Acta Scientiarum Naturalium Universitatis Pekinensis ›› 2019, Vol. 55 ›› Issue (5): 871-877.DOI: 10.13209/j.0479-8023.2019.026

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Study on Strong and Weak Coupling for Surface Plasmon Resonance in Both Frequency and Time Domain

SONG Hanfa, HU Xiaoyong   

  1. State Key Laboratory for Artificial Microstructure and Mesoscopic Physics, School of Physics, Peking University, Beijing 100871
  • Received:2018-09-11 Revised:2018-09-26 Online:2019-09-20 Published:2019-09-20
  • Contact: HU Xiaoyong, E-mail: xiaoyonghu(at)


宋瀚法, 胡小永   

  1. 北京大学物理学院人工微结构和介观物理重点实验室, 北京 100871
  • 通讯作者: 胡小永, E-mail: xiaoyonghu(at)


A study is proposed creatively on the strong and weak coupling properties of plasmon coupling systems in both frequency domain and time domain. Theoretically, calculations on the eigen-frequencies, decay rates and the evolutions of bright and dark mode with respect to the strength of coupling under a certain system are performed. Numerically, in the frequency domain calculations on the features of hybridized modes and scattering spectrum and also the splitting phenomenon of bright and dark modes are performed. In the time domain, the periodicity of the beat pattern from the hybridized modes with a difference in frequency is utilized to determine the precise eigen-frequencies of the hybridized modes. From the time domain calculations, the precise eigenfrequencies are close but do not absolutely correspond to the two peaks of the scattering spectrum. By sweeping the coupling distance and measuring the mode evolution, the area where the exceptional point exists is found and specified by fitting to the frequency domain response. In the weak coupling domain, time domain calculations show as expected that both the bright mode and dark mode decay with their individual decay rates.

Key words: localized surface plasmon polartion, strong coupling, weak coupling, exceptional point, coupled mode equation


从频域和时域两个维度研究表面等离激元耦合系统在强耦合与弱耦合区域的特性, 在理论上研究给定参数的表面等离激元耦合系统的本征频率、损耗以及亮暗模式随耦合强度的演化。在频域上对门结构在强耦合区域的杂化模式特征、散射光谱特性、偶极子与四极子模式的劈裂情况进行数值计算; 在时域上, 由于激发出两个不同频率的杂化模式叠加形成拍频, 利用拍频信号周期可以精确地给出杂化模式的频率, 得到散射光谱对应的频率不是精确的模式频率的结论。通过扫描耦合距离观察模式演化, 找到奇异点所处区域, 通过系统的频域响应拟合, 确定奇异点的位置。在弱耦合区域, 时域计算给出亮暗模式分别按自身衰减速率衰减的预期结果。

关键词: 局域表面表面等离激元, 强耦合, 弱耦合, 奇异点, 耦合模方程