Relaxation of excited states of an emitter near a metal nanoparticle: An analysis based on superradiance theory

Methods of superradiance theory are employed for determining the relaxation rate of the excited state of a resonant emitter (atom, molecule, or quantum dot) near a metal nanoparticle under resonant excitation of plasmons in it, viz., modes of spatially uniform (dipole) harmonic oscillations of the electron density. Detuning from resonance and nonradiative loss suppressing radiation from the emitter near the nanoparticle surface are taken into account. The results are used to estimate the threshold conditions for generating a plasmon (“dipole”) nanolaser. It is shown that the threshold conditions of induced (laser) generation of plasmons for the emitter at a distance of 5–40 nm from an ellipsoidal nanoparticle are satisfied for relatively low emitter pumping rates (on the order of the rate of spontaneous emission of the emitter into the free space).     

Dynamics of a Quantum Emitter Coupled to a Metal Nanostructure in the Presence of External Resonant Field

The relaxation dynamics of a quantum dipole emitter coupled to a metal nanostructure in the presence of an external resonant pump field is studied. It was found that in the mode of weak pumping, the phase of the response from a metallic nanostructure plays a key role in the dynamics of the quantum dipole emitter and allows one to control the fluorescence process. It is shown that when the phase shift is set close to π/2, the quantum emitter makes a quick transition into the ground state, then slowly passes into a superposition state with a small probability to remain in an excited state. Meanwhile, in the case of phase shift values close to 3π/2, the system relaxes into a stationary superposition state where the probability to be in the excited state is close to unity. It was established that the dynamics of the system also depends on the intensity of the external field and with the amplification of the latter, the system enters into the mode of the asymmetric Rabi oscillations.     

Plasmonic modes in periodic metal nanoparticle chains: a direct dynamic eigenmode analysis

We demonstrate an efficient eigendecomposition method for analyzing the guided modes in metal nanoparticle chains. The proposed method has the advantage of simultaneously showing the dispersion relation and the mode quality. It can also separate the material properties from the geometrical properties. Its efficiency therefore does not depend on the complexity of the material polarizability. We used the method to analyze the guided modes of a single and a pair of metal nanoparticle chains. The rigorous dynamic dipole polarizability typically gives a redshift compared with the results obtained from the broadly used quasi-static dipole polarizability with radiation correction.     

偶极子位置及偏振对激发光子晶体H1微腔的影响

光子晶体微腔和量子点的集成是实现量子信息处理非常具有潜力的平台之一,利用微腔和量子点的耦合可以制备纠缠光子对,实现对量子态的操控.因为光子晶体微腔具有品质因子高、模场体积小等优点,可以极大地增强光与物质之间的相互作用,从而易于实现量子态在不同物理体系之间的转换.通过单量子点和光子晶体H1微腔的耦合可以产生纠缠光子对,因为H1微腔具有简并的、模式偏振正交的基态模式.通常微腔模式的激发随着量子点在微腔中的位置变化而改变,本文用时域有限差分方法研究了偶极子光源的位置及偏振对激发光子晶体H1微腔模式的影响.结果表明:通过改变偶极子光源位置可以选择性地激发H1微腔简并模式中的一个;具有某一偏振的偶极子光源只能激发相应偏振的微腔模式;模式激发强度的大小也是由偶极子光源在微腔中的位置决定的.鉴于目前量子点在微腔中的位置尚不能精确控制,所以微腔模式受激发光源位置的影响的研究具有重要意义.     

Identification of molecules through the fluorescence enhancement by a metal tip

A fluorescence enhancement phenomenon, which is realized as a result of a sharp increase in the radiative decay rate of a quantum dipole emitter (QDE) is investigated theoretically in the vicinity of a conical metal tip. The QDE relaxation process is considered as a self-stimulated transition from an excited state into the ground state due to the feedback field formation from the tip. The dynamics of the system shows a stepped relaxation behavior that differs significantly from the conventional exponential decay. This effect can be observed in a small region of the resonance frequency, which is defined by an angle of conical tip. The increase of fluorescence when approaching of molecule to the metal tip on the surface enables one to determine its location.     

Enhancement of spontaneous emission from the resonant modes of a photonic crystal slab single-defect cavity

Modification of the spontaneous-emission lifetime in photonic crystal single-defect resonant modes is studied with the finite-difference time domain method. We investigate spontaneous-emission enhancement from the monopole and the dipole modes of a hexagonal lattice cavity, considering the effects of the finite emitter linewidth and spectral detuning. Large spontaneous-emission enhancement of > 50 is achieved numerically from the high-quality-factor monopole mode when the emitter linewidth is comparable with the resonant-mode linewidth. However, if broad-linewidth material is used and a detuning effect is included, the dipole mode with a low quality factor and a smaller mode volume could be more advantageous for spontaneous-emission enhancement.     

