scholarly journals Trapped modes and reflectionless modes as eigenfunctions of the same spectral problem

2018 ◽  
Vol 474 (2213) ◽  
pp. 20180050 ◽  
Author(s):  
Anne-Sophie Bonnet-Ben Dhia ◽  
Lucas Chesnel ◽  
Vincent Pagneux
Keyword(s):  
Spectral Problem ◽  
Bound States ◽  
The Other ◽  
Trapped Modes ◽  
Perfectly Matched Layers ◽  
Complex Eigenvalues ◽  
Weak Reflection ◽  
Incident Waves ◽  
Matched Layers ◽  
The Continuum

We consider the reflection–transmission problem in a waveguide with obstacle. At certain frequencies, for some incident waves, intensity is perfectly transmitted and the reflected field decays exponentially at infinity. In this work, we show that such reflectionless modes can be characterized as eigenfunctions of an original non-self-adjoint spectral problem. To select ingoing waves on one side of the obstacle and outgoing waves on the other side, we use complex scalings (or perfectly matched layers) with imaginary parts of different signs. We prove that the real eigenvalues of the obtained spectrum correspond either to trapped modes (or bound states in the continuum) or to reflectionless modes. Interestingly, complex eigenvalues also contain useful information on weak reflection cases. When the geometry has certain symmetries, the new spectral problem enters the class of P T -symmetric problems.

scholarly journals Fourier-plane investigation of plasmonic bound states in the continuum and molecular emission coupling

Nanophotonics ◽  
2020 ◽  
Vol 9 (15) ◽  
pp. 4565-4577
Author(s):  
In Cheol Seo ◽  
Seongheon Kim ◽  
Byung Hoon Woo ◽  
Il-Sug Chung ◽  
Young Chul Jun
Keyword(s):  
White Light ◽  
Dielectric Layer ◽  
Bound States ◽  
Plasmonic Nanostructures ◽  
Light Reflection ◽  
Trapped Modes ◽  
Optical Mode ◽  
Fourier Plane ◽  
Metal Grating ◽  
The Continuum

AbstractBound states in the continuum (BICs) or trapped modes can provide an important new avenue for strong light confinement via destructive interference. Dielectric photonic structures have been extensively studied for optical BICs. However, BICs in plasmonic nanostructures have not been explored much yet. Herein, we present a thorough experimental study of plasmonic BICs via Fourier-plane spectroscopy and imaging. Optical mode dispersion in a metal grating covered by a dielectric layer is directly measured in an angle-resolved white light reflection spectrum. Two dielectric layer thicknesses are considered. Both plasmonic and photonics modes are supported in the visible range using a thicker dielectric film; hence, either hybrid or purely plasmonic BICs can be formed. With a thinner dielectric layer, only plasmonic modes are strongly excited and purely plasmonic BICs appear. Our measurements exhibit all features expected for BICs, including a substantial increase in the Q factor. We also demonstrate that the BIC position can be switched from one optical mode branch to the other by tuning a metal grating parameter. Moreover, by mixing luminescent dyes in a dielectric layer, light emission coupling into BICs is investigated. We find that the photoluminescence peak disappears at the BIC condition, which is attributed to the trapping of molecular emission at plasmonic BICs. Therefore, both white light reflection and dye emission measurements in the Fourier plane clearly indicate the formation of trapped modes in plasmonic nanostructures. Our observation implies that plasmonic BICs can enable a highly effective light trapping device despite the simple structure of the device geometry. Plasmonic supercavity design based on the BIC concept may provide many interesting future opportunities for nanolasers, optical sensing, and nonlinear enhancement.

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.

C. The Continuous Spectrum of Pulsating Variable Stars

1967 ◽  
Vol 28 ◽  
pp. 177-206
Author(s):  
J. B. Oke ◽  
C. A. Whitney
Keyword(s):  
Continuous Spectrum ◽  
Variable Stars ◽  
Velocity Fields ◽  
The Other ◽  
Line Spectrum ◽  
Direct Information ◽  
Thermodynamic Structure ◽  
Diagnostic Interpretation ◽  
Pulsating Variable Stars ◽  
The Continuum

Pecker:The topic to be considered today is the continuous spectrum of certain stars, whose variability we attribute to a pulsation of some part of their structure. Obviously, this continuous spectrum provides a test of the pulsation theory to the extent that the continuum is completely and accurately observed and that we can analyse it to infer the structure of the star producing it. The continuum is one of the two possible spectral observations; the other is the line spectrum. It is obvious that from studies of the continuum alone, we obtain no direct information on the velocity fields in the star. We obtain information only on the thermodynamic structure of the photospheric layers of these stars–the photospheric layers being defined as those from which the observed continuum directly arises. So the problems arising in a study of the continuum are of two general kinds: completeness of observation, and adequacy of diagnostic interpretation. I will make a few comments on these, then turn the meeting over to Oke and Whitney.

The Continuum of Conscientiousness: The Antagonistic Interests among Obsessive and Antisocial Personalities

2014 ◽  
Vol 45 (2) ◽  
pp. 167-178 ◽  
Author(s):  
Steven C. Hertler
Keyword(s):  
Personality Disorder ◽  
Evolutionary Theory ◽  
Antisocial Personality Disorder ◽  
The Other ◽  
Antisocial Personality ◽  
Obsessive Compulsive ◽  
Demographic Differences ◽  
Other Hand ◽  
The Continuum

Abstract The five factor trait of conscientiousnessis a supertrait, denoting on one hand a pattern of excessive labor, rigidity, orderliness and compulsivity,and on the other hand a pattern of strict rectitude, scrupulosity, dutifulness and morality. In both respects the obsessive-compulsive personality is conscientious; indeed, it has been labeled a disorder of extreme conscientiousness (Widiger et al., 2009). Antisocial personality disorder, in the present paper, is described as occupying the opposite end of the conscientiousness continuum. The antisocial is impulsive rather than compulsive, illicit rather than licit, and furtive rather than forthright.After clinically comparing the obsessive and antisocial personalities, the present paper invokes evolutionary theory to explain their resultant behavioral, ideological, political and demographic differences.

On Commutation Properties of the Composition Relation of Convergent and Divergent Permutations (Part I)

2014 ◽  
Vol 58 (1) ◽  
pp. 13-22
Author(s):  
Roman Wituła ◽  
Edyta Hetmaniok ◽  
Damian Słota
Keyword(s):  
Finite Order ◽  
Convergent Series ◽  
The Other ◽  
Other Hand ◽  
The Family ◽  
Composition Relation ◽  
The Continuum

Abstract In the paper we present the selected properties of composition relation of the convergent and divergent permutations connected with commutation. We note that a permutation on ℕ is called the convergent permutation if for each convergent series ∑an of real terms, the p-rearranged series ∑ap(n) is also convergent. All the other permutations on ℕ are called the divergent permutations. We have proven, among others, that, for many permutations p on ℕ, the family of divergent permutations q on ℕ commuting with p possesses cardinality of the continuum. For example, the permutations p on ℕ having finite order possess this property. On the other hand, an example of a convergent permutation which commutes only with some convergent permutations is also presented.

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.

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