The orthogonal eigenmodes are well-defined solutions of Hermitian equations describing many physical situations from quantum mechanics to acoustics. However, a large variety of non-Hermitian problems, including gravitational waves close to black holes or leaky electromagnetic cavities, require the use of a bi-orthogonal eigenbasis with consequences challenging our physical understanding^1,2,3,4. The need to compensate for energy losses made the few successful attempts^5,6,7,8 to experimentally probe non-Hermiticity extremely complicated. We overcome this problem by considering localized plasmonic systems. As the non-Hermiticity in these systems does not stem from temporal invariance breaking but from spatial symmetry breaking, its consequences can be observed more easily. We report on the theoretical and experimental evidence for non-Hermiticity-induced strong coupling between surface plasmon modes of different orders within silver nanodaggers. The symmetry conditions for triggering this counter-intuitive self-hybridization phenomenon are provided. Similar observable effects are expected to exist in any system exhibiting bi-orthogonal eigenmodes.

正交本征模是厄米方程的明确定义的解，描述了从量子力学到声学的许多物理情况。但是，各种各样的非Hermitian问题，包括靠近黑洞的重力波或泄漏的电磁腔，都需要使用双正交本征基，其结果挑战了我们的物理理解^1,2,3,4。弥补能量损失的需要进行了几次成功的尝试^5,6,7,8在实验上探测非赫米蒂性极为复杂。我们通过考虑局部等离子体系统克服了这个问题。由于这些系统中的非赫米特性不是源于时间不变性的破坏，而是源于空间对称性的破坏，因此可以更轻松地观察到其后果。我们报告了在银纳米匕首内不同阶数的表面等离子体激元模式之间的非费米特性诱导的强耦合的理论和实验证据。提供了触发这种违反直觉的自我杂交现象的对称条件。预期在任何表现出双正交本征模态的系统中都将存在类似的可观察到的效果。