Electromagnetic Green's Tensor Research Articles

Strong Coupling Dynamics of a Quantum Emitter near a Topological Insulator Nanoparticle.

We study the spontaneous emission dynamics of a quantum emitter near a topological insulator Bi2Se3 spherical nanoparticle. Using the electromagnetic Green's tensor method, we find exceptional Purcell factors of the quantum emitter up to 1010 at distances between the emitter and the nanoparticle as large as half the nanoparticle's radius in the terahertz regime. We study the spontaneous emission evolution of a quantum emitter for various transition frequencies in the terahertz and various vacuum decay rates. For short vacuum decay times, we observe non-Markovian spontaneous emission dynamics, which correspond perfectly to values of well-established measures of non-Markovianity and possibly indicate considerable dynamical quantum speedup. The dynamics turn progressively Markovian as the vacuum decay times increase, while in this regime, the non-Markovianity measures are nullified, and the quantum speedup vanishes. For the shortest vacuum decay times, we find that the population remains trapped in the emitter, which indicates that a hybrid bound state between the quantum emitter and the continuum of electromagnetic modes as affected by the nanoparticle has been formed. This work demonstrates that a Bi2Se3 spherical nanoparticle can be a nanoscale platform for strong light-matter coupling.

Pump-Probe Optical Response and Four-Wave Mixing in a Zinc-Phthalocyanine-Metal Nanoparticle Hybrid System.

We investigate theoretically the optical response of a zinc-phthalocyanine molecular quantum system near a gold spherical nanoparticle with a radius of 80 nm. The quantum system is irradiated by a strong pump and a weak probe coherent electromagnetic field. Using the density matrix methodology, we obtain analytical expressions for the absorption, dispersion, and the four-wave-mixing coefficients. The influence of the nanoparticle on the spontaneous decay rate of the quantum system, as well as on the external fields, are obtained by an electromagnetic Green's tensor method. The spectroscopic parameters of the molecule are also obtained by ab initio methods. For the studied optical spectra, we find that, below a critical distance between the molecule and the plasmonic nanoparticle, determined by the minimal value of the effective Rabi frequency, single-peaked spectra are observed. Above this critical distance, the spectra exhibit the characteristic Mollow-shaped profiles. The enhancement of the pump field detuning induces the shift of the sideband resonances away from the origin. Lastly, and most importantly, regardless of the value of the detuning, the optical response of the system is maximized for an intermediate value of the interparticle distance.

Purcell factors and Förster-resonance energy transfer in proximity to helical structures

Both spontaneous emission and resonant energy transfer can be enhanced significantly when the emitter is placed in the vicinity of metallic or crystal structures. This enhancement can be described using the electromagnetic Green tensor and is determined by the dominant surface modes of the structure. Here we use the eigenpermittivity formalism to derive the spontaneous emission and FRET rates in the quasistatic regime in a two-constituent medium with an anisotropic inclusion. We then apply our results to a helical structure supporting synchronous vibrations and evaluate the contribution of these modes, which are associated with a strong and delocalized response. We show that this contribution can result in large Purcell factors and long-range FRET, which oscillates with the helix pitch. These findings may have implications in understanding and controlling the interactions of molecules close to helical structures such as the microtubules.

Resonance energy transfer between two atoms in a conducting cylindrical waveguide

We consider the energy transfer process between two identical atoms placed inside a perfectly conducting cylindrical waveguide. We first introduce a general analytical expression of the energy transfer amplitude in terms of the electromagnetic Green's tensor; we then evaluate it in the case of a cylindrical waveguide made of a perfect conductor, for which analytical forms of the Green's tensor exist. We numerically analyse the energy transfer amplitude when the radius of the waveguide is such that the transition frequency of both atoms is below the lower cutoff frequency of the waveguide, so that the resonant photon exchange is strongly suppressed. We consider both cases of atomic dipoles parallel and orthogonal to the axis of the guide. In both cases, we find that the energy transfer is modified by the presence of the waveguide. In the near zone, that is when the atomic separation is smaller than the atomic transition wavelength, the change, with respect to the free-space case, is small for axial dipoles, while it is larger for radial dipoles; it grows when the intermediate region between near and far zone is approached. In the far zone, we find that the energy transfer amplitude is strongly suppressed by the waveguide, becoming virtually zero. A physical interpretation of these results is discussed. Finally, we discuss the resonance interaction energy and force between two identical correlated atoms in the waveguide, one excited and the other in the ground state, prepared in their symmetric or antisymmetric superposition.

Optical properties of hybrid spherical nanoclusters containing quantum emitters and metallic nanoparticles

We study theoretically the optical response of a hybrid spherical cluster containing quantum emitters and metallic nanoparticles. The quantum emitters are modeled as two-level quantum systems whose dielectric function is obtained via a density matrix approach wherein the modified spontaneous emission decay rate at the position of each quantum emitter is calculated via the electromagnetic Green's tensor. The problem of light scattering off the hybrid cluster is solved by employing the coupled-dipole method. We find, in particular, that the presence of the quantum emitters in the cluster, even in small fractions, can significantly alter the absorption and extinction spectra of the sole cluster of the metallic nanoparticles, where the corresponding electromagnetic modes can have a weak plexcitonic character under suitable conditions.

