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arXiv · 2606.11630

Impact of mode completeness on the accuracy of the coupling theory of quasinormal modes: a strict numerical demonstration

Can Tao·Junda Zhu·Haitao Liu
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Abstract

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)], and can achieve superior computational efficiency and physical intuitiveness compared with full-wave numerical methods if a small set of modes can achieve a high accuracy. The QNMs suffer from an exponential divergence of far field and can form a complete basis inside but not outside the resonator. In the QNM coupling theory (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, which can be achieved by using regularized QNMs (RQNMs). However, a strict numerical demonstration of the impact of the mode completeness of RQNMs on the accuracy of QCT by 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 RQNMs into the QCT. The RQNMs are obtained by introducing an equivalent surface current (ESC) encircling the resonator (called ESC-RQNMs) or the perfectly matched layer (PML) surrounding the computational domain (called PML-RQNMs). The numerical example is selected as two one-dimensional resonators of slabs in the extreme coupling case of direct contact, for which a virtually complete basis of RQNMs can be solved either analytically (for ESC-RQNMs) or numerically (for PML-RQNMs). 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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Can Tao, Junda Zhu, Haitao Liu. 2026-06-10. Impact of mode completeness on the accuracy of the coupling theory of quasinormal modes: a strict numerical demonstration. https://arxiv.org/abs/2606.11630

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