Electromagnetic modes and resonances of two-dimensional bodies

Abstract

The electromagnetic modes and the resonances of homogeneous, finite size, two-dimensional bodies are examined in the frequency domain by a rigorous full wave approach based on an integro-differential formulation of the electromagnetic scattering problem. Using a modal expansion for the current density that disentangles the geometric and material properties of the body the integro-differential equation for the induced surface (free or polarization) current density field is solved. The current modes and the corresponding resonant values of the surface conductivity (eigen-conductivities) are evaluated by solving a linear eigenvalue problem with a non-Hermitian operator. They are inherent properties of the body geometry and do not depend on the body material. The material only determines the coefficients of the modal expansion and hence the frequencies at which their amplitudes are maximum (resonance frequencies). The eigen-conductivities and the current modes are studied in detail as the frequency, the shape and the size of the body vary. Open and closed surfaces are considered. The presence of vortex current modes, in addition to the source-sink current modes (no whirling modes), which characterize plasmonic oscillations, is shown. Important topological features of the current modes, such as the number of sources and sinks, the number of vortexes, the direction of the vortexes are preserved as the size of the body and the frequency vary. Unlike the source-sink current modes, in open surfaces the vortex current modes can be resonantly excited only in materials with positive imaginary part of the surface conductivity. Eventually, as examples, the scattering by two-dimensional bodies with either positive or negative imaginary part of the surface conductivity is analyzed and the contributions of the different modes are examined.

Time-Domain Formulation of Electromagnetic Scattering Based on a Polarization Mode Expansion and the Principle of Least Action

“…The transverse (magnetostatic) modes of the particle are solution of the eigenvalue problem [22], [23] V…”

Resonance frequency and radiative Q-factor of plasmonic and dielectric modes of small objects

“…All these nomenclatures are equivalent. It was shown that this two sets of modes, even if this distinction is made in the long-wavelength regime, remain well distinguishable and have different properties even in the full-wave regime 23,27,28 .…”

“…where both the set of modes {u h (r)} and {v h (r)} are normalized, u * h , u h = 1 and v * h , v h = 1 for any h. This expansion is very useful because it separates the dependence on the material from the dependence on the geometry 23,24,27,45,46 , and has been used in different contexts 28,47,48 .…”

“…Refs. 17,18 ), surface [19][20][21][22][23] , and line integral formulations of the Maxwell's equations 24 , differential formulations (e.g. 25,26 ), Mie Theory (e.g.…”

Enhancing Electric Fields in High-Index Resonators by Flux Conservation of the Displacement Current Density

“…2a with minor radius r, major radius R, with R = 2r, corresponding width w 0 = R − r = r, and a thickness h. To simplify our analysis, and only within the current subsection, we make the additional assumption that the ring has thickness h much smaller than R: under this hypothesis we can use the approximated method introduced in Ref. 41 to calculate the magnetoquasistatic modes of the ring, instead of the threedimensional but more computationally intensive method presented in. 22 The first seven modes exhibited by the ring resonator are shown in Figure 3a, which are are independent of h as long as h l c .…”