Tao Qiyong, Su Yuhang, Tao Can, Zhong Ying, Liu Haitao
Opt Express. 2024 Feb 26;32(5):7171-7184. doi: 10.1364/OE.515087.
We propose an efficient method for calculating the electromagnetic field of a large-scale array of optical nanoresonators based on the coupling theory of quasinormal mode (QNM). In this method, two approaches of the scattered-field reconstruction and stationary-phase-principle calculated plane-wave expansion are developed to obtain the regularized QNM (RQNM) in different regions. This accurate and efficient calculation of RQNM resolves the far-field divergence issue of QNMs in the QNM-coupling theory, thus enabling a rapid computation of the electromagnetic field of a large-scale array of optical nanoresonators, which is a challenging task for full-wave numerical methods. Using this method, we consider the numerical example of the radiation problem of a single point source in a large-scale periodic array of optical nanoantennas. In comparison to full-wave numerical methods, this method significantly reduces the computation time by 1∼2 orders of magnitude while maintaining accuracy. The high computational efficiency and physical intuitiveness of the method enables to clarify the impact of array size (exceeding 50 × 50 wavelengths), period and field-coupling range (far beyond the tight-binding approximation) on the optical response. The proposed method and results can provide an efficient tool and guidance for the design of large-scale arrays of optical nanoresonators.
我们提出了一种基于准正常模式（QNM）耦合理论计算大规模光学纳米谐振器阵列电磁场的有效方法。在该方法中，开发了散射场重建和基于驻相原理计算的平面波展开这两种方法，以在不同区域获得正则化的QNM（RQNM）。这种对RQNM的精确高效计算解决了QNM耦合理论中QNMs的远场发散问题，从而能够快速计算大规模光学纳米谐振器阵列的电磁场，而这对于全波数值方法来说是一项具有挑战性的任务。使用该方法，我们考虑了大规模周期性光学纳米天线阵列中单个点源辐射问题的数值示例。与全波数值方法相比，该方法在保持精度的同时，显著减少了1至2个数量级的计算时间。该方法的高计算效率和物理直观性能够阐明阵列尺寸（超过50×50波长）、周期和场耦合范围（远超出紧束缚近似）对光学响应的影响。所提出的方法和结果可为大规模光学纳米谐振器阵列的设计提供一种有效的工具和指导。
