外力驱动下耦合弹簧振子的法诺共振

法诺共振是物理体系中普遍存在的一种非对称共振现象,它最早起源于量子物理,其微观图像是原子谱线中窄的分离态与宽的连续态之间的相干干涉.本文利用经典力学体系中两个弹簧振子的耦合,使其中一个弹簧振子受到周期性外力的驱动,成功类比了量子力学中的法诺共振现象.通过分析每个弹簧振子的动力学方程,严格求解它们的振动公式,从而得到每个弹簧振子的振幅和位相与外部驱动力频率之间的关系.结果表明,耦合体系中受外力驱动的那个弹簧振子既可以发生非对称的法诺共振,又可以发生对称的洛仑兹共振,而另一个弹簧振子只能发生洛仑兹共振.本文的推导与分析能够使读者更好地理解法诺共振现象及其激发条件.

Fano resonance excited in coupled spring oscillators driven by an external force

Fano resonance which features asymmetric resonant line shape is a general resonance phenomenon occurred in all kinds of physical systems.It originates from quantum physics and the corresponding microscopic image is the interference between a narrow discrete state with a broad continuous state in atomic spectra.In this paper,taking two coupled spring oscillators in classical mechanics as an example and one of the coupled spring oscillators is driven by a periodic external force,a Fano resonance phenomenon which occurred in quantum mechanics is successfully analogized in classical mechanics.By analyzing the dynamic equation of each oscillator and solving their vibration formula rigorously,the relationships between the amplitude and phase of each oscillator and the frequency of the external driving force are obtained.The results show that the oscillator driven by the external force in the coupled system can excite both asymmetric Fano resonance and symmetric Lorentz resonance,while the other oscillator can only excite Lorentz resonance.The derivation and analysis of this paper give readers a deeper understanding of the Fano resonance and its excitation conditions.