- Accepted Paper
Impact of mode completeness on the accuracy of the coupling theory of quasinormal modes: A strict numerical demonstration
Phys. Rev. A - Accepted 13 November, 2026
DOI: https://doi.org/10.1103/8y3b-j27m
Phys. Rev. A - Accepted 13 November, 2026
DOI: https://doi.org/10.1103/8y3b-j27m
The coupling theory of quasinormal modes (QNMs) for a coupled system of generally lossy and dispersive optical nanoresonators has been established in a rigorous manner based on the first principle of Maxwell’s equations [Phys. Rev. B 102, 045430 (2020)]. Compared with full-wave numerical methods, this QNM coupling theory (QCT) can offer superior computational efficiency and physical intuitiveness if a small set of modes can achieve a high accuracy. In the QCT, it is required that the QNMs of each resonator form a complete basis in expanding the scattered field both inside and outside the resonator. This requirement can be satisfied by using the regularized QNMs (RQNMs) since the physical QNMs can form a complete basis inside but not outside the resonator. However, a strict numerical demonstration of the accuracy of QCT when using a virtually complete basis of RQNMs is still absent. In this paper, we will provide such a numerical demonstration along with an improvement of the QCT and some theoretical demonstrations on a rigorous incorporation of the RQNMs into the QCT. The RQNMs are obtained by introducing either an equivalent surface current encircling the resonator or the perfectly matched layer surrounding the whole computational domain. The numerical example is selected as two one-dimensional resonators of slabs in the extreme coupling case of direct contact. The results show that by using a virtually complete basis of RQNMs, the QCT can achieve a high accuracy in predicting both the source-free eigenmodes and the source-excited scattered field of the coupled system, which is not true if using the incomplete basis of not-regularized QNMs (i.e., physical QNMs).
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