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.

References in corpus (13)

• 2D materials and van der Waals heterostructures
• Two-Dimensional Material Nanophotonics
• Optical modulators with two-dimensional layered materials
• Polaritons in layered 2D materials
• A new electromagnetic mode in graphene
• Light interaction with photonic and plasmonic resonances
• Light matter interaction in transition metal dichalcogenides and their heterostructures
• Analytical Modeling of Graphene Plasmons
• Plasmonic eigenmodes in individual and bow-tie graphene nanotriangles
• The resonant dynamics of arbitrarily-shaped meta-atoms
• Material-independent modes for electromagnetic scattering
• Volume Integral Formulation for the Calculation of Material Independent Modes of Dielectric Scatterers
• Resonances in small scatterers with impedance boundary

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• Operative Approach to Quantum Electrodynamics in Dispersive Dielectric Objects Based on a Polarization Modal Expansion
• Time-Domain Formulation of Electromagnetic Scattering Based on a Polarization Mode Expansion and the Principle of Least Action
• Lower Bounds to the Q factor of Electrically Small Resonators through Quasistatic Modal Expansion
• Static surface mode expansion for the full-wave scattering from penetrable objects
• Enhancing Electric Fields in High-Index Resonators by Flux Conservation of the Displacement Current Density
• Electromagnetic Scattering by Networks of High-Permittivity Thin Wires