用久期微扰理论将弹簧振子模型退化为耦合模理论  

The spring oscillator model degenerated into the coupledmode theory by using secular perturbation theory

作　　者：朱存远 李朝刚 方泉 汪茂胜[1] 彭雪城[1] 黄万霞[1,2] Zhu Cun-Yuan;Li Chao-Gang;Fang Quan;Wang Mao-Sheng;Peng Xue-Cheng;Huang Wan-Xia(School of Physics and Electronic Information,Anhui Normal University,Wuhu 241002,China;State Key Laboratory of Surface Physics and Department of Physics,Fudan University,Shanghai 200433,China)

机构地区：[1]安徽师范大学物理与电子信息学院,芜湖241002 [2]复旦大学,应用表面物理国家重点实验室,上海200433

出　　处：《物理学报》2020年第7期114-120,共7页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:11304002);复旦大学应用表面物理国家重点实验室(批准号:KF2018_01)资助的课题.

摘　　要：尽管耦合模理论在过去几十年内已经被广泛研究,但它的理论来源还是困扰着广大研究者.在这里,基于久期微扰理论,将经典弹簧振子模型退化为耦合模理论,并将该理论用于解释音叉耦合的实验现象.研究表明这种方法将耦合模理论中每一项的系数都与经典力学中的相关物理量建立关联,且理论和实验结果符合得很好.该研究为耦合模理论中每一项的来源提供了一种较严谨的推导方法,在线性耦合体系的理论研究方面有一定的指导意义.In the past few decades,although coupled-mode theory(CMT)has been extensively studied in quantum system,atomic system,plasmon system,circuit system,and so on,the theoretical origin is still plaguing many researchers.In the book of waves and fields in optoelectronics,the second-order differential equations of the simplest LC simple harmonic vibration circuit was turned into the first-order differential equation using the method of variable substitution by Haus.However,there is not loss in the simplest LC simple harmonic vibration circuit,loss term is introduced by qualitative analysis.Although this method of dealing with problems has no problems from a physical point of view,it is not rigorous enough from a mathematical point of view.In this paper,based on the secular perturbation theory,the well-known spring oscillator model is degenerated into two-mode CMT.Starting from the second-order differential equations of the spring oscillator model,the secular perturbation theory is used to obtain first order differential equations of two-mode CMT.The results show the relationships between each term’s coefficients in two-mode CMT and the physical quantities in Classical Mechanics are established by using the secular perturbation theory.Through solving two-mode coupled-mode equations,the energy transfer efficiency has been obtained.To verify the correctness of two-mode CMT,we design a coupled tuning fork mechanical vibration system,which consists of two experimental instruments to provide driving force and receive signals,two tuning forks and springs.The amplitude spectra are measured by an experimental instrument of forced vibration and resonance(HZDH4615),which provides a periodic driving signal for the tuning fork.To clarify the mechanism of the spectra,the numerical fitting has been performed by mathematica software based on the energy transfer efficiency.Theoretically,the obtained fitting parameters can also evaluate some important attributes of the system.The theoretical results are in close correspondence with th

关 键 词：线性耦合体系 弹簧振子模型 耦合模理论 久期微扰理论 

分 类 号：O32[理学—一般力学与力学基础]