scholarly journals Spectral Singularities do not Correspond to Bound States in the Continuum

10.14311/1813 ◽  
2013 ◽  
Vol 53 (3) ◽  
Author(s):  
Ali Mostafazadeh
Keyword(s):  
Bound States ◽  
Von Neumann ◽  
Spectral Singularities ◽  
Scattering States ◽  
Made In ◽  
The Continuum

We show that, contrary to a claim made in arXiv:1011.0645, the von Neumann-Winger bound states that lie in the continuum of the scattering states are fundamentally different from Naimark’s spectral singularities.

scholarly journals CASIMIR EFFECTS IN RENORMALIZABLE QUANTUM FIELD THEORIES

2002 ◽  
Vol 17 (06n07) ◽  
pp. 846-869 ◽  
Author(s):  
NOAH GRAHAM ◽  
ROBERT L. JAFFE ◽  
HERBERT WEIGEL
Keyword(s):  
Density Of States ◽  
Bound States ◽  
Phase Shifts ◽  
Feynman Diagrams ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Scattering States ◽  
Extended Field ◽  
The Continuum

We present a framework for the study of one–loop quantum corrections to extended field configurations in renormalizable quantum field theories. We work in the continuum, transforming the standard Casimir sum over modes into a sum over bound states and an integral over scattering states weighted by the density of states. We express the density of states in terms of phase shifts, allowing us to extract divergences by identifying Born approximations to the phase shifts with low order Feynman diagrams. Once isolated in Feynman diagrams, the divergences are canceled against standard counterterms. Thus regulated, the Casimir sum is highly convergent and amenable to numerical computation. Our methods have numerous applications to the theory of solitons, membranes, and quantum field theories in strong external fields or subject to boundary conditions.

scholarly journals Exact scattering and bound states solutions for novel hyperbolic potentials with inverse square singularity

2019 ◽  
Vol 34 (03) ◽  
pp. 1950020
Author(s):  
A. D. Alhaidari
Keyword(s):  
Jacobi Polynomial ◽  
Schrodinger Equation ◽  
Short Range ◽  
Bound States ◽  
Scattering States ◽  
Wilson Polynomial ◽  
Integrable Functions ◽  
Expansion Coefficients ◽  
Square Integrable Functions ◽  
The Continuum

We use the Tridiagonal Representation Approach (TRA) to obtain exact scattering and bound states solutions of the Schrödinger equation for short-range inverse-square singular hyperbolic potentials. The solutions are series of square integrable functions written in terms of the Jacobi polynomial with the Wilson polynomial as expansion coefficients. The series is finite for the discrete bound states and infinite but bounded for the continuum scattering states.

scholarly journals Bound states in the continuum and time evolution of the generalized eigenfunctions

2018 ◽  
Vol 64 (5) ◽  
pp. 464 ◽  
Author(s):  
David Lohr ◽  
Enriqueta Hernandez ◽  
Antonio Jauregui ◽  
Alfonso Mondragon
Keyword(s):  
Time Evolution ◽  
Bound States ◽  
Scattering Problem ◽  
Bound State ◽  
The Other ◽  
Von Neumann ◽  
Generalized Eigenfunctions ◽  
Jost Solutions ◽  
Type Potential ◽  
The Continuum

We study the Jost solutions for the scattering problem of a von Neumann-Wigner type potential, constructed by means of a two times iterated and completely degenerated Darboux transformation. We show that for a particular energy the unnormalizedJost solutions coalesce to give rise to a Jordan cycle of rank two. Performing a pole decomposition of the normalized Jost solutions we find the generalized eigenfunctions: one is a normalizable function corresponding to the bound state in the continuum and the other is a bounded, non-normalizable function. We obtain the time evolution of these functions as pseudo-unitary, characteristic of a pseudo-Hermitian system.

