Continuum Of Modes Research Articles

Plasmonic leaky-mode lasing in active semiconductor nanowires

Leaky modes are below-cutoff waveguide modes that lose part of their energy to the continuum of radiation modes during propagation. In photonic nanowire lasers, leaky modes have to compete with almost lossless above-cutoff modes and are therefore usually prevented from crossing the lasing threshold. The situation is drastically different in plasmonic nanowire systems where the above-cutoff plasmonic modes are very lossy because of their strong confinement to the metal surface. Due to gain guiding, the threshold gain of the hybrid electric leaky mode does not increase strongly with reduced wire diameter and stays below that of all other modes, making it possible to observe leaky-mode lasing. Plasmonic ZnO nanowire lasers operating in the gain-guided regime could be used as coherent sources of surface plasmon polaritons at the nanoscale or as surface plasmon emitting diodes with an emission angle that depends on the nanowire diameter and the color of the surface plasmon polariton.

Ultrasensitive optical absorption in graphene based on bound states in the continuum.

We have designed a sphere-graphene-slab structure so that the electromagnetic wave can be well confined in the graphene due to the formation of a bound state in a continuum (BIC) of radiation modes. Based on such a bound state, we have realized strong optical absorption in the monolayer graphene. Such a strong optical absorption exhibits many advantages. It is ultrasensitive to the wavelength because the Q factor of the absorption peak can be more than 2000. By taking suitable BICs, the selective absorption for S and P waves has not only been realized, but also all-angle absorption for the S and P waves at the same time has been demonstrated. We have also found that ultrasensitive strong absorptions can appear at any wavelength from mid-infrared to far-infrared band. These phenomena are very beneficial to biosensing, perfect filters and waveguides.

A singular finite element technique for calculating continuum damping of Alfvén eigenmodes

Damping due to continuum resonances can be calculated using dissipation-less ideal magnetohydrodynamics provided that the poles due to these resonances are properly treated. We describe a singular finite element technique for calculating the continuum damping of Alfvén waves. A Frobenius expansion is used to determine appropriate finite element basis functions on an inner region surrounding a pole due to the continuum resonance. The location of the pole due to the continuum resonance and mode frequency is calculated iteratively using a Galerkin method. This method is used to find the complex frequency and mode structure of a toroidicity-induced Alfvén eigenmode in a large aspect ratio circular tokamak and is shown to agree closely with a complex contour technique.

A master equation for a two-sided optical cavity

Quantum optical systems, like trapped ions, are routinely described by master equations. The purpose of this paper is to introduce a master equation for two-sided optical cavities with spontaneous photon emission. To do so, we use the same notion of photons as in linear optics scattering theory and consider a continuum of travelling-wave cavity photon modes. Our model predicts the same stationary state photon emission rates for the different sides of a laser-driven optical cavity as classical theories. Moreover, it predicts the same time evolution of the total cavity photon number as the standard standing-wave description in experiments with resonant and near-resonant laser driving. The proposed resonator Hamiltonian can be used, for example, to analyse coherent cavity-fiber networks [E. Kyoseva et al., New J. Phys. 14, 023023 (2012)].

Acoustical Phonons Transport through a Stepped Quantum Wire

This work presents a theoretical approach for the study of phonon dynamics and scattering properties of an infinite linear atomic chain perturbed by a mono atomic step. The coherent transmittance scattering cross-sections for incident phonons on the atomic waveguide structure are calculated using the Landauer-Buttiker electron scattering description and the matching method formalism with the nearest and next nearest neighbour interactions. Numerical results for different configurations yield an understanding of the chain dynamical properties and the effects on phonon transmittance due to incoming phonons. The reflectance and transmittance coefficients show spectral characteristic features depending on the cut-off frequencies for the propagating phonons. They illustrate the occurrence of Fano resonances in the scattering spectra that result from degeneracy of step localized modes and propagating continuum modes due to the breakdown of the translation symmetry in the propagating direction. Furthermore, the interferences between diffused and reflected waves in the step regions generate Fabry-Perot oscillations whose number is determined by the distance between steps and the number of terraces.

Boundary waves in ferromagnetically ordered two-dimensional arrays of magnetic dots

The existence of surface modes localized at the boundary of magnetic-dot arrays with magnetization perpendicular to the plane of array is predicted. Numerical and analytic calculations show that the excitation energy of these boundary modes is above the continuum of modes propagating in the array.

