时域耦合模理论引入“理论力学”教学中的可行性的探究

An investigation on the feasibility of introducing temporal coupled-mode theory into the teaching of theoretical mechanics

被广泛地用于力学、光学、电学等相关学科中的时域耦合模理论,在前沿科学研究中扮演着越来越重要的角色.在教学和科研相结合的本科教学理念下,将时域耦合模理论引入“理论力学”中已刻不容缓.本文结合拉格朗日方程和久期微扰理论,将振子耦合的二阶微分方程退化为一阶微分方程,即时域耦合模理论的主方程.该探究为本科生顺利接受时域耦合模理论提供了一种方案,并且在本科生素质培养方面有一定的意义.

Temporal coupled-mode theory,playing an increasingly important role in frontier scientific research,is widely used in Mechanics,Optics,Electricity and other related disciplines.Under the concept of combining teaching and research in undergraduate,the introduction of temporal coupled-model theory into Theoretical Mechanics is a matter of urgency.In this paper,combine the Lagrangian equation and the secular perturbation theory,the second-order differential equation of oscillator coupling is degenerated to the first-order differential equation,that is,the main equation of temporal coupled-mode theory.The study provides a scheme for the smooth acceptance of temporal coupled-mode theory by undergraduate students and has implications in terms of undergraduate quality development.