任意非均匀分层介质中耦合波的传播理论
Theory of the propagation of coupled waves in arbitrarily-inhomogeneous stratified media
摘要：
本文推广了波传播的不变嵌入理论，导出了任意非均匀分层介质中任意数量的任意类型耦合波传播的新的不变嵌入方程，其中的波动方程是有效的一维方程。这样就把原来的耦合二阶微分方程的边值问题转化为耦合一阶微分方程的初值问题，从而使耦合波方程的数值求解变得容易。利用不变嵌入方程，我们可以准确、高效地计算非均匀介质中的矩阵反射系数、透射系数和波幅值。我们建立的有效性和有用性，我们的结果，将它们应用到圆偏振电磁波的传播在一维光子晶体的各向同性手征介质。我们发现在这些结构中存在三种带隙，并通过精确计算阐明了这些带隙的性质。
英文摘要：
We generalize the invariant imbedding theory of the wave propagation and derive new invariant imbedding equations for the propagation of arbitrary number of coupled waves of any kind in arbitrarily-inhomogeneous stratified media, where the wave equations are effectively one-dimensional. By doing this, we transform the original boundary value problem of coupled second-order differential equations to an initial value problem of coupled first-order differential equations, which makes the numerical solution of the coupled wave equations much easier. Using the invariant imbedding equations, we are able to calculate the matrix reflection and transmission coefficients and the wave amplitudes inside the inhomogeneous media exactly and efficiently. We establish the validity and the usefulness of our results by applying them to the propagation of circularly-polarized electromagnetic waves in one-dimensional photonic crystals made of isotropic chiral media. We find that there are three kinds of bandgaps in these structures and clarify the nature of these bandgaps by exact calculations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
