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

The response of any open system is closely related to the complex frequencies of the quasinormal modes (QNMs) of the system. While QNM-based expansion theories in electromagnetism have successfully elucidated the modal physics within resonator boundaries, their application beyond these confines into the surrounding open space has been limited. This limitation stems from the exponential spatial growth, or divergence, of QNM fields beyond resonator boundaries, posing challenges to the completeness of QNM expansions and often leading to misconceptions about modal physics in the open space. We address these challenges by investigating fundamentals, such as first-order perturbation theory and dissipative coupling between distant bodies, shedding light on the implications of the divergence. Our analysis reveals that QNMs are increasingly influenced by perturbers as they move farther away from the resonator body in open space. Furthermore, we demonstrate that the coupling coefficients between QNMs of distant resonators amplify with separation distance, indicating entanglement between their QNMs and challenging our intuition that remote resonators behave independently. These insights, easily understandable, hold significant implications for contemporary developments in QNM electromagnetic theory. They aid in discerning between questionable and promising trends and suggest innovative avenues for QNM expansions across near, intermediate, and far-field zones.