element dynamic-matrix method, we first calculate the eigenfrequencies and the…
A non-Hermitian system can exhibit extensive sensitivity of its complex energy spectrum to the imposed boundary conditions, which is beyond any known phenomenon from Hermitian systems. In addition to topologically protected boundary modes,…
One dimensional topological insulators are characterized by edge states with exponentially small energies. According to one generalization of topological phases to non-Hermitian systems, a finite system in a non-trivial topological phase…
In this paper, we establish an effective edge theory to characterize non-Hermitian edge-skin modes in higher dimensions. We begin by proposing a bulk projection criterion to straightforwardly identify the localized edges of skin modes.…
In a finite one-dimensional non-Hermitian system, the number of zero modes does not necessarily reflect the topology of the system. This is known as the breakdown of the bulk-boundary correspondence and has led to misconceptions about the…