On solutions of Maxwell's equations with dipole sources over a thin conducting film

TL;DR

This paper derives explicit solutions for Maxwell's equations with dipole sources near a thin conducting film, revealing wave behaviors including surface plasmon-polaritons, with simplified formulas under certain conditions.

Contribution

It provides exact and simplified analytical expressions for electromagnetic fields near a thin conducting film with dipole sources, highlighting wave excitation mechanisms.

Findings

Explicit solutions for all field components are derived.

Solutions reveal two types of propagating waves, including surface plasmon-polaritons.

Formulas are simplified for large surface resistivity relative to ambient impedance.

Abstract

We derive and interpret solutions of time-harmonic Maxwell's equations with a vertical and a horizontal electric dipole near a planar, thin conducting film, e.g. graphene sheet, lying between two unbounded isotropic and non-magnetic media. Exact expressions for all field components are extracted in terms of rapidly convergent series of known transcendental functions when the ambient media have equal permittivities and both the dipole and observation point lie on the plane of the film. These solutions are simplified for all distances from the source when the film surface resistivity is large in magnitude compared to the intrinsic impedance of the ambient space. The formulas reveal the analytical structure of two types of waves that can possibly be excited by the dipoles and propagate on the film. One of these waves is intimately related to the surface plasmon-polariton of transverse-magnetic (TM) polarization of plane waves.