用科尔-霍普夫变换法求非均匀光波导导模本征方程的严格解  

Rigorous Solution of Eigenvalue Equations for Guided Modes in Inhomogeneous Optical Waveguides by Cole-Hopf Transformation

作　　者：佘守宪[1] 

机构地区：[1]北方交通大学物理系,北京100044

出　　处：《光学学报》2003年第7期809-814,共6页Acta Optica Sinica

基　　金：北方交通大学科技论文基金资助课题

摘　　要：采用科尔霍普夫 (Cole Hