Understanding the physics related to the spatial exponential growth of electromagnetic quasinormal modes

The electromagnetic interaction between distant bodies exerts foundational influences across various physics domains. In contexts involving non-Hermitian dissipative systems, the interaction is driven by the inherent quasinormal modes (QNMs) of each body. So far, in electromagnetism, QNMs have proven effective in understanding the modal physics inside resonator bodies, but not beyond in the surrounding open space. Indeed, QNM frequencies are complex valued, and the associated fields undergo an exponential spatial growth beyond the resonator bodies. This growth, often referred to as divergence, challenges our intuition and often leads to misconceptions regarding the modal physics of those regions of space. By investigating model problems where the diverging field can be precisely computed well beyond the resonator body, we reveal that the divergence holds meaningful implications for various elementary phenomena involving dissipative coupling between distant bodies. For instance, we highlight that QNMs are increasingly influenced by perturbers moving farther away from the resonator body in the open space. Additionally, we demonstrate that divergence is a tangible physical phenomenon observable in real-world scenarios. These findings carry great significance in analyzing contemporary developments in QNM electromagnetic theory, aiding in the distinction between questionable and promising trends and proposing new tangible pathways for QNM expansions in near, intermediate, and far-field zones.