Ultrafast coherent energy transfer with high efficiency based on plasmonic nanostructures.

The theory of energy transfer dynamics of a pair of donor and acceptor molecules located in the plasmonic hot spots is developed by means of the master equation approach and the electromagnetic Green's tensor technique. A nonlocal effect has been considered by using a hydrodynamic model. The coherent interaction between the two molecules in plasmonic nanostructures is investigated, and we find that the coupling strength between two molecules can be larger than dissipation. It is shown that the energy transfer efficiency of a pair of molecules can be improved largely and the transfer time decreases to dozens of femtoseconds when the contribution of quantum coherence is considered. The physical origin for such a phenomenon has also been analyzed. This ultrafast and high-efficiency energy transfer mechanism could be beneficial for artificial light-harvesting devices.

Non-Markovian dynamics in plasmon-induced spontaneous emission interference

We investigate theoretically the non-Markovian dynamics of a degenerate V-type quantum emitter in the vicinity of a metallic nanosphere, a system that exhibits quantum interference in spontaneous emission due to the anisotropic Purcell effect. We calculate numerically the electromagnetic Green's tensor and employ the effective modes differential equation method for calculating the quantum dynamics of the emitter population, with respect to the resonance frequency and the initial state of the emitter, as well as its distance from the nanosphere. We find that the emitter population evolution varies between a gradually total decay and a partial decay combined with oscillatory population dynamics, depending strongly on the specific values of the above three parameters. Under strong coupling conditions, coherent population trapping can be observed in this system. We compare our exact results with results when the flat continuum approximation for the modified by the metallic nanosphere vacuum is applied. We conclude that the flat continuum approximation is an excellent approximation only when the spectral density of the system under study is characterized by non-overlapping plasmonic resonances.

Fluorescence in nonlocal dissipative periodic structures

We present an approach for the description of fluorescence from optically active material embedded in layered periodic structures. Based on an exact electromagnetic Green's tensor analysis, we determine the radiative properties of emitters such as the local photonic density of states, Lamb shifts, line widths etc. for a finite or infinite sequence of thin alternating plasmonic and dielectric layers. In the effective medium limit, these systems may exhibit hyperbolic dispersion relations so that the large wave-vector characteristics of all constituents and processes become relevant. These include the finite thickness of the layers, the nonlocal properties of the constituent metals, and local-field corrections associated with an emitter's dielectric environment. In particular, we show that the corresponding effects are non-additive and lead to considerable modifications of an emitter's luminescence properties.

Plasmon-induced enhancement of nonlinear optical rectification in organic materials

We show that nonlinear optical rectification (NOR) can be greatly enhanced in the proximity of plasmonic nanostructures. The NOR enhancement in the visible frequency range near Cu-coated SiO${}_{2}$ nanospheres is calculated by a rigorous first-principle electromagnetic Green's tensor technique. Exemplary compounds with absorption in the visible optical spectrum based on and metalloporphyrin molecules are discussed, exhibiting enhancement factors typically larger than ten. Their spectral properties in relation to NOR are obtained by first-principle electronic structure calculations.

Plasmon-Induced Enhancement of Quantum Interference near Metallic Nanostructures

We show that the quantum interference between two spontaneous emission channels can be greatly enhanced when a three-level V-type atom is placed near plasmonic nanostructures such as metallic slabs, nanospheres, or periodic arrays of metal-coated spheres. The spontaneous emission rate is calculated by a rigorous first-principles electromagnetic Green's tensor technique. The enhancement of quantum interference is attributed to the strong dependence of the spontaneous emission rate on the orientation of an atomic dipole relative to the surface of the nanostructure at the excitation frequencies of surface plasmons.

Short-distance expansion for the electromagnetic half-space Green's tensor: general results and an application to radiative lifetime computations

We obtain a short-distance expansion for the half-space, frequency domain electromagnetic Green's tensor. The small parameter of the theory is , where ω is the frequency, ϵ1 is the permittivity of the upper half-space, in which both the source and the point of observation are located, and which is assumed to be transparent, c is the speed of light in vacuum and is a characteristic length, defined as the distance from the point of observation to the reflected (with respect to the planar interface) position of the source. In the case when the lower half-space (the substrate) is characterized by a complex permittivity ϵ2, we compute the expansion to third order. For the case when the substrate is a transparent dielectric, we compute the imaginary part of the Green's tensor to seventh order. The analytical calculations are verified numerically. The practical utility of the obtained expansion is demonstrated by computing the radiative lifetime of two electromagnetically interacting molecules in the vicinity of a transparent dielectric substrate. The computation is performed in the strong interaction regime when the quasi-particle pole approximation is inapplicable. In this regime, the integral representation for the half-space Green's tensor is difficult to use while its electrostatic limiting expression is grossly inadequate. However, the analytical expansion derived in this paper can be used directly and efficiently. The results of this study are also relevant to nano-optics and near-field imaging, especially when tomographic image reconstruction is involved.

