Related papers: Level Repulsion and Band Sorting in Phononic Cryst…
Level repulsion is associated with exceptional points which are square root singularities of the energies as functions of a (complex) interaction parameter. This is also valid for resonance state energies. Using this concept it is argued…
In many physical systems it is important to be aware of the crossings and avoided crossings which occur when eigenvalues of a physical observable are varied using an external parameter. We have discovered a powerful algebraic method of…
Avoided level crossings are associated with exceptional points which are the singularities of the spectrum and eigenfunctions, when they are considered as functions of a coupling parameter. It is shown that the wave function of {\it one}…
We systematically engineer a series of square and rectangular phononic crystals to create experimental realisations of complex topological phononic circuits. The exotic topological transport observed is wholly reliant upon the underlying…
The refraction properties of phononic crystals are revealed by examining the anti-plane shear waves in doubly periodic elastic composites with unit cells containing rectangular and/or elliptical inclusions. The band-structure, group…
This study explores exceptional points (EPs) in photonic crystals (PhCs) and introduces a novel method for their single-shot observation. Exceptional points are spectral singularities found in non-Hermitian systems, such as leaky PhC slabs.…
This work theoretically and experimentally reports the evanescent connections between propagating bands in periodic acoustic materials. The complex band structures obtained by solving for the $k(\omega)$ problem reveal a complete…
We propose an exceptional-point (EP) framework for black-hole ringdown beyond the standard quasinormal-mode (QNM) paradigm. It provides a first-principles characterization of the resonance associated with avoided crossings near EPs, an…
The spectra of, e.g. open quantum systems are typically given as the superposition of resonances with a Lorentzian line shape, where each resonance is related to a simple pole in the complex energy domain. However, at exceptional points two…
The complex band structures calculated using the Extended Plane Wave Expansion (EPWE) reveal the presence of evanescent modes in periodic systems, never predicted by the classical \omega(\vec{k}) methods, providing novel interpretations of…
Phononic crystals enable precise manipulation of elastic wave propagation through engineered bandgaps; however, designing defect states within these bandgaps for frequency-selective applications remains a significant challenge. Existing…
Many novel properties of non-Hermitian systems are found at or near the exceptional points-branch points of complex energy surfaces at which eigenvalues and eigenvectors coalesce. In particular, higher-order exceptional points can result in…
Dispersion relations govern wave behaviors, and tailoring them is a grand challenge in wave manipulation. We demonstrate inverse design of phononic dispersion using non-local interactions on one-dimensional spring-mass chains. For both…
In this paper gradient based topology optimization (TO) is used to discover 3-D phononic structures that exhibit ultra-wide normalized all-angle all-mode band gaps. The challenging computational task of repeated 3-D phononic band-structure…
In a recent publication [Phys. Rev. A 79, 065602 (2009)] it was shown that an avoided-crossing resonance can be defined in different ways, according to level-structural or dynamical aspects, which do not coincide in general. Here a simple…
Calculations of the photonic band structure, transmission coefficients, and quality factors of various two-dimensional, periodic and aperiodic, dielectric photonic crystals by using the finite element method (FEM) are reported. The…
Ideal Weyl points, which are related by symmetry and thus reside at the same frequency, could promote the deep development and utilization of the Weyl physics. Although the ideal type-I Weyl points have been achieved in photonic crystals,…
Super-resolution is a fundamental task in imaging, where the goal is to extract fine-grained structure from coarse-grained measurements. Here we are interested in a popular mathematical abstraction of this problem that has been widely…
We examine structural and dynamical properties of quantum resonances associated with an avoided crossing and identify the parameter shifts where these properties attain maximal or extreme values, first at a general level, and then for a…
Photonic crystals (PhCs) are periodic dielectric structures that exhibit unique electromagnetic properties, such as the creation of band gaps where electromagnetic wave propagation is inhibited. Accurately predicting dispersion relations,…