scholarly journals Coexistence of a new type of bound state in the continuum and a lasing threshold mode induced by PT symmetry

2020 ◽  
Vol 6 (34) ◽  
pp. eabc1160
Author(s):  
Qianju Song ◽  
Jiashun Hu ◽  
Shiwei Dai ◽  
Chunxiong Zheng ◽  
Dezhuan Han ◽  
...  
Keyword(s):  
Bound States ◽  
External Source ◽  
Bound State ◽  
Pt Symmetry ◽  
Lasing Threshold ◽  
Symmetric Perturbation ◽  
New Type ◽  
The Rich ◽  
Symmetric Systems ◽  
The Continuum

Some photonic systems support bound states in the continuum (BICs) that have infinite lifetimes, although their frequencies and momenta are matched to vacuum modes. Using a prototypical system that can be treated analytically, we show that each of these BICs always splits into a pair of new type BIC and lasing threshold mode when a parity-time (PT)–symmetric perturbation is introduced. The radiation loss at the lasing threshold is exactly balanced by the net gain of the particles. These PT symmetry-induced BICs are different from ordinary BICs, as they can be excited by an external source but do not radiate, and they carry a different quality factor divergence rate from that of the ordinary BICs. While most of the attention of PT-symmetric systems is captured by the coalescence of modes at exceptional points, the splitting of ordinary BICs is a new phenomenon that illustrates the rich physics embedded in PT-symmetric systems.

PT Symmetry Induced Rings of Lasing Threshold Modes Embedded with Discrete Bound States in the Continuum

2021 ◽  
Vol 38 (8) ◽  
pp. 084203
Author(s):  
Qianju Song ◽  
Shiwei Dai ◽  
Dezhuan Han ◽  
Z. Q. Zhang ◽  
C. T. Chan ◽  
...  
Keyword(s):  
Bound States ◽  
Pt Symmetry ◽  
Lasing Threshold ◽  
The Continuum

The theory of conditional invariance. I

1968 ◽  
Vol 305 (1482) ◽  
pp. 405-427 ◽  
Keyword(s):  
Bound States ◽  
General Relation ◽  
Variable Parameter ◽  
Geometric Invariance ◽  
Hermitian Conjugate ◽  
New Type ◽  
Definition Of ◽  
Conditional Invariance ◽  
Conditional Constant ◽  
The Continuum

In order to extend the use of group theoretical arguments to the problem of accidental degeneracy in quantum mechanics, a new type of constant of the motion, known as a conditional constant of the motion, is introduced. Such a quantity, instead of commuting with the Hamiltonian H for the system, satisfies the more general relation H A = A † H , where A † denotes the hermitian conjugate (adjoint) of the conditional constant of the motion A . This expression reduces, if A is hermitian, to the usual definition of a constant of the motion. Otherwise it defines a new type of invariance, and it is this which will be referred to as conditional invariance. A discussion of the difficulties arising from the lack of hermiticity of A , which is of course essential to its definition, is given. In particular it is shown, under fairly general conditions, that the process of introducing a variable parameter in the Hamiltonian enabling it to have simultaneous eigenfunctions with A , gives rise to an eigenvalue equation in this parameter with respect to which A may be chosen to be hermitian. Conditional invariance is contrasted with both dynamical and geometric invariance. It is found to be sometimes replaceable by either of the latter forms of invariance and for such, explicit conditions are given. Some applications of conditional invariance are discussed. These include a study of the crossing of potential energy curves, a new model of symmetry breaking, a possible means of calculating the exact number of bound states for certain potentials and conditions for the existence of bound states near to the continuum.

scholarly journals (1+1)-Dirac bound states in one dimension, with position-dependent Fermi velocity and mass

Open Physics ◽  
2013 ◽  
Vol 11 (4) ◽  
Author(s):  
Omar Mustafa
Keyword(s):  
Harmonic Oscillator ◽  
Bound States ◽  
Bound State ◽  
One Dimension ◽  
Fermi Velocity ◽  
Dirac Particles ◽  
The Continuum ◽  
Oscillator Models

