Electromagnetic Green Research Articles

Scale-Dependent Heat Transport in Dissipative Media via Electromagnetic Fluctuations.

We develop a theory for heat transport via electromagnetic waves inside media, and use it to derive a spatially nonlocal thermal conductivity tensor, in terms of the electromagnetic Green's function and potential, for any given system. While typically negligible for optically dense bulk media, the electromagnetic component of conductivity can be significant for optically dilute media, and shows regimes of Fourier transport as well as unhindered transport. Moreover, the electromagnetic contribution is relevant even for dense media, when in the presence of interfaces, as exemplified for the in-plane conductivity of a nanosheet, which shows a variety of phenomena, including absence of a Fourier regime.

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.

Modeling of a Plasmonic Biosensor Based on a Graphene Nanoribbon Superlattice

A semi‐analytical theoretical model is presented, which describes the operation of a selective molecular sensor employing a double resonance between a dipole‐active molecular vibration mode, tunable surface plasmons in a periodic structure of graphene nanoribbons (NRs), and the incident light, in the THz‐to‐IR range, used for testing. The model is based on the solution of Maxwell's equations for the NR structure deposited on a dielectric substrate, using the electromagnetic Green's function, and is extended to the case of an additional (buffer) layer present between the NRs and the substrate. Both the graphene NRs and the layer of adsorbed molecules are considered as 2D, since their thicknesses are very small in comparison with the wavelength of the incident light. The model is applied to different molecular systems, the protein studied by Rodrigo et al. [Science 2015, 349, 165], for which an excellent agreement with experimental data is obtained, and an organometallic molecule Cd(CH3)2. Two different assumptions concerning the way of sticking of the analyte molecules to the sensor's surface are considered and the limitations of these sensing principles are discussed.

Full- Wave Modeling of the Emission of a Microwave Frequency Single Photon Source

Single photon sources are an important component in many quantum information processing systems. Despite their importance, current modeling methods predominantly focus on developing optimistic performance bounds, and are not conducive to performing engineering optimization studies. To enhance the capability of modeling methods, we propose a process to utilize the classical electromagnetic dyadic Green's function of a system as an integral component of determining the emitted photon states produced by a single photon source. Importantly, the Green's function can be readily computed using standard fullwave numerical methods, making it a viable analysis tool. We demonstrate this process by characterizing the emission of a microwave frequency single photon source that uses a transmon as a quantum emitter, and find qualitative agreement with a fabricated device that has similar design characteristics.

Green's-function formalism for resonant interaction of x rays with nuclei in structured media

The resonant interaction between x-ray photons and nuclei is one of the most exciting subjects of the burgeoning field of x-ray quantum optics. A resourceful platform used so far are thin-film x-ray cavities with embedded layers or M\"ossbauer nuclei such as $^{57}\mathrm{Fe}$. A new quantum optical model based on the classical electromagnetic Green's function is developed to investigate theoretically the nuclear response inside the x-ray cavity. The model is versatile and provides an intuitive picture about the influence of the cavity structure on the resulting spectra. We test its predictive powers with the help of the semiclassical coherent scattering formalism simulations and discuss our results for increasing complexity of layer structures.

Full electromagnetic Green's dyadic of spherically symmetric open optical systems and elimination of static modes from the resonant-state expansion

A general analytic form of the full 6x6 dyadic Green's function of a spherically symmetric open optical system is presented, with an explicit solution provided for a homogeneous sphere in vacuum. Different spectral representations of the Green's function are derived using the Mittag-Leffler theorem, and their convergence to the exact solution is analyzed, allowing us to select optimal representations. Based on them, more efficient versions of the resonant-state expansion (RSE) are formulated, with a particular focus on the static mode contribution, including versions of the RSE with a complete elimination of static modes. These general versions of the RSE, applicable to non-spherical optical systems, are verified and illustrated on exactly solvable examples of a dielectric sphere in vacuum with perturbations of its size and refractive index, demonstrating the same level of convergence to the exact solution for both transverse electric and transverse magnetic polarizations.

Dimensional reduction of the electromagnetic sector of the nonminimal standard model extension

In the current paper, we construct a Lorentz-violating electrodynamics in (1+2) spacetime dimensions from the electromagnetic sector of the nonminimal Standard-Model Extension (SME) in (1+3) dimensions. Subsequently, we study some of the basic properties of this framework. We obtain the field equations, the Green's functions, and the perturbative Feynman rules. Furthermore, the modified dispersion relations are computed at leading order in Lorentz violation. We then remove the unphysical degrees of freedom from the electromagnetic Green's function that are present due to gauge invariance. The resulting object is used to construct the general solutions of the uncoupled field equations with external inhomogeneities present. This modified planar electrodynamics may be valuable to describe electromagnetic phenomena in two-dimensional condensed-matter systems. Furthermore, it supports a better understanding of the electromagnetic sector of the nonminimal SME.

The antenna spacetime system theory of wireless communications

A general deterministic spacetime system theory of antennas suitable for the analysis and design of wireless communication links is rigorously developed using the recently introduced antenna current Green's function formalism. We provide the first complete derivation of the antenna spatio-temporal response to a delta source using only electromagnetic Green's functions, effectively eliminating all field and current distributions in the final expressions. While the theory works well in both space and time, it puts into sharper focus how the spatio-temporal structure of electromagnetic processes imposes restrictions on the signal processing capabilities of antenna systems by constraining the allowable mathematical form of the effective impulse response of the global wireless communication link. It is shown that the antenna current Green's functions of both the receive and transmit terminals, plus the propagation environment Green's functions, are the only quantities needed to obtain the single input–single output link response function in closed form. One of the results deduced from the theory is that an exact impulse response cannot be ascribed to an arbitrary antenna in general, but may be approximated for many applications. The theory can be deployed for future antenna systems research to boost up spectral efficiency (without increasing physical bandwidth) by directly incorporating electromagnetic knowledge into the design of the communication system's signal processing functions.

