Green formulation for studying electromagnetic scattering from graphene-coated wires of arbitrary section

Abstract

We present a rigorous electromagnetic method based on Green's second identity for studying the plasmonic response of graphene-coated wires of arbitrary shape. The wire is illuminated perpendicular to its axis by a monochromatic electromagnetic wave and the wire substrate is homogeneous and isotropic. The field is expressed everywhere in terms of two unknown source functions evaluated on the graphene coating which can be obtained from the numerical solution of a coupled pair of inhomogeneous integral equations. To assess the validity of the Green formulation, the scattering and absorption efficiencies obtained numerically in the particular case of circular wires are compared with those obtained from the multipolar Mie theory. An excellent agreement is observed in this particular case, both for metallic and dielectric substrates. To explore the effects that the break of the rotational symmetry of the wire section introduces in the plasmonic features of the scattering and absorption response, the Green formulation is applied to the case of graphene-coated wires of elliptical section. As might be expected from symmetry arguments, we find a two-dimensional anisotropy in the angular optical response of the wire, particularly evident in the frequency splitting of multipolar plasmonic resonances. The comparison between the spectral position of the enhancements in the scattering and absorption efficiency spectra for low-eccentricity elliptical and circular wires allows us to guess the multipolar order of each plasmonic resonance. We present calculations of the near field distribution for different frequencies which explicitly reveal the multipolar order of the plasmonic resonances. They also confirm the previous guess and serve as a further test on the validity of the Green formulation.

Spontaneous emission in plasmonic graphene subwavelength wires of arbitrary sections

“…To find these functions we convert the system of integral equations into matrix equations which are solved numerically (see [28] and references therein). Once the functions ϕ 1 and ∂ϕ 1 /∂n are determined, the scattered field, given by Eqs.…”

“…(7) can be greatly simplified using the asymptotic expansion of the Hankel function for large argument [38]. After some algebraic manipulation, we obtain [28] …”

Dispersion properties of plasmonic sub-wavelength elliptical wires wrapped with graphene

“…( 35) with i = x and i = y for x and y polarization, respectively, (continuous line). The calculation also was made by using a rigorous method based on the Green surface integral method (GSIM) (dashed line) [35]. Two peaks are observed.…”

“…We also provided analytical expressions for the scattered power when the graphene elliptical wire is excited by a plane wave. All scattering curves are compared with those obtained by applying a rigorous formalism based in the Green surface integral method [35,36] valid for arbitrary shaped cross sections.…”

Combined plasmon-resonance and photonic-jet effect in the THz wave scattering by dielectric rod decorated with graphene strip

“…Curved graphene-dielectric configurations studied so far have been mainly restricted to fully covered circular dielectric rods [22][23][24][25]. Arbitrary dielectric rod, fully covered with graphene, was analyzed with boundary integral equation in [26]. The authors of [27] considered a finite-width graphene strip attached to the surface of arbitrary dielectric rod using quasi-static approximations.…”