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One-dimensional structures of non-Hermitian plasmonic metallic nanospheresare studied in this paper. For a single sphere, solving Maxwell's equationsresults in quasi-stationary eigenmodes with complex quantized frequencies.Coupled mode theory is employed in order to study more complex structures. Thesimilarity between the coupled mode equations and the effective non-HermitianHamiltonians governing open quantum systems allows us to translate a series ofcollective phenomenon emerging in condensed matter and nuclear physics to thesystem of plasmonic spheres. A nontrivial physics emerges as a result of strongnon-radiative near field coupling between adjacent spheres. For a system of twoidentical spheres, this occurs when the width of the plasmonic resonance of theuncoupled spheres is twice the imaginary component of the coupling constant.The two spheres then become coupled through a single continuum channel and theeffect of coherent interaction between the spheres becomes noticeable. Theeigenmodes of the system fall into two distinct categories: superradiant stateswith enhanced radiation and dark states with no radiation. The transmissionthrough one-dimensional chains with an arbitrary number of spheres is alsoconsidered within the effective Hamiltonian framework which allows us tocalculate observables such as the scattering and transmission amplitudes. Thisnano-scale waveguide can undergo an additional superradiance phase transitionthrough its coupling to the external world. It is shown that perfecttransmission takes place when the superradiance condition is satisfied.

Superradiant and Dark States in Non-Hermitian Plasmonic Antennas and Waveguides