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.

Incoherent component of light scattered by a monolayer of spherical particles: analysis of angular distribution and absorption of light.

We have derived an analytical solution for an incoherent component of light scattered by a normally illuminated monolayer of homogeneous spherical particles. It is based on the quasi-crystalline approximation of the theory of multiple scattering of waves as well as on the multipole expansion of electromagnetic fields and tensor Green's function in terms of vector spherical wave functions. We apply the solution to a description of scattering and absorption characteristics of partially ordered monolayers and monolayers with imperfect lattices. The impact of particle size and type of particle spatial order on light absorption is studied. The comparison of calculated and available experimental data is made on the angular and spectral position of the first diffraction order peak for a monolayer with an imperfect triangular lattice from silicon dioxide particles. The theoretical and experimental data are in close agreement.

Electromagnetic δ -function sphere

We develop a formalism to extend our previous work on the electromagnetic $\delta$-function plates to a spherical surface. The electric ($\lambda_e$) and magnetic ($\lambda_g$) couplings to the surface are through $\delta$-function potentials defining the dielectric permittivity and the diamagnetic permeability, with two anisotropic coupling tensors. The formalism incorporates dispersion. The electromagnetic Green's dyadic breaks up into transverse electric and transverse magnetic parts. We derive the Casimir interaction energy between two concentric $\delta$-function spheres in this formalism and show that it has the correct asymptotic flat plate limit. We systematically derive expressions for the Casimir self-energy and the total stress on a spherical shell using a $\delta$-function potential, properly regulated by temporal and spatial point-splitting, which are different from the conventional temporal point-splitting. In strong coupling, we recover the usual result for the perfectly conducting spherical shell but in addition, there is an integrated curvature-squared divergent contribution. For finite coupling, there are additional divergent contributions; in particular, there is a familiar logarithmic divergence occurring in the third order of the uniform asymptotic expansion that renders it impossible to extract a unique finite energy except in the case of an isorefractive sphere, which translates into $\lambda_g=-\lambda_e$.

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.

Atom-light interactions in quasi-one-dimensional nanostructures: A Green's-function perspective

Based on a formalism that describes atom-light interactions in terms of the classical electromagnetic Green's function, we study the optical response of atoms and other quantum emitters coupled to one-dimensional photonic structures, such as cavities, waveguides, and photonic crystals. We demonstrate a clear mapping between the transmission spectra and the local Green's function that allows to identify signatures of dispersive and dissipative interactions between atoms. We also demonstrate the applicability of our analysis to problems involving three-level atoms, such as electromagnetically induced transparency. Finally we examine recent experiments, and anticipate future observations of atom-atom interactions in photonic bandgaps.

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.

Simultaneously giant enhancement of Förster resonance energy transfer rate and efficiency based on plasmonic excitations

By using an exact multiscattering electromagnetic Green's function method, we present rigorous calculations on the rate and efficiency of F\"orster resonance energy transfer (FRET) from a donor to an acceptor when they are located in the hotspots of nanoparticle clusters. A nonlocal effect has been considered by using a hydrodynamic model. It is found that the FRET rate and efficiency can be enhanced simultaneously by more than 9 and 3 orders of magnitude, respectively, due to the strong coupling plasmon resonances originating from collective excitations of nanoparticle clusters. The physical origins for these phenomena have been disclosed. Two opposite phenomena, the energy transfer rate being independent or dependent on the local density of optical states (LDOS), have been observed in the same system under different conditions. These findings not only help us to understand the unresolved debate on how the FRET rate depends on the LDOS, but also provide a way to realize ultrafast the energy transfer process with ultrahigh efficiency.

Electromagnetic Green's function for layered topological insulators

The dyadic Green's function of the inhomogeneous vector Helmholtz equation describes the field pattern of a single frequency point source. It appears in the mathematical description of many areas of electromagnetism and optics including both classical and quantum, linear and nonlinear optics, dispersion forces (such as the Casimir and Casimir-Polder forces) and in the dynamics of trapped atoms and molecules. Here, we compute the Green's function for a layered topological insulator. Via the magnetoelectric effect, topological insulators are able to mix the electric, E, and magnetic induction, B, fields and, hence, one finds that the TE and TM polarizations mix on reflection from/transmission through an interface. This leads to novel field patterns close to the surface of a topological insulator.

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.

A fast Fourier transform accelerated Ewald summation technique for the vector electromagnetic rectangular cavity Green's function

A fast Fourier transform accelerated Ewald method for the computation of the vector electromagnetic rectangular cavity Green's function in terms of the electric field due to electric currents is presented and used in a boundary integral formulation. The Ewald summation technique suffers from the high-frequency breakdown when it is applied to Green's functions of wave problems. In the case of the rectangular cavity Green's function, the number of necessary terms in the spectral series grows, therefore, cubically with frequency for a given accuracy. To counteract the high-frequency breakdown, the evaluation of the spectral series is accelerated with an inverse fast Fourier transform in this work. At high frequencies, a speed-up of up to four orders of magnitude is achieved. As an application example, a reverberation chamber containing a metallic enclosure and a mode-stirrer is modeled.