AbstractWe extend Panella and Roy’s [17] work for massless Dirac particles with position-dependent (PD) velocity. We consider Dirac particles where the mass and velocity are both position-dependent. Bound states in the continuum (BIC)-like and discrete bound state solutions are reported. It is observed that BIC-like solutions are not only feasible for the ultra-relativistic (massless) Dirac particles but also for Dirac particles with PDmass and PD-velocity that satisfy the condition m(x) v F2 (x) = A, where A ≥ 0 is constant. Dirac Pöschl-Teller and harmonic oscillator models are also reported.

scholarly journals Lasing threshold of the bound states in the continuum in the plasmonic lattices

2018 ◽  
Vol 26 (22) ◽  
pp. 28948 ◽  
Author(s):  
Andrey Pavlov ◽  
Ilya Zabkov ◽  
Vasily Klimov
Keyword(s):  
Bound States ◽  
Lasing Threshold ◽  
The Continuum

scholarly journals Bound states in the continuum in resonant nanostructures: an overview of engineered materials for tailored applications

Nanophotonics ◽  
2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Shereena Joseph ◽  
Saurabh Pandey ◽  
Swagato Sarkar ◽  
Joby Joseph
Keyword(s):  
Bound States ◽  
Beam Steering ◽  
Functional Materials ◽  
Bound State ◽  
Dielectric Medium ◽  
Quality Factors ◽  
Theoretical Frameworks ◽  
Experimental Realization ◽  
Promising Tool ◽  
The Continuum

Abstract From theoretical model to experimental realization, the bound state in the continuum (BIC) is an emerging area of research interest in the last decade. In the initial years, well-established theoretical frameworks explained the underlying physics for optical BIC modes excited in various symmetrical configurations. Eventually, in the last couple of years, optical-BICs were exploited as a promising tool for experimental realization with advanced nanofabrication techniques for numerous breakthrough applications. Here, we present a review of the evolution of BIC modes in various symmetry and functioning mediums along with their application. More specifically, depending upon the nature of the interacting medium, the excitations of BIC modes are classified into the pure dielectric and lossy plasmonic BICs. The dielectric constituents are again classified as photonic crystal functioning in the subwavelength regime, influenced by the diffraction modes and metasurfaces for interactions far from the diffraction regime. More importantly, engineered functional materials evolved with the pure dielectric medium are explored for hybrid-quasi-BIC modes with huge-quality factors, exhibiting a promising approach to trigger the nanoscale phenomena more efficiently. Similarly, hybrid modes instigated by the photonic and plasmonic constituents can replace the high dissipative losses of metallic components, sustaining the high localization of field and high figure of merit. Further, the discussions are based on the applications of the localized BIC modes and high-quality quasi-BIC resonance traits in the nonlinear harmonic generation, refractometric sensing, imaging, lasing, nanocavities, low loss on-chip communication, and as a photodetector. The topology-controlled beam steering and, chiral sensing has also been briefly discussed.

Observation of Excitonic n-Strings In A Quasi-one-Deviensional Charge-Transfer Crystal

1993 ◽  
Vol 328 ◽  
Author(s):  
N. Peyghambarian ◽  
K. Meissner ◽  
B. Fluegel ◽  
S. Mazumdar ◽  
F. Guo ◽  
...  
Keyword(s):  
Charge Transfer ◽  
Bound States ◽  
Theoretical Calculations ◽  
Exchange Interactions ◽  
Bound State ◽  
Collective Excitations ◽  
One Dimension ◽  
Coulomb Interactions ◽  
Light Pulses ◽  
New Type

ABSTRACTCollective excitations, such as plasmons, rotons, electron-hole liquid, and excitonic Molecules, have been extensively studied in condensed Matter.1 Wannier excitons in inorganic semiconductors are bound by the exchange interactions between two electrons of the exciton, and the bound state of More than two excitons is not possible. We demonstrate here a new type of collective excitations,2 bound states of Multiple charge-transfer (CT) excitons. Coulomb interactions in one dimension are shown to bind a train of several (More than two) CT excitons. Experimental evidence for these new type of elementary excitations is reported in a quasi-one-dimensional CT crystal of anthracene PMDA. High density excitation by femtosecond light pulses generates Multi-exciton chains, which we refer to as excitonic n-strings with n = 1, 2, 3, etc., along the stack axis of the crystal. Both the n = 2 excitonic string (biexciton) and the n = 3 string (tri-exciton) are observed. This report provides evidence for an n > 2 exciton chain in this system.2 The stability of the n-string exciton is supported by our theoretical calculations based on the extended Hubbard Hamiltonian in one dimension.

