Abstract
A key quantity in the design of plasmonic antennas and metasurfaces, as well as metamaterials, is the electrodynamic polarizability of a single scattering building block. In particular, in the current merging of plasmonics and metamaterials, subwavelength scatterers are judged by their ability to present a large, generally anisotropic electric and magnetic polarizability, as well as a bi-anisotropic magnetoelectric polarizability. This bi-anisotropic response, whereby a magnetic dipole is induced through electric driving, and vice versa, is strongly linked to the optical activity and chiral response of plasmonic metamolecules. We present two distinct methods to retrieve the polarizibility tensor from electrodynamic simulations. As a basis for both, we use the surface integral equation (SIE) method to solve for the scattering response of arbitrary objects exactly. In the first retrieval method, we project scattered fields onto vector spherical harmonics with the aid of an exact discrete spherical harmonic Fourier transform on the unit sphere. In the second, we take the effective current distributions generated by SIE as a basis to calculate dipole moments. We verify that the first approach holds for scatterers of any size, while the second is only approximately correct for small scatterers. We present benchmark calculations, revisiting the zero-forward scattering paradox of Kerker et al (1983 J. Opt. Soc. Am. 73 765–7) and Alù and Engheta (2010 J. Nanophoton. 4 041590), relevant in dielectric scattering cancelation and sensor cloaking designs. Finally, we report the polarizability tensor of split rings, and show that split rings will strongly influence the emission of dipolar single emitters. In the context of plasmon-enhanced emission, split rings can imbue their large magnetic dipole moment on the emission of simple electric dipole emitters. We present a split ring antenna array design that is capable of converting the emission of a single linear dipole emitter in forward and backward beams of directional emission of opposite handedness. This design can, for instance, find application in the spin angular momentum encoding of quantum information.
Highlights
We show that the insights gained from the polarizability tensor can be used to construct new types of plasmonic array antennas that have the directivity of Yagi–Uda antennas [22, 23], but with unique polarization properties
The integral equation formalism, it is useful to solve for the electromagnetic response by first finding the effective auxiliary electric and magnetic surface current densities J and M on the interface between medium 1 and medium 2 that are used to satisfy the boundary conditions for continuity of tangential E and H, and normal B and D
Having understood the split ring as a system composed of an electric and a magnetic coupled dipole moment whose maximal response to circularly polarized plane waves occurs for a certain polar angle θMAX, and having studied the way in which electric dipoles couple to single split rings, we turn to the design of an array of split rings and to the study of the special properties that arise from it
Summary
Any electromagnetic problem is completely specified by the Maxwell equations, together with a definition of the source, and the boundary condition. Note how M self-consistently contains the interactions between all the discretized current elements, as evident from the appearance of Gi (r, r ) After this matrix is calculated, it can be inverted and multiplied by the vector q, which is the projection of the incident field that drives the scatterer into the RWG functions. The projections of the fields on the sphere on vector spherical harmonics (VSH) directly define the multipole moments through the expansion coefficients anm and bnm, as explained by Jackson [25, chapter 10] as well as by Muhlig et al [16]. For this first retrieval method we use two steps. We first discuss the multipole expansion method and the direct definition based on J and M
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