Spectrum of surface plasmons excited by spontaneous quantum dot transitions

We consider quantum fluctuations of near fields of a quantum emitter (two-level system (TLS) with population inversion sustained by incoherent pumping) in the near-field zone of a plasmon (metallic) nanoparticle. The spectrum of surface plasmons excited by spontaneous transitions in the quantum emitter is obtained below the lasing threshold of such a system (spaser) in the approximation of a small number of plasmons. It is shown that the relaxation rate is the sum of the quantum emitter’s rates of relaxation to its thermal reservoir and the plasmon cavity. The resulting dependence of the average number of plasmons on the pump intensity indicates the nonthreshold nature of the process.     

Probing the acoustic vibrations of single metal nanoparticles by ultrashort laser pulses

The strong interaction of metal nanoparticles with light makes it possible to detect individual particles by far‐field optical methods. In this article, the interaction of a metal nanoparticle with a short laser pulse is discussed, with the emphasis on the coherent excitation of mechanical (acoustic) modes and the optical detection of these vibrations. The literature on acoustic vibrations of single metal nanoparticles of different shapes (spheres, dumbbells, rods, cubes, wires, prisms) is reviewed, and the modes that have been excited and detected in these particles are discussed. Finally, the insights and potential applications enabled by these studies are summarized.     

Configuration interaction study of single and double dipole plasmon excitations in Na8

We carry out a microscopic analysis of the ground and excited states of the Na₈ metal cluster within the jellium model. We perform a series of configuration interaction calculations on a Hartree–Fock basis and construct eigenstates of the Hamiltonian which carry up to 4-particle 4-hole components. Based on the analysis of the dipole transition strengths, we single out those states which can be interpreted as the collective dipole plasmon and its double excitations. These modes are found to possess a high degree of harmonicity, deviations from the harmonic limit remaining, however, of the order of 10%.     

Dynamic dipole–dipole induction of coherence among a quantum dot ensemble

The quantum mechanical dynamic resonance due to dipole–dipole interaction is shown possibly to induce coherent modes of electrons within an ensemble of two-level systems or quantum dots. The physical origin of this coherence would naturally be postulated as the parity inheritance into a site being excited from another site being de-excited. An experimental spectrum suggestive of this dipole–dipole mode is also shown. This coherence is expected to be useful for quantum computing.     

The fluorescence rate of a single molecule close to a spherical metallic nanoparticle

The theoretical study of fluorescence rate of a single molecule close to a spherical metallic nanoparticle is presented. The dielectric function of the metallic nanoparticle and its polarizability is analyzed when the radii of the nanoparticle is rather small. Based on dipole–dipole model, the distance dependence of the excitation rate, radiation rate, nonradiation rate and quantum yield of the emitter molecule are derived out. The results show that the quantum yield is rather small at the vicinity of the metallic nanoparticle surface.     

Enhancement of light trapping in thin-film solar cells through Ag

Forward-scattering efficiency (FSE) is first proposed when an Ag nanoparticle serves as the light-trapping structure for thin-film (TF) solar cells because the Ag nanoparticle’s light-trapping efficiency lies on the light-scattering direction of metal nanoparticles.Based on FSE analysis of Ag nanoparticles with radii of 53 and 88 nm,the forward-scattering spectra and light-trapping efficiencies are calculated.The contributions of dipole and quadrupole modes to light-trapping effect are also analyzed quantitatively.When the surface coverage of Ag nanoparticles is 5%,light-trapping efficiencies are 15.5% and 32.3%,respectively,for 53and 88-nm Ag nanoparticles.Results indicate that the plasmon quadrupole mode resonance of Ag nanoparticles could further enhance the light-trapping effect for TF solar cells.     

Local Surface-Plasmons in Nonspherical Metal Nanoparticles

When a small metallic nanoparticle.is irradiated by incident light, the oscillating electric field can cause the conduction electrons to oscillate coherently, which excites the local surface plasmons （LSPs）. As is well known, excited LSPs can gather the energy of incident light to the surface of metallic nanoparticle. Recently, some nonspherical particles, e.g. tetrahedron, are suggested to obtain stronger localized electric field. We employ the discrete dipole approximation method to calculate the optical response of the tetrahedron nanoparticle, including the extinction and distribution of the electric field around the particle. The influences of some parameters, including the nanoparticle size, incident direction and polarization, are investigated to analyse the response modes and to obtain stronger localized electric field.     

Spontaneous radiation of a two-level atom into multipole modes of a plasmonic nanoparticle

We consider the relaxation of an excited two-level system (TLS) positioned near a spherical plasmonic nanoparticle (NP). The transition frequency of the TLS is assumed to coincide with the frequency of the condensation point of NP plasmonic resonances. We show that the relaxation of the TLS excitation is a two-step process. Following an initial exponential decay, the TLS breaks in to Rabi oscillations. Depending upon the distance between the TLS and NP, the probability of the TLS being in the excited state exhibits either chaotic or nearly regular oscillations. In the latter case, the eigenfrequency of the TLS-NP system coincides with one of NP multipole modes.     

