我们在 axion electrodynamics（轴子电动力学）框架内构建了拓扑绝缘体（TI）分层球的并矢格林函数（DGFs）。对于这些 DGFs，包含了额外的展开系数以解释轴子耦合效应。通过应用这些 DGFs，我们推导了偶极子附近 TI 分层球的光散射公式。在我们的数值研究中，我们给出了三种配置（金属涂覆的 TI 球、金属-TI-金属涂覆的 TI 球和交替的金属-TI 分层球），以研究 TI 球（壳）的 topological magneto-electric（TME，拓扑磁电）响应如何影响金属壳的多极等离激元共振。对于这些类型，结果表明 TME 效应导致偶极子附近 TI 分层球的衰变率光谱发生了一些修正。对于金属壳的多极共振，观察到 TME 诱导的成键和低阶反成键模式的红移，但高阶反成键模式的红移不显著。此外，对于金属涂覆的 TI 球，我们考虑了 TI 核心中的损耗效应，其介电函数选择为 bulk 或五层五重层（5QL）板的形式，然后 TME 诱导的衰变率光谱的一些修正被明显抑制。这些现象学特征为通过分子荧光实验探测 TME 效应提供了有用的指导。
英文摘要：
We construct the dyadic Greens functions (DGFs) for a topological insulator (TI) stratified sphere within the framework of axion electrodynamics. For these DGFs, the additional expansion coefficients are included to account for the axion coupling effect. With the application of these DGFs, we derive the formulation of light scattering from a dipole near a TI stratified sphere. In our numerical studies, we give three types of configurations (a metal-coated TI sphere, a metal-TI-metal-coated TI sphere and an alternating metal-TI stratified sphere) to investigate how the topological magneto-electric (TME) response of the TI sphere (shells) influences on the multipolar plasmonic resonance of the metal shells. For these types, the results show that the TME effect causes some modifications of the decay rate spectrum for an emitting dipole near a TI stratified sphere. For the multipolar resonances of the metal shells, it is observed that the TME-induced red-shifts for the bonding and lower order antibonding modes are found but those for the higher order antibonding modes are insignificant. In addition, for a metal-coated TI sphere, we take into account the effects of losses in the TI core of which the dielectric function is chosen to be the form of the bulk or five quintuple layers (5QL) slab and then the some modifications of the TME-induced decay rate spectrum are obviously suppressed. These phenomenological characteristics provide useful guidance to probing the TME effect via molecular fluorescence experiments.
In this paper, we have derived planar multilayer dyadic Greens functions by Fourier expansion method and have checked its correctness by comparing results for reflected electric fields from dipole emissions near such structures available in previous literature. Furthermore, we show how these dyadic Greens functions can be applied to calculate reflected fields from a dipole source with arbitrary orientations. We believe our formulation will be powerful in the modeling of molecular fluorescence near these structures.
Dyadic Green functions for time-harmonic fields in a homogeneous, isotropic, dielectric-magnetic medium, moving with constant velocity, are derived by first implementing a simple transformation and then using the dyadic Green functions available for uniaxial dielectric-magnetic mediums.
The dyadic Green function for a homogeneous electromagnetic medium inspired by the spatiotemporally nonhomogeneous constitutive equations of gravitationally affected vacuum is derived.
The spectral functions are studied in conjunction with the dyadic Green's functions for various media. The dyadic Green's functions are found using the eigenfunction expansion method for homogeneous, inhomogeneous, periodic, lossless, lossy, and anisotropic media, guided by the Bloch- Floquet theorem. For the lossless media cases, the spectral functions can be directly related to the photon local density of states, and hence, to the electromagnetic energy density. For the lossy case, the spectral function can be related to the field correlation function. Because of these properties, one can de…
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…
A comprehensive theoretical analysis of photo-induced forces in an illuminated nanojunction, formed between an atomic force microscopy tip and a sample, is presented. The formalism is valid within the dipolar approximation and includes multiple scattering effects between the tip, sample and a planar substrate through a dyadic Green's function approach. This physically intuitive description allows a detailed look at the quantitative contribution of multiple scattering effects to the measured photo-induced force, effects that are typically unaccounted for in simpler analytical models. Our findin…
Based on the dyadic Green's function (DGF) method, we present a formalism to study the propagation of electromagnetic fields with slowly varying amplitude (EMFSVA) in dispersive anisotropic media with two dyadic constitutive parameters, the dielectric permittivity and the magnetic permeability. We find the matrix elements of the envelope DGFs by applying the formalism for uniaxial anisotropic metamaterials. We present the relations for the velocity of the EMFSVA envelopes which agree with the known definition of the group velocity in dispersive media. We consider examples of propagation of the…
We discuss the renormalization of the polarizability of a nanoparticle in the presence of either (i) a continuous graphene sheet or (ii) a plasmonic graphene grating, taking into account retardation effects. Our analysis demonstrates that the excitation of surface plasmon-polaritons in graphene produces a large enhancement of the real and imaginary parts of the renormalized polarizability. We show that the imaginary part can be changed by a factor of up to 100 relatively to its value in the absence of graphene. We also show that the resonance in the case of the grating is narrower than in the …
We present all the periodic Green function dyadics that enter a description of a 2d array of emitters at the level that includes the electric dipole, magnetic dipole and electric quadrupole moment of each emitter. We find a concise analytic form for the radiative contributions to the periodic Green function dyadics that give rise to radiation reaction fields, and we give the non-radiative contributions that do not affect energy balance in the form of rapidly converging series. Finally, we present an approximation scheme for evaluating periodic Green function dyadics at long wavelengths that ri…
The near-field spectroscopic information is critically important to determine the Forster resonant energy transfer(FRET) rate and the distance dependence in the vicinity of metal surfaces. The high density of evanescent near-field modes in the vicinity of a metal surface can strongly modulate the FRET in multichromophoric systems. Based on the previous generalized FRET [A. Poudel, X. Chen and M. Ratner, J. Phys. Chem. Lett. 7(2016) 955], the theory of FRET is generalized for the multichromophore aggregates and nonequilibrium situations in the vicinity of evanescent surface electromagnetic wave…
pyGDM is a python toolkit for electro-dynamical simulations of individual nano-structures, based on the Green Dyadic Method (GDM). pyGDM uses the concept of a generalized propagator, which allows to solve cost-efficiently monochromatic problems with a large number of varying illumination conditions such as incident angle scans or focused beam raster-scan simulations. We provide an overview of new features added since the initial publication [Wiecha, Computer Physics Communications 233, pp.167-192 (2018)]. The updated version of pyGDM is implemented in pure python, removing the former dependenc…
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…
The dyadic Green functions for a uniaxial dielectric-magnetic medium, together with a reversible field transformation, were implemented to derive a formulation of the Huygens principle appropriate to a uniaxial dielectric-magnetic medium with gyrotropic-like magnetoelectric properties.
Hybrid spectral-spatial representations are introduced to rapidly calculate periodic scalar and dyadic Green's functions of the Helmholtz equation for 2D and 3D configurations with a 1D (linear) periodicity. The presented schemes work seamlessly for any observation location near the array and for any practical array periodicities, including electrically small and large periodicities. The representations are based on the expansion of the periodic Green's functions in terms of the continuous spectral integrals over the transverse (to the array) spectral parameters. To achieve high convergence an…
We develop an analytic formalism to describe dipole radiation near the Dirac cone of a two-dimensional photonic crystal slab. In contrast to earlier work, we account for all polarization effects and derive a closed-form expression for the dyadic Green's function of the geometry. Using this analytic Green's function, we demonstrate that the dipolar interaction mediated by the slab exhibits winding phases, which are key ingredients for engineering topological systems for quantum emitters, as discussed in detail in J. Perczel et al., (2018), arXiv:1810.12299. As an example, we study the coherent …
We theoretically investigate the enhancement of surface enhanced Raman spectroscopy (SERS) using hyperbolic stratified nanostructures and compare to metal nanoresonators. The photon Green function of each nanostructure within its environment is first obtained from a semi-analytical modal theory, which is used in a quantum optics formalism of the molecule-nanostructure interaction to model the SERS spectrum. An intuitive methodology is presented for calculating the single molecule enhancement factor (SMEF), which is also able to predict known experimental SERS enhancement factors of an example …
