Discussions on the spatial exponential growth of electromagnetic quasinormal modes

Abstract: The temporal response of open systems is marked by damped oscillations. These oscillations, often referred to as ringings, are the signature of the decay of quasinormal modes (QNMs). A major research objective across various fields is to represent the response of open systems using QNM expansions, akin to the treatment of normal modes in closed systems. In electromagnetism, it is widely acknowledged that QNM expansions provide a relevant representation of the modal physics within the interior of compact resonators in free space, where QNMs form a complete set of the resonator. However, challenges emerge in the exterior of the resonator, where QNM fields exhibit exponential divergence, rendering QNM expansions incomplete. The divergence poses delicate mathematical issues that often lead to misinterpretations on the physics side. Hereafter, we analyze foundational concepts such as cavity perturbation theory and dissipative coupling between resonators. By studying model problems, we show that the exponential growth is physical and meaningful for understanding the interaction between remote electromagnetic bodies. The analysis consistently reveals that the coupling coefficients between QNMs of two distant bodies strengthen as the separation distance increases, therein challenging the intuition that distant bodies behave independently. These insights that shed light on the origin and implications of the divergence hold significant implications for understanding the ability of contemporary electromagnetic QNM theories in offering a modal representation of the physics in the open space surrounding resonator bodies. Our critical examination of these theories reveals the existence of two distinct perspectives and elucidates the significance of their contrasting viewpoints.