Mathematical Analysis of the Generalized Natural Modes of an Inhomogeneous Optical Fiber
Mathematical Analysis of the Generalized Natural Modes of an Inhomogeneous Optical Fiber
复制标题
非均匀光纤广义自然模式的数学分析
DOI：
--
复制
发表时间：
2005
影响因子：
1.9
通讯作者：
G. Hanson
中科院分区：
文献类型：
--
作者：
E. Kartchevski;A. Nosich;G. Hanson
本文将无尖边界非均匀光纤的广义自然模的本征值问题转化为在截面无穷远处满足Reichardt条件的时谐麦克斯韦方程组的问题。这个问题的广义本征值（包括众所周知的导模和漏模作为子集）是对数黎曼曲面上的复传播常数。首先证明了一个谱局部化定理，然后将原问题转化为一个带紧积分算子的非线性谱问题。证明了原问题的所有特征值的集合只能是黎曼曲面上的孤立点的集合，同时也证明了每个特征值连续地依赖于频率和折射率，只能在黎曼曲面的边界出现和消失。
The eigenvalue problem for generalized natural modes of an inhomogeneous optical fiber without a sharp boundary is formulated as a problem for the set of time-harmonic Maxwell equations with the Reichardt condition at infinity in the cross-sectional plane. The generalized eigenvalues (including,as subsets, the well-known guided and leaky modes) of this problem are the complex propagation constants on a logarithmic Riemann surface. A theorem on spectrum localization is proved, and then the original problem is reduced to a nonlinear spectral problem with a compact integral operator. It is proved that the set of all eigenvalues of the original problem can only be a set of isolated points on the Riemann surface, and it is also proved that each eigenvalue depends continuously on the frequency and refraction index and can appear and disappear only at the boundary of the Riemann surface.