Additivity of Integral Optical Cross Sections for a Fixed Tenuous Multi-Particle Group

We use the volume integral equation formulation of frequency-domain electromagnetic scattering to settle the issue of additivity of the extinction, scattering, and absorption cross sections of a fixed tenuous group of particles. We show that all the integral optical cross sections of the group can be obtained by summing up the corresponding individual-particle cross sections provided that the single-scattering approximation applies

Simulating electron energy-loss spectroscopy and cathodoluminescence for particles in arbitrary host medium using the discrete dipole approximation

Electron energy-loss spectroscopy (EELS) and cathodoluminescence (CL) are widely used experimental techniques for characterization of nanoparticles. The discrete dipole approximation (DDA) is a numerically exact method for simulating interaction of electromagnetic waves with particles of arbitrary shape and internal structure. In this work we extend the DDA to simulate EELS and CL for particles embedded into arbitrary (even absorbing) unbounded host medium. The latter includes the case of the dense medium, supporting the Cherenkov radiation of the electron, which has never been considered in EELS simulations before. We build a rigorous theoretical framework based on the volume-integral equation, final expressions from which are implemented in the open-source software package ADDA. This implementation agrees with both the Lorenz-Mie theory and the boundary-element method for spheres in vacuum and moderately dense host medium. And it successfully reproduces the published experiments for particles encapsulated in finite substrates. The latter is shown for both moderately dense and Cherenkov cases - a gold nanorod in $\text{SiO}_{\text{2}}$ and a silver sphere in $\text{SiN}_{\text{x}}$ respectively.Comment: 36 pages, 15 figure

On the Concept of Random Orientation in Far-Field Electromagnetic Scattering by Nonspherical Particles

Although the model of randomly oriented nonspherical particles has been used in a great variety of applications of far-field electromagnetic scattering, it has never been defined in strict mathematical terms. In this Letter we use the formalism of Euler rigid-body rotations to clarify the concept of statistically random particle orientations and derive its immediate corollaries in the form of most general mathematical properties of the orientation-averaged extinction and scattering matrices. Our results serve to provide a rigorous mathematical foundation for numerous publications in which the notion of randomly oriented particles and its light-scattering implications have been considered intuitively obvious

Retrieving refractive index of single spheres using the phase spectrum of light-scattering pattern

We analyzed the behavior of the complex Fourier spectrum of the angle-resolved light scattering pattern (LSP) of a sphere in the framework of the Wentzel-Kramers-Brillouin (WKB) approximation. Specifically, we showed that the phase value at the main peak of the amplitude spectrum almost quadratically depends on the particle refractive index, which was confirmed by numerical simulations using both the WKB approximation and the rigorous Lorenz-Mie theory. Based on these results, we constructed a method for characterizing polystyrene beads using the main peak position and the phase value at this point. We tested the method both on noisy synthetic LSPs and on the real data measured with the scanning flow cytometer. In both cases, the spectral method was consistent with the reference non-linear regression one. The former method leads to comparable errors in retrieved particle characteristics but is 300 times faster than the latter one. The only drawback of the spectral method is a limited operational range of particle characteristics that need to be set a priori due to phase wrapping. Thus, its main application niche is fast and precise characterization of spheres with small variation range of characteristics.Comment: 16 pages, 9 figures, 2 table

A point electric dipole: From basic optical properties to the fluctuation–dissipation theorem

We comprehensively review the deceptively simple concept of dipole scattering in order to uncover and resolve all ambiguities and controversies existing in the literature. First, we consider a point electric dipole in a non-magnetic environment as a singular point in space whose sole ability is to be polarized due to the external electric field. We show that the postulation of the Green’s dyadic of the specific form provides the unified description of the contribution of the dipole into the electromagnetic properties of the whole space. This is the most complete, concise, and unambiguous definition of a point dipole and its polarizability. All optical properties, including the fluctuation–dissipation theorem for a fluctuating dipole, are derived from this definition. Second, we obtain the same results for a small homogeneous sphere by taking a small-size limit of the Lorenz–Mie theory. Third, and most interestingly, we generalize this microscopic description to small particles of arbitrary shape. Both bare (static) and dressed (dynamic) polarizabilities are defined as the double integrals of the corresponding dyadic transition operator over the particle’s volume. While many derivations and some results are novel, all of them follow from or are connected with the existing literature, which we review throughout the paper

Addendum to "Impressed Sources and Fields in the Volume-Integral-Equation Formulation of Electromagnetic Scattering by a Finite Object: A Tutorial"

Our recent tutorial referred to in the title has summarized a general theoretical formalism of electromagnetic scattering by an arbitrary finite object in the presence of arbitrarily distributed impressed currents. This addendum builds on the tutorial to provide a streamlined discussion of specific far-field limits and the corresponding reciprocity relations by introducing appropriate far-field operators and linear maps and deriving the reciprocity relations through the pseudo adjoint of these maps. We thereby extend the compact operator calculus used previously to consider the fields and sources near or inside the scattering object