Long-lived Higgs mode in a two-dimensional confined Fermi system

The Higgs mode corresponds to the collective motion of particles due to the vibrations of an invisible field. It plays a fundamental role in our understanding of both low- and high-energy physics, giving elementary particles their mass and leading to collective modes in condensed-matter and nuclear systems. The Higgs mode has been observed in a limited number of table-top systems, where it however is characterized by a short lifetime due to decay into a continuum of modes. A major goal which has remained elusive so far is, therefore, to realize a long-lived Higgs mode in a controllable system. Here, we show how an undamped Higgs mode can be observed unambiguously in a Fermi gas in a two-dimensional trap, close to a quantum phase transition between a normal and a superfluid phase. We develop a first-principles theory of the pairing and the associated collective modes, which is quantitatively reliable when the pairing energy is much smaller than the trap level spacing, yet simple enough to allow the derivation of analytical results. The theory includes the trapping potential exactly, which is demonstrated to stabilize the Higgs mode by making its decay channels discrete. It is shown to be realistic to realize the proposed system using atoms in microtraps. The unrivaled flexibility of atomic gases combined with the quantitatively accurate theory opens the door to a systematic study of the Higgs mode, including the role of confinement and finite-size effects.

A depth-dependent formula for shallow water propagation.

In shallow water propagation, the sound field depends on the proximity of the receiver to the sea surface, the seabed, the source depth, and the complementary source depth. While normal mode theory can predict this depth dependence, it can be computationally intensive. In this work, an analytical solution is derived in terms of the Faddeeva function by converting a normal mode sum into an integral based on a hypothetical continuum of modes. For a Pekeris waveguide, this approach provides accurate depth dependent propagation results (especially for the surface decoupling) without requiring complex calculation methods for eigenvalues and corresponding eigenfunctions.

Initial value problem approach of two regions of system solar: the continuous spectrum

The standard mathematical procedures in Helioseismology field are based on normal mode approach for various models of solar interior and atmosphere. We consider a two region model of a system solar interior and solar atmosphere. For simplicity, the two different regions are assumed quasi-isothermal, semi-infinite, without magnetic fields and separated by a boundary z=0. It was found useful to phrase of stability as initial value problem (IPV) in order to ensure the inclusion of certain continuum modes otherwise neglected. In addition to discrete mode (f-mode), sets of continuum modes due to a branch cuts in the complex plane, not treated explicitly in the literature, appears. It will be seen that an ambiguity of the usual normal mode method is avoided.

A review on Lamb's atmospheric oscillations using initial value problem approach

Waves at a surface of discontinuity in the atmosphere were analysed in 1910 by Lamb, who derived, using normal mode approach, an analytical dispersion relation for a discrete mode (surface mode). Lamb examined the case of waves propagated along a horizontal plane where the equilibrium temperature is discontinuous. For simplicity, the upper and the lower regions are considered incompressible. The oscillations are treated in the ideal (dissipationless) limit and the uniform gravitational acceleration is taken to be co-aligned with the prevailing temperature gradient. In this work, in order to show how the modes appear in the response of a surface discontinuity to an initial perturbation, we consider the initial value problem (IPV). The main difference from the standard analysis is that solutions to the linearized equations of motion which satisfy general conditions are obtained in terms of Fourier-Laplace transform of the hydrodynamics variables. These transforms can be inverted explicitly to express the fluid variables as integrals of Green's functions multiplied by initial data. In addition to discrete mode (surface mode), sets of continuum modes due to branch cuts in the complex plane, not treated explicitly in the literature, appears.

Linear dispersion relation of beta-induced Alfvén eigenmodes in presence of anisotropic energetic ions

Using the theoretical framework of the generalized fishbone-like dispersion relation, the linear properties of beta-induced Alfvén eigenmodes (BAEs) and energetic particle continuum modes (EPMs) excited by anisotropic slowing-down energetic ions are investigated analytically and numerically. The resonant contribution of energetic ions to the potential energy perturbation as well as fluid-like term describing the background plasma and adiabatic contribution of energetic ions are derived. For high-mode numbers, numerical results show smooth transition between the EP continuous spectrum and BAEs in the gap. EPMs and/or BAEs are destabilized by energetic ions, with real frequencies and growth rates strongly dependent on the energetic particle density and resonant frequency.