scholarly journals Acousto-optic modulation of photonic bound state in the continuum

2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Zejie Yu ◽  
Xiankai Sun
Keyword(s):  
Refractive Index ◽  
Integrated Circuits ◽  
Acoustic Waves ◽  
Bound States ◽  
Quantum Information Processing ◽  
Modulation Frequency ◽  
Surface Acoustic Waves ◽  
High Refractive Index ◽  
Bound State ◽  
The Continuum

AbstractPhotonic bound states in the continuum (BICs) have recently been studied in various systems and have found wide applications in sensors, lasers, and filters. Applying BICs in photonic integrated circuits enables low-loss light guidance and routing in low-refractive-index waveguides on high-refractive-index substrates, which opens a new avenue for integrated photonics with functional single-crystal materials. Here, we demonstrate high-quality integrated lithium niobate microcavities inside which the photonic BIC modes circulate and further modulate these BIC modes acousto-optically by using piezoelectrically actuated surface acoustic waves at microwave frequencies. With a high acousto-optic modulation frequency, the acousto-optic coupling is well situated in the resolved-sideband regime. This leads to coherent coupling between microwave and optical photons, which is exhibited by the observed electro-acousto-optically induced transparency and absorption. Therefore, our devices serve as a paradigm for manipulating and controlling photonic BICs on a chip, which will enable many other applications of photonic BICs in the areas of microwave photonics and quantum information processing.

scholarly journals On the Two-Magnon Bound States for the Quantum Heisenberg Chain with Variable Range Exchange

1997 ◽  
Vol 11 (11) ◽  
pp. 453-459 ◽  
Author(s):  
J. Dittrich ◽  
V. I. Inozemtsev
Keyword(s):  
Wave Function ◽  
Finite Difference ◽  
Bound States ◽  
Nearest Neighbor ◽  
Bound State ◽  
Spin Interaction ◽  
Heisenberg Chain ◽  
Variable Range ◽  
New Type

The spectrum of finite-difference two-magnon operator is investigated for quantum S=1/2 chain with variable range exchange of the form h(j-k)∝ sinh -2a(j-k). It is found that usual bound state appears for some values of the total pseudomomentum of two magnons as for the Heisenberg chain with nearest-neighbor spin interaction. Besides this state, a new type of bound state with oscillating wave function appears at larger values of the total pseudomomentum.

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.

scholarly journals Quasi-BIC laser enabled by high-contrast grating resonator for gas detection

Nanophotonics ◽  
2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Haoran Zhang ◽  
Tao Wang ◽  
Jingyi Tian ◽  
Jiacheng Sun ◽  
Shaoxian Li ◽  
...  
Keyword(s):  
Bound States ◽  
Signal To Noise Ratio ◽  
Bound State ◽  
Gain Medium ◽  
Gas Detection ◽  
Visible Range ◽  
High Signal ◽  
High Contrast ◽  
High Contrast Grating ◽  
The Continuum

Abstract In this work, we propose and numerically investigate a two-dimensional microlaser based on the concept of bound states in the continuum (BIC). The device consists of a thin gain layer (Rhodamine 6G dye-doped silica) sandwiched between two high-contrast-grating layers. The structure supports various BIC modes upon a proper choice of topological parameters; in particular it supports a high-Q quasi-BIC mode when partially breaking a bound state in the continuum at Γ point. The optically-pumped gain medium provides sufficient optical gain to compensate the quasi-BIC mode losses, enabling lasing with ultra-low pump threshold (fluence of 17 μJ/cm2) and very narrow optical linewidth in the visible range. This innovative device displays distinguished sensing performance for gas detection, and the emission wavelength sensitively shifts to the longer wavelength with the changing of environment refractive index (in order of 5 × 10−4). The achieved bulk sensitivity is 221 nm/RIU with a high signal to noise ratio, and a record-high figure of merit reaches to 4420 RIU−1. This ultracompact and low threshold quasi-BIC laser facilitated by the ultra-narrow resonance can serve as formidable candidate for on-chip gas sensor.

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