耦合模理论及其在光纤光学中的应用

Coupled-Mode Theory and Its Application to Fiber Optics

首先简要叙述了耦合模理论早期从微波领域逐渐发展起来而延伸到导波光学和其他领域的历程,该理论的数学描述是联立的一阶线性常微分方程组,即耦合模方程。然后明确指出一阶导数形式是该理论的特色,指明该方程在具体的边值问题下严格地与Maxwell方程相等效,并确定其解的主要近似来源与误差量级。最后还扼要叙述了耦合模理论在光纤光学各类问题中的应用,包括建模和模拟。还就使用耦合理论中出现的问题提出了自己的见解。

Firstly, the development and application of the coupled-mode theory in microwaves and its extension to fiber optics in the early years are briefly reviewed, and it is well known that coupling among modes is described mathematically by the coupled-mode equations which are linear differential equation group of the first order. Then, it is noted that the coupled-mode equations are rigorously transformed from the Maxwell equations along with a perturbed boundary condition, the approximation methods are used when solving these equations and the order of the approximation is given. The coupled-mode method is attributed to its simplicity in principle, intuitiveness in physics and capacity of simulating complete transfer of power. Finally, a variety of applications of coupled-mode theory to fiber optics, including modeling and simulation are shortly introduced. Misuses of coupled-mode theory are also commented.