We study the poloidal modes (modes whose variations are strictly along the direction of the torus axis) of toroidal nanoparticles. We show that the modes may be understood in terms of the symmetry breaking that occurs when an infinite cylinder is folded to form a torus. This symmetry breaking results in the splitting of the transverse cylinder modes into two distinct sets of modes on a torus. One set of these modes was known to exist already. We show the existence of the second set and also analytically derive the surface charge structure for that set of modes. We also consolidate recent advances made in studying the modal structure on torus particles and complete our understanding of the plasmonic modes of a torus.

中文翻译：

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圆环上破碎的极谱对称性和等离子本征模式

我们研究了环形纳米粒子的极向模式（模式严格沿环面轴的方向变化）。我们表明，可以根据无限圆柱体折叠形成圆环时发生的对称破坏来理解这些模式。这种对称性破坏导致横向圆柱体模式在圆环上分裂成两组不同的模式。已知这些模式中的一组已经存在。我们显示了第二组的存在，并且还分析得出了该组模式的表面电荷结构。我们还巩固了在研究圆环颗粒的模态结构方面取得的最新进展，并完善了对圆环的等离子体模式的理解。