Bound states in the continuum in double-hole array perforated in a layer of photonic crystal slab

2019 ◽  
Vol 12 (12) ◽  
pp. 125002 ◽  
Author(s):  
Suxia Xie ◽  
Changzhong Xie ◽  
Song Xie ◽  
Jie Zhan ◽  
Zhijian Li ◽  
...  
Keyword(s):  
Photonic Crystal ◽  
Bound States ◽  
Hole Array ◽  
Photonic Crystal Slab ◽  
The Continuum

scholarly journals Differentiating and quantifying exosome secretion from a single cell using quasi-bound states in the continuum

Nanophotonics ◽  
2020 ◽  
Vol 9 (5) ◽  
pp. 1081-1086 ◽  
Author(s):  
Abdoulaye Ndao ◽  
Liyi Hsu ◽  
Wei Cai ◽  
Jeongho Ha ◽  
Junhee Park ◽  
...  
Keyword(s):  
Single Cell ◽  
Optical Sensors ◽  
Figure Of Merit ◽  
Bound States ◽  
Single Cell Analysis ◽  
Optical Cavity ◽  
High Sensitivity ◽  
Cell Secretion ◽  
The Continuum ◽  
Refractive Index Detection

AbstractOne of the key challenges in biology is to understand how individual cells process information and respond to perturbations. However, most of the existing single-cell analysis methods can only provide a glimpse of cell properties at specific time points and are unable to provide cell secretion and protein analysis at single-cell resolution. To address the limits of existing methods and to accelerate discoveries from single-cell studies, we propose and experimentally demonstrate a new sensor based on bound states in the continuum to quantify exosome secretion from a single cell. Our optical sensors demonstrate high-sensitivity refractive index detection. Because of the strong overlap between the medium supporting the mode and the analytes, such an optical cavity has a figure of merit of 677 and sensitivity of 440 nm/RIU. Such results facilitate technological progress for highly conducive optical sensors for different biomedical applications.

scholarly journals Plasmonic hot-electron photodetection with quasi-bound states in the continuum and guided resonances

Nanophotonics ◽  
2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Wenhao Wang ◽  
Lucas V. Besteiro ◽  
Peng Yu ◽  
Feng Lin ◽  
Alexander O. Govorov ◽  
...  
Keyword(s):  
Bound States ◽  
Structural Parameters ◽  
Hybrid Structure ◽  
Fine Tuning ◽  
Hot Electrons ◽  
Hot Electron ◽  
Perfect Absorption ◽  
High Loss ◽  
Guided Mode ◽  
The Continuum

Abstract Hot electrons generated in metallic nanostructures have shown promising perspectives for photodetection. This has prompted efforts to enhance the absorption of photons by metals. However, most strategies require fine-tuning of the geometric parameters to achieve perfect absorption, accompanied by the demanding fabrications. Here, we theoretically propose a Ag grating/TiO2 cladding hybrid structure for hot electron photodetection (HEPD) by combining quasi-bound states in the continuum (BIC) and plasmonic hot electrons. Enabled by quasi-BIC, perfect absorption can be readily achieved and it is robust against the change of several structural parameters due to the topological nature of BIC. Also, we show that the guided mode can be folded into the light cone by introducing a disturbance to become a guided resonance, which then gives rise to a narrow-band HEPD that is difficult to be achieved in the high loss gold plasmonics. Combining the quasi-BIC and the guided resonance, we also realize a multiband HEPD with near-perfect absorption. Our work suggests new routes to enhance the light-harvesting in plasmonic nanosystems.

scholarly journals Active nonlocal metasurfaces

Nanophotonics ◽  
2020 ◽  
Vol 10 (1) ◽  
pp. 655-665
Author(s):  
Stephanie C. Malek ◽  
Adam C. Overvig ◽  
Sajan Shrestha ◽  
Nanfang Yu
Keyword(s):  
Bound States ◽  
Fano Resonances ◽  
Spatial Control ◽  
Technical Challenge ◽  
Materials Engineering ◽  
Narrow Bandwidth ◽  
Wavefront Shaping ◽  
Mechanical Stretching ◽  
Proof Of Principle ◽  
The Continuum

