Abstract
The generic model of two coupled multimode plasmonic nanospheres with gain and loss forming a parity-time $(\mathcal{PT})$ symmetric dimer is considered. Analytical solutions based on a quasistatic approximation are used to explore the behavior of the eigenmodes in such a coupled nanoantenna system as a function of their separation distances and their gain-loss level. It is shown that the introduction of the same amount of gain and loss modifies the composition of eigenmodes and breaks their orthogonality. The resulting entanglement of different spatial order and symmetry modes can be advantageously exploited to actively control the scattering properties of such multimode $\mathcal{PT}$-symmetric nanoantennas.
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