General theory based on fluctuational electrodynamics for van der Waals interactions in colloidal systems

A rigorous theory for the determination of the van der Waals interactions in colloidal systems is presented. The method is based on fluctuational electrodynamics and a multiple-scattering method which provides the electromagnetic Green's tensor. In particular, expressions for the Green's tensor are presented for arbitrary, finite collections of colloidal particles, for infinitely periodic or defected crystals, as well as for finite slabs of crystals. The presented formalism allows for ab initio calculations of the van der Waals interactions in colloidal systems since it takes fully into account retardation, many-body, multipolar, and near-field effects.

Surface plasmon polariton scattering by finite-size nanoparticles

The electromagnetic Green's tensor approach (GTA) is used to obtain the differential and total scattering cross sections of a finite-size nanoparticle located at a metal surface and illuminated with surface plasmon polaritons (SPPs). The scattering process comprehends either elastic scattering of the incident SPP into other SPPs propagating in different directions or scattering into field components propagating away from the surface, as well as the radiation absorption by the (metal) nanoparticle. Once the total electric field inside the scatterer is known, the expressions obtained allow for a comparison of the efficiency of the different scattering channels. Connection between the GTA and the point-dipole approximation (PDA) of the scattering problem is discussed, including the absorption of the SPP and the transition from the GTA to the PDA when the scatterer is approximated by a spherical particle of the same volume. SPP extinction spectra for gold cubic particles of various sizes placed in the vicinity of a flat gold surface are calculated with the GTA and compared with the results obtained using the PDA.

Travelling and evanescent parts of the optical near field

The optical near field of a localized source has been studied by means of the angular spectrum representation of the electromagnetic Green's tensor. This Green's tensor can be expressed in terms of four auxiliary functions, which depend on the field point through the dimensionless radial distance q to the source, or origin of coordinates, and the polar angle ρ with the z axis. Each function separates into a part containing travelling (radiative) waves and a part which is a superposition of evanescent (decaying) waves. We have derived series expansions in q of the four functions, both for the travelling and for the evanescent parts. It is shown that the travelling waves are finite at the origin of coordinates, and that all singular behaviour of the radiation field is governed by the evanescent waves. It is illustrated numerically that the series expansions are applicable up to about five wavelengths from the origin. In order to extend the range to also cover larger values of q, we have derived series expansions of the auxiliary functions which converge rapidly near the x-y plane, and a full asymptotic expansion with the z coordinate as the large variable. Finally, from the properties of the Taylor coefficients we have derived simple new integral representations for the auxiliary functions.

Travelling and evanescent parts of the optical near field

Abstract The optical near field of a localized source has been studied by means of the angular spectrum representation of the electromagnetic Green's tensor. This Green's tensor can be expressed in terms of four auxiliary functions, which depend on the field point through the dimensionless radial distance q to the source, or origin of coordinates, and the polar angle ρ with the z axis. Each function separates into a part containing travelling (radiative) waves and a part which is a superposition of evanescent (decaying) waves. We have derived series expansions in q of the four functions, both for the travelling and for the evanescent parts. It is shown that the travelling waves are finite at the origin of coordinates, and that all singular behaviour of the radiation field is governed by the evanescent waves. It is illustrated numerically that the series expansions are applicable up to about five wavelengths from the origin. In order to extend the range to also cover larger values of q, we have derived series expansions of the auxiliary functions which converge rapidly near the x-y plane, and a full asymptotic expansion with the z coordinate as the large variable. Finally, from the properties of the Taylor coefficients we have derived simple new integral representations for the auxiliary functions.

Traveling and evanescent parts of the electromagnetic Green's tensor.

The angular spectrum representation of the electromagnetic Green's tensor has a part that is a superposition of exponentially decaying waves in the +z and -z directions (evanescent part) and a part that is a superposition of traveling waves, both of which are defined by integral representations. We have derived an asymptotic expansion for the z dependence of the evanescent part of the Green's tensor and obtained a closed-form solution in terms of the Lommel functions, which holds in all space. We have shown that the traveling part can be extracted from the Green's tensor by means of a filter operation on the tensor, without regard to the angular spectrum integral representation of this part. We also show that the so-called self-field part of the tensor is properly included in the integral representation, and we were able to identify this part explicitly.

Theory of light scattering by surface polaritons in gyrotropic media

AbstractIn recent years considerable effort has been devoted to the experimental and theoretical investigation of surface polaritons in dielectric and conducting media. In metals and semiconductors containing free carriers, interesting phenomena are exhibited by surface plasmon polaritons in the presence of an external magnetic field. A useful tool for probing such phenomena is the inelastic scattering of light. The theory of light scattering from surface polaritons can be conveniently developed in terms of the electromagnetic Green's tensor for the medium with a free surface. We have calculated the elements of the electromagnetic Green's tensor for a homopolar medium containing free carriers which is placed in a constant magnetic field normal to the surface. An expression for the light scattering cross‐section has been derived. Other applications of the electromagnetic Green's tensor are discussed.