Effects of shape of terminus on excitation of surface plasmon modes on metal nanowires

The effects of the shape of a nanowire terminus on the excited surface plasmon polariton （SPP） modes are investigated. The conical terminus and terminus cut at a certain angle are studied. For the first time, the quantitative mode decompositions are carried out to derive the full information about excited SPP modes. It is demonstrated that tuning the shape of the terminus provides an effective method to control the composition of excited SPP modes on metal nanowires. It is especially found that some important patterns, such as the pure TM0 mode and the superposition of TM0 and HE＋1 or HE-1 modes, can be generated by some specific shapes of the terminus, whereas there is no way to produce these patterns using flat-end nanowires.     

Low-lying Collective Modes of a 1D Dipolar Quantum Gas in an Anharmonic Trap

The low-lying collective modes of an anharmonically confined one-dimensional ultracold dipolar Bose gas are investigated by using time-dependent variational method. The frequencies of dipole mode and breathing mode are obtained analytically in the full crossover regime from a Tonks-Girardeau gas to a dipolar density wave state. We find that the frequency shifts caused by quartic distortion of the potential can be amplified by interparticle interaction and the collapse and revival of the collective excitations can be observed in the anharmonic trap.     

Radiative and non-radiative decay of a single molecule close to a metallic nanoparticle

We study the spontaneous emission of a single emitter close to a metallic nanoparticle, with the aim to clarify the distance dependence of the radiative and non-radiative decay rates. We derive analytical formulas based on a dipole-dipole model, and show that the non-radiative decay rate follows a R⁻⁶ dependence at short distance, where R is the distance between the emitter and the center of the nanoparticle, as in Förster’s energy transfer. The distance dependence of the radiative decay rate is more subtle. It is chiefly dominated by a R⁻³ dependence, a R⁻⁶ dependence being visible at plasmon resonance. The latter is a consequence of radiative damping in the effective dipole polarizability of the nanoparticle. The different distance behavior of the radiative and non-radiative decay rates implies that the apparent quantum yield always vanishes at short distance. Moreover, non-radiative decay is strongly enhanced when the emitter radiates at the plasmon-resonance frequency of the nanoparticle.     

Non-radiative decay of a dipole emitter close to a metallic nanoparticle: Importance of higher-order multipole contributions

The contribution of higher-order multipoles to radiative and non-radiative decay of a single dipole emitter close to a spherical metallic nanoparticle is re-examined. Taking a Ag spherical nanoparticle (AgNP) with the radius of 5 nm as an example, a significant contribution (between 50% and 101% of the total value) of higher-order multipoles to non-radiative rates is found even at the emitter distance of 5 nm from the AgNP surface. On the other hand, the higher-order multipole contribution to radiative rates is negligible. Consequently, a dipole-dipole approximation can yield only an upper bound on the apparent quantum yield. In contrast, the non-radiative rates calculated with the quasistatic Gersten and Nitzan method are found to be in much better agreement with exact electrodynamic results. Finally, the size corrected metal dielectric function is shown to decrease the non-radiative rates near the dipolar surface plasmon resonance.     

Relaxation in systems with hierarchical organization: Analytical derivation of the relaxation and dispersion functions

We report a successful attempt to derive a closed-form expression for the relaxation function of a complex system by solving a set of coupled kinetic equations connecting the excitation/de-excitation rates to the number of particles (such as electrical charges, dipoles, etc.) in excited states. Our approach, originating from developments in dielectric and mechanical relaxation studies, allows the use of a unified treatment for a wide array of natural processes which often pose challenges to theoretical modeling. We use the notions that (i) a dipole represents any pair formed by a particle in an excited state (such as an energy level in optically excited molecules, or an electrode in dielectric spectroscopy) and its image in the ground state (or reference electrode), that (ii) coupling between such dipoles may be described as particle transfer from one excited state to another with lower energy, and that (iii) the relaxation function for such a system of dipoles is mathematically equivalent to the cumulative distribution function of particles, i.e., the total number of particles that are still in an excited state at a time t following excitation. Taken together, these ideas naturally lead to the identification of two types of relaxation – parallel and serial relaxation – and allow one to tackle systems with either geometrical or physical self-similarity within a unified mathematical scheme.     

Chaos dynamics in semiconductor lasers with polarization-rotated optical feedback

By using polarization-rotated optical feedback from the transverse-electric (TE) mode to the transverse-magnetic (TM) mode, chaotic oscillations for both polarization modes are excited in a semiconductor laser. We find different correlations between these chaotic oscillations than those found in previous studies. In this study, the dynamics are strongly dependent on their radio-frequency (RF) components and they are divided into three RF regions. For low-pass filtered signals lower than the laser relaxation oscillation, there is an antiphase correlation between the two polarization modes. On the other hand, the two polarization modes have an in-phase correlation for the RF components of the high-pass filtered signals, which are higher than the relaxation oscillation. However, no correlations were observed between the two modes for the intermediate RF components that include the relaxation oscillation frequency. We also perform numerical calculations for the model and obtain good agreement between the theoretical and experimental results.