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Going beyond Axisymmetry: 2.5D Vector Electromagnetics


Y.A. Urzhumov1,2 N.I. Landy1,2 C. Ciraci2 D.R. Smith1,2
1Department of Electrical and Computer Engineering, Pratt School of Engineering, Duke University, Durham, NC, USA
2Center for Metamaterials and Integrated Plasmonics, Pratt School of Engineering, Duke University, Durham, NC, USA


2.5 D vector-field simulations of a gold nanoparticle held above a gold film substrate with a thin (1nm) self-assembled polymer layer [4]. Left: The surface charge wave associated with the surface plasmon polariton of the film is visualized using the Deformed Surface plotting tool in COMSOL. Right: a more conventional color surface plot showing the actual film and the particle.

Linear wave propagation through inhomogeneous structures of size R≫λ (Fig.1) is a computationally challenging problem, in particular when using finite element methods, due to the steep increase of the number of degrees of freedom as a function of R/λ. Fortunately, when the geometry of the problem possesses symmetries, one may choose an appropriate basis in which the stiffness matrix of the discretized problem is block-diagonal. A particular scenario is the case of a cylindrically-symmetric geometry, where an appropriate basis is the set of cylindrical waves with all possible azimuthal numbers (m). Each of the excited cylindrical harmonics propagate through the structure independently of all other harmonics, and therefore the fields associated with that harmonic can be found by solving an essentially two-dimensional PDE problem in the ρ-z (half)-plane. The cylindrical waves have a prescribed dependence on the azimuthal angle variable (φ), hence the name – 2.5D electromagnetics. This novel approach is applied to the problem of cloaking and wave scattering off a spherical nanoparticle on metallic and/or dielectric substrates.

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