Multipole Expansion of Electromagnetic Scattering Wave by a Small Cylindrical Pore on a Perfect Conducting Semi-Infinite Half Space

Abstract

Abstract-The scattering of an oblique electromagnetic wave incident on a sub-wavelength circular pore with a finite depth on the surface of a semi-infinite perfect conductor is investigated analytically. We use the method of matched asymptotic expansion to find the multipole structure. The expansion is based on the duality property of the source-free Maxwell equations, and the resultant scattering fields are fully expressed in terms of the scalar and the conjugate vector potentials. There are two regions defined by the analytical method: the electro/magneto-static inner region and the radiation outer wave region. For both TM and TE incidences, the scattering waves are lead by leading dipoles. In the next order of the scattering waves, a mixture of the dipole, the quadrupole and the octupole is found. This is a striking finding, that the multipoles are not organized in a strictly ascending manner when the size of the pore is considered. In addition, the sophisticated three-dimensional interplay of the multipoles, the pore depth, and the incident angle is revealed. The magnitudes of the scattering dipoles are confirmed convergent smoothly to those of the back-scattering dipoles of electromagnetic waves transmitted through a hole in a perfect conducting plate with a finite thickness when the pore depth is larger than about 1, normalize to the pore radius.

Cartesian Multipole Expansions and Tensorial Identities

“…The special properties of toroid moments make them very interesting in constructing metamaterials with particular characteristics. Controlling the trajectory and polarization of light in media containing toroidal metamolecules is also an attractive subject (see [3][4][5] and references therein). Such advanced researches which mainly exploit the special symmetry properties of the toroid multipole family require a correct knowledge of all the same order multipolar contributions.…”