Spontaneous emission inhibition of telecom-band quantum disks inside single nanowire on different substrates.

We investigate the inhibited spontaneous emission of telecom-band InAs quantum disks (Qdisks) in InP nanowires (NWs). We have evaluated how the inhibition is affected by different disk diameter and thickness. We also compared the inhibition in standing InP NWs and those NWs laying on silica (SiO(2)), and silicon (Si) substrates. We found that the inhibition is altered when we put the NW on the high-refractive-index materials of Si. Experimentally, the inhibition factor ζ of the Qdisk emission at 1,500 nm decreases from 4.6 to 2.5 for NW on SiO(2) and Si substrates, respectively. Those inhibitions are even much smaller than that of 6.4 of the standing NW. The inhibition factors well agree with those calculated from the coupling of the Qdisk to the fundamental guided mode and the continuum of radiative modes. Our observation can be useful for the integration of the NW as light sources in the photonic nanodevices.

Scattering of coherent pulses on a two-level system—single-photon generation

In this paper, we consider a two-level system (TLS) coupled to a one-dimensional continuum of bosonic modes in a transmission line (TL). Using the master equation approach, a method for determining the photon number distribution of the scattered field is outlined. Specifically, results for the reflected field when driving the TLS with a coherent pulse are given. While the one-photon probability is enhanced compared to the incident coherent field, the system is still not a good deterministic single-photon source. Extending the system to contain two separate TLs, however, output fields with one-photon probabilities close to unity can be reached.

Energetic-particle-driven instabilities and induced fast-ion transport in a reversed field pinch

Multiple bursty energetic-particle (EP) driven modes with fishbone-like structure are observed during 1 MW tangential neutral-beam injection in a reversed field pinch (RFP) device. The distinguishing features of the RFP, including large magnetic shear (tending to add stability) and weak toroidal magnetic field (leading to stronger drive), provide a complementary environment to tokamak and stellarator configurations for exploring basic understanding of EP instabilities. Detailed measurements of the EP mode characteristics and temporal-spatial dynamics reveal their influence on fast ion transport. Density fluctuations exhibit a dynamically evolving, inboard-outboard asymmetric spatial structure that peaks in the core where fast ions reside. The measured mode frequencies are close to the computed shear Alfvén frequency, a feature consistent with continuum modes destabilized by strong drive. The frequency pattern of the dominant mode depends on the fast-ion species. Multiple frequencies occur with deuterium fast ions compared to single frequency for hydrogen fast ions. Furthermore, as the safety factor (q) decreases, the toroidal mode number of the dominant EP mode transits from n=5 to n=6 while retaining the same poloidal mode number m=1. The transition occurs when the m=1, n=5 wave-particle resonance condition cannot be satisfied as the fast-ion safety factor (qfi) decreases. The fast-ion temporal dynamics, measured by a neutral particle analyzer, resemble a classical predator-prey relaxation oscillation. It contains a slow-growth phase arising from the beam fueling followed by a rapid drop when the EP modes peak, indicating that the fluctuation-induced transport maintains a stiff fast-ion density profile. The inferred transport rate is strongly enhanced with the onset of multiple EP modes.

New insights into the decay of ion waves to turbulence, ion heating, and soliton generation

The decay of a single-frequency, propagating ion acoustic wave (IAW) via two-ion wave decay to a continuum of IAW modes is found to result in a highly turbulent plasma, ion soliton production, and rapid ion heating. Instability growth rates, thresholds, and sensitivities to plasma conditions are studied via fully kinetic Vlasov simulations. The decay rate of IAWs is found to scale linearly with the fundamental IAW potential amplitude ϕ1 for ZTe/Ti≲20, beyond which the instability is shown to scale with a higher power of ϕ1, where Z is the ion charge number and Te (Ti) is the electron (ion) thermal temperature. The threshold for instability is found to be smaller by an order of magnitude than linear theory estimates. Achieving a better understanding of the saturation of stimulated Brillouin scatter levels observed in laser-plasma interaction experiments is part of the motivation for this study.

Canonical quantization of electromagnetism in spatially dispersive media

We find the action that describes the electromagnetic field in a spatially dispersive, homogeneous medium. This theory is quantized and the Hamiltonian is diagonalized in terms of a continuum of normal modes. It is found that the introduction of nonlocal response in the medium automatically regulates some previously divergent results, and we calculate a finite value for the intensity of the electromagnetic field at a fixed frequency within a homogeneous medium. To conclude we discuss the potential importance of spatial dispersion in taming the divergences that arise in calculations of Casimir-type effects.

The Fano Resonance in Symmetry Broken Terahertz Metamaterials

The spectral characteristic of a Fano resonance is a distinct and unique asymmetric line shape. It arises from the destructive interference between a bright continuum mode and a discrete dark mode. Metamaterials and plasmonics have facilitated the observation of Fano resonances in the realm of classical electrodynamics and have spurred intense interest to study and to exploit their peculiarities due their low loss and very sharp resonant features. Here, we survey the excitation of Fano resonance at terahertz frequencies by using asymmetric metamaterial structures. In particular, we discuss the high Q of Fano resonances, their sensitivity to the asymmetry parameter and potential applications. We believe that the manipulation of terahertz radiation by exploiting Fano resonances in terahertz metamaterials could usher in next-generation terahertz photonic devices for delay, storage, filtering, sensing, and nonlinear applications.

Alfvén Instabilities Excited by Energetic Particles in a Parameter Regime Similar to EAST Operation

The kinetic excitation of ideal magnetohydrodynamic (MHD) Alfvén instabilities is investigated for operations at the EAST tokamak. The instabilities include α-induced toroidal Alfvén eigenmodes (αTAE; here, α = −q2Rdβ/dr, with q being the safety factor, β the ratio between the plasma and magnetic pressures, R the major radius, and r the minor radius), toroidicity-induced Alfvén eigenmodes (TAE), and the energetic particle continuum mode (EPM). The αTAE, trapped by α-induced potential wells along the magnetic field line, can be readily destabilized by energetic particles due to negligible continuum damping via wave energy tunneling. It is shown for the geometry and the parameters similar to those of the EAST equilibrium that αTAE is different not only from the EPM by the potential-well determined frequency, but also from the TAE by the broad frequency spectrum outside the toroidal frequency gap.

Observation of trapped light within the radiation continuum

The ability to confine light is important both scientifically and technologically. Many light confinement methods exist, but they all achieve confinement with materials or systems that forbid outgoing waves. These systems can be implemented by metallic mirrors, by photonic band-gap materials, by highly disordered media (Anderson localization) and, for a subset of outgoing waves, by translational symmetry (total internal reflection) or by rotational or reflection symmetry. Exceptions to these examples exist only in theoretical proposals. Here we predict and show experimentally that light can be perfectly confined in a patterned dielectric slab, even though outgoing waves are allowed in the surrounding medium. Technically, this is an observation of an 'embedded eigenvalue'--namely, a bound state in a continuum of radiation modes--that is not due to symmetry incompatibility. Such a bound state can exist stably in a general class of geometries in which all of its radiation amplitudes vanish simultaneously as a result of destructive interference. This method to trap electromagnetic waves is also applicable to electronic and mechanical waves.

Bloch surface eigenstates within the radiation continuum

From detailed numerical calculations, we demonstrate that in simple photonic crystal structures, a discrete number of Bloch surface-localized eigenstates can exist inside the continuum of free-space modes. Coupling to the free space causes the surface modes to leak, but the forward and back-reflected leakage may interfere destructively to create a perfectly bound surface state with zero leakage. We perform analytical temporal coupled-mode theory analysis to show the generality of such phenomenon and its robustness from variations of system parameters. Periodicity, time-reversal invariance, two-fold rotational symmetry and a perfectly reflecting boundary are necessary for these unique states. Inside the periodic structure of a photonic crystal, photons behave analogously to electrons in solid-state materials. Localized light patterns can be found at the interface between a photonic crystal and the surrounding air. Such surface states can exist even when the light has a possibility of escaping into the air, as Marin Soljacic and co-workers at the Massachusetts Institute of Technology and Harvard University, USA, now show in a theoretical study. They demonstrate that under certain conditions, different leakage channels from the crystal surface interfere destructively and thus cancel each other completely. These findings should help in the design of photonic-crystal structures for applications such as sensing and spectroscopy, where strongly localized light states are desired.