Electromagnetic resonances observed in small, charged particles

Highlights

• Electromagnetic waves resonate with surface excitations of a charged dielectric particle.

• Physics interpretation of resonance mode is an excitation of the odd surface plasmon.

• Net electric charge enhances scattering efficiency and absorption of electromagnetic field.

• Electric charge reduces scattering and absorption in very small particles.

• The effect can have important consequences for remote sensing of particulate systems.

Abstract

When a particle is charged, electrons can move freely along its surface and influence its optical properties in the same way as a thin, nonuniform metallic layer. These electrons contribute to scattering phenomena, including resonances. We model the light scattering from charged particles and demonstrate that these resonances result from excitation of an anti-symmetric surface plasmon at the layer interfaces. The modeling explains suppression of absorption when the size of the charged particle decreases, as well as differences in the light-scattering efficiencies of as much as a factor of 2 that occur before and after the resonance. These light-scattering properties must be taken into consideration when performing remote-sensing studies of charged particles, like those in the interstellar medium and dust storms.

Introduction

The observation [1] and explanation [2] of optical resonances in micron-size particles opened a new field of particle characterization [3]. Resonances in nanometer-size particles also have shown potential to manipulate light and characterize material properties [4], [5], [6]. The focus of this work is the recent efforts performed within the last decade on how excess charge also can resonate with the incident electromagnetic field and influence the light scattered by nanometer-size particles [7], [8]. Charge-induced resonances encompass a large family of optical effects that could be useful new tools. These can include light manipulation using optical switches, which, for example, can be constructed by applying a charge to a particle to transform it from a predominantly forward-scattering particle to predominately backward-scattering particle. Another research investment that escalated in the last decade resulted in new means of particle characterization using net charge optical effects, e.g. charged particles were found to change the radar power ratio [9], affect the magnitude of the radiation pressure cross-sections that may be used for optical tweezers [10], or result in an increase of the Global Positioning System (GPS) signal attenuation by almost two orders of magnitude, thus providing a new tool for exploration of electrostatic processes in plumes using GPS [11].

Resonances of a charged spherical particle with an incident wave can be formulated mathematically in terms of the conventional Lorenz-Mie solution with a modified boundary condition on the particle surface (see e.g. [12], [13], [14]). While early attempts by Xie et al. [15] and Li et al. [16] to introduce a piecewise rectangular function to simulate the surface current density on a partially charged particle, it was later demonstrated by Klačka et al. [17] that the use of a separation-of-variables method is not applicable to such a model, and this was later corrected by Zhou et al. [18]. Charged-particle resonances in the long-wavelength limit have been demonstrated in a number of numerical studies [19], [20], while the optical enhancement is specifically massive in absorption [21], [22]. However, the physics of charge-induced resonances still remains largely unexplored. Our goal in this work is to interpret the nature of that optical phenomena and provide a better understanding of an underlying physics.

We propose a simple physical model which reproduces, both qualitatively and quantitatively, the observed resonant phenomena when an electromagnetic wave is scattered by a charged particle. In our model, additional electric charge is allowed to move freely at the particle surface, which could be described as a thin metallic layer coating the dielectric sphere. The incident electromagnetic field excites in the metallic layer a surface plasmon resonance [23], [24], which strongly enhances the scattering and absorption of the charged particle. In contrast to photonics, where the wavelength of the electromagnetic wave is comparable to the size of the coated or metallic particles, we are interested in the long-wavelength limit in which the wavelength is much larger than the radius of the spherical particle. Nevertheless, the extraordinary scattering efficiency has the same origin: excitation of a surface plasmon at the interface between a metal and dielectric [25], [26], [27].

The paper is organized as follows: In Section 2 we introduce the model and present the method of calculation of the electric field and scattering parameters. Of particular importance is a system of linear equations that determines the coefficients of expansion of the electric field into a series of spherical functions. In Section 3 we present a simple model to calculate the scattering parameters for a thin metallic spherical shell. For lossless metal, we observe sharp resonance in the long wavelength limit, which is due to the excitation of the anti-symmetric plasmonic resonance in the metallic shell, which is demonstrated by the spatial dependence of radial electric field. In the resonance, the electric field inside the shell increases by orders of magnitude. A more accurate and rigorous model is analyzed in Section 4. We calculate the scattering efficiency for a real dielectric particle and study how the scattering properties change with the thin metallic coating. This model mimics a free charge adsorbed at the particle surface. Finally, in Section 5 we compare our findings to other modeling results. In particular, we have found very good agreement with the quasi-static approximation. The results are discussed in Section 6.