Resonant dynamics of arbitrarily shaped meta-atoms

Abstract

Meta-atoms, nano-antennas, plasmonic particles and other small scatterers are commonly modeled in terms of their modes. However these modal solutions are seldom determined explicitly, due to the conceptual and numerical difficulties in solving eigenvalue problems for open systems with strong radiative losses. Here these modes are directly calculated from Maxwell's equations expressed in integral operator form, by finding the complex frequencies which yield a homogenous solution. This gives a clear physical interpretation of the modes, and enables their conduction or polarization current distribution to be calculated numerically for particles of arbitrary shape. By combining the modal current distribution with a scalar impedance function, simple yet accurate models of scatterers are constructed which describe their response to an arbitrary incident field over a broad bandwidth. These models generalize both equivalent-dipole and and equivalent-circuit models to finite sized structures with multiple modes. They are applied here to explain the frequency-splitting for a pair of coupled split rings, and the accompanying change in radiative losses. The approach presented in this paper is made available in an open-source code.

Polarization‐Induced Chirality in Metamaterials via Optomechanical Interaction

“…[38][39][40][41] The coupled equations for a two-resonator system can be expressed explicitly as follows i 11 12…”

“…The impedance matrix describes the self and mutual interaction of the meta-atoms, in which Z ii and Z ij are the effective self-impedance and mutual impedance, respectively. All the matrix elements can be defined by the normalized current and charge distribution of the eigenmode of each individual meta-atom; [38][39][40][41] from symmetry we get Z 11 = Z 22 , Z 12 = Z 21 . E is the effective electromotive force imposed by the incident field; for plane wave excitation, i E = ⋅ l l E E , where l = p/Q is the normalized dipole moment of a single meta-atom.…”

New degrees of freedom in nonlinear metamaterials

“…As a result, even relatively weak electromagnetic forces are sufficient to initiate mutual rotation. The rotation, however, changes mutual orientation of the gaps in the two split rings, which affects the pattern of the electromagnetic modes excited in the pair , and shifts the frequency of the resonance. This creates the required nonlinear feedback and results in a hysteresis‐like behavior, with remarkable angles of rotation achieved in experiment .…”

Hybridization and the origin of Fano resonances in symmetric nanoparticle trimers

“…If we were to consider the doubly-degenerate eigenmodes in complex frequency space (s-space) to find and/or analyze their resonances [19], there are points in s-space where the expressions for |v 2 and |v 3 are the same, specifically: when δ = 0. At such points, the two eigenmodes coalesce and the eigenspace of these two eigenmodes subsequently reduces in dimension, indicating a nontrivial topology of the eigenspace.…”