Akhlesh Lakhtakia, Tom G. Mackay
The dyadic Green function for a homogeneous electromagnetic medium inspired by the spatiotemporally nonhomogeneous constitutive equations of gravitationally affected vacuum is derived.
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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.
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.
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…
General and concise operator approach to the dyadic Green's function of layered media
本文提出一种通用简洁的算子方法，用于推导各向异性平面层介质的二阶格林函数，适用于电场和磁场，通过演算算子和表面阻抗张量简化了问题理解和应用。
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 …
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…
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…
Dyadic Greens function for a topological insulator stratified sphere
本文在轴子电动力学框架内构建了拓扑绝缘体分层球的并矢格林函数，推导了偶极子光散射公式，并通过数值研究三种分层球配置揭示了拓扑磁电效应对多极等离激元共振和衰变率光谱的修正作用，为分子荧光实验提供了指导。
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.
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…
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…
Accelerating Inverse Design of Optical Metasurfaces: Analytic Gradients of Periodic Green's Functions via Quasi-Modular Forms
本研究提出了一种解析梯度引擎，通过拟模形式理论实现周期格林函数的精确梯度计算，从而加速光学超材料的逆设计。
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 …
A medium which is an isotropic chiral medium from the perspective of a co-moving observer is a Faraday chiral medium (FCM) from the perspective of a non-co-moving observer. The Tellegen constitutive relations for this FCM are established. By an extension of the Beltrami field concept, these constitutive relations are exploited to show that planewave propagation is characterized by four generally independent wavenumbers. This FCM can support negative phase velocity at certain translational velocities and with certain wavevectors, even though the corresponding isotropic chiral medium does not. T…
Coupled Dipole Oscillation Enabled Scintillation Compensation in Turbulence-Impacted Laser Beam
本工作扩展洛伦兹模型至非线性恢复力，结合并矢格林函数建立非局域介质框架，通过简正模式微扰展开获得有效非线性磁化率核，并利用标量格林函数推导输出场，桥接微观偶极动力学与宏观光学传播，为湍流影响下的激光闪烁补偿提供理论支撑。
TorchGDM: A GPU-Accelerated Python Toolkit for Multi-Scale Electromagnetic Scattering with Automatic Differentiation
本文提出基于 PyTorch 和 GDM 的 GPU 加速框架 torchGDM，支持混合离散/偶极模型与多尺度近场模拟，并利用自动微分求解纳米光子优化及逆问题。
Dynamical Drexhage Effect: Amplified Emission in Time-Modulated Electromagnetic Environments
研究非相对论运动对靠近反射界面的偶极子发射动力学的影响，通过宏观量子电动力学框架推导偶极子振幅的运动方程，发现动态扩展的Drexhage效应，特定调制轨迹可使偶极子振幅和辐射强度增强。
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