AbstractActively tunable and reconfigurable wavefront shaping by optical metasurfaces poses a significant technical challenge often requiring unconventional materials engineering and nanofabrication. Most wavefront-shaping metasurfaces can be considered “local” in that their operation depends on the responses of individual meta-units. In contrast, “nonlocal” metasurfaces function based on the modes supported by many adjacent meta-units, resulting in sharp spectral features but typically no spatial control of the outgoing wavefront. Recently, nonlocal metasurfaces based on quasi-bound states in the continuum have been shown to produce designer wavefronts only across the narrow bandwidth of the supported Fano resonance. Here, we leverage the enhanced light-matter interactions associated with sharp Fano resonances to explore the active modulation of optical spectra and wavefronts by refractive-index tuning and mechanical stretching. We experimentally demonstrate proof-of-principle thermo-optically tuned nonlocal metasurfaces made of silicon and numerically demonstrate nonlocal metasurfaces that thermo-optically switch between distinct wavefront shapes. This meta-optics platform for thermally reconfigurable wavefront shaping requires neither unusual materials and fabrication nor active control of individual meta-units.

scholarly journals Effective Interactions of Relativistic Composite Particles in Unified Nonlinear Spinor-Field Models. I

1985 ◽  
Vol 40 (1) ◽  
pp. 14-28
Author(s):  
H. Stumpf
Keyword(s):  
Spinor Field ◽  
Bound States ◽  
Composite Particle ◽  
Composite Particles ◽  
Statistical Interpretation ◽  
Particle Spectrum ◽  
Nonlinear Spinor ◽  
Effective Interactions ◽  
Scattering States ◽  
Diagonal Part

Unified nonlinear spinor field models are selfregularizing quantum field theories in which all observable (elementary and non-elementary) particles are assumed to be bound states of fermionic preon fields. Due to their large masses the preons themselves are confined. In preceding papers a functional energy representation, the statistical interpretation and the dynamical equations were derived. In this paper the dynamics of composite particles is discussed. The composite particles are defined to be eigensolutions of the diagonal part of the energy representation. Corresponding calculations are in preparation, but in the present paper a suitable composite particle spectrum is assumed. It consists of preon-antipreon boson states and threepreon- fermion states with corresponding antifermions and contains bound states as well as preon scattering states. The state functional is expanded in terms of these composite particle states with inclusion of preon scattering states. The transformation of the functional energy representation of the spinor field into composite particle functional operators produces a hierarchy of effective interactions at the composite particle level, the leading terms of which are identical with the functional energy representation of a phenomenological boson-fermion coupling theory. This representation is valid as long as the processes are assumed to be below the energetic threshold for preon production or preon break-up reactions, respectively. From this it can be concluded that below the threshold the effective interactions of composite particles in a unified spinor field model lead to phenomenological coupling theories which depend in their properties on the bound state spectrum of the self-regularizing spinor theory.

scholarly journals Near-Field Excitation of Bound States in the Continuum in All-Dielectric Metasurfaces through a Coupled Electric/Magnetic Dipole Model

Nanomaterials ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 998
Author(s):  
Diego R. Abujetas ◽  
José A. Sánchez-Gil
Keyword(s):  
Magnetic Dipole ◽  
Density Of States ◽  
Bound States ◽  
Local Density ◽  
Near Field ◽  
Field Pattern ◽  
Local Density Of States ◽  
Optical Modes ◽  
Source Excitation ◽  
The Continuum

Resonant optical modes arising in all-dielectric metasurfaces have attracted much attention in recent years, especially when so-called bound states in the continuum (BICs) with diverging lifetimes are supported. With the aim of studying theoretically the emergence of BICs, we extend a coupled electric and magnetic dipole analytical formulation to deal with the proper metasurface Green function for the infinite lattice. Thereby, we show how to excite metasurface BICs, being able to address their near-field pattern through point-source excitation and their local density of states. We apply this formulation to fully characterize symmetry-protected BICs arising in all-dielectric metasurfaces made of Si nanospheres, revealing their near-field pattern and local density of states, and, thus, the mechanisms precluding their radiation into the continuum. This formulation provides, in turn, an insightful and fast tool to characterize BICs (and any other leaky/guided mode) near fields in all-dielectric (and also plasmonic) metasurfaces, which might be especially useful for the design of planar nanophotonic devices based on such resonant modes.

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