One-dimensional structures of non-Hermitian plasmonic metallic nanospheres are studied in this paper. For a single sphere, solving Maxwell's equations results in quasi-stationary eigenmodes with complex quantized frequencies. Coupled mode theory is employed in order to study more complex structures. The similarity between the coupled mode equations and the effective non-Hermitian Hamiltonians governing open quantum systems allows us to translate a series of collective phenomenon emerging in condensed matter and nuclear physics to the system of plasmonic spheres. A nontrivial physics emerges as a result of strong non-radiative near field coupling between adjacent spheres. For a system of two identical spheres, this occurs when the width of the plasmonic resonance of the uncoupled spheres is twice the imaginary component of the coupling constant. The two spheres then become coupled through a single continuum channel and the effect of coherent interaction between the spheres becomes noticeable. The eigenmodes of the system fall into two distinct categories: superradiant states with enhanced radiation and dark states with no radiation. The transmission through one-dimensional chains with an arbitrary number of spheres is also considered within the effective Hamiltonian framework which allows us to calculate observables such as the scattering and transmission amplitudes. This nano-scale waveguide can undergo an additional superradiance phase transition through its coupling to the external world. It is shown that perfect transmission takes place when the superradiance condition is satisfied.

本文研究了非Hermitian等离子体金属纳米球的一维结构。对于单个球体，求解麦克斯韦方程组将导致具有复杂量化频率的准平稳本征模。为了研究更复杂的结构，采用了耦合模式理论。耦合模式方程与控制开放量子系统的有效非埃尔米特哈密顿量之间的相似性，使我们能够将凝聚态和核物理学中出现的一系列集体现象转化为等离激元球体系统。相邻球体之间的强非辐射近场耦合产生了非平凡的物理学。对于两个相同球体的系统，当未耦合球体的等离子体共振的宽度是耦合常数的虚部的两倍时，就会发生这种情况。然后，两个球体通过一个连续的通道耦合，并且球体之间的连贯交互作用变得明显。系统的本征模式分为两类：具有增强辐射的超辐射状态和不具有辐射的暗状态。在有效的哈密顿量框架内，还考虑了通过具有任意数量球体的一维链的透射，这使我们能够计算可观测值，例如散射和透射幅度。这种纳米级波导可以通过耦合到外部世界而经历额外的超辐射相变。结果表明，当满足超辐射条件时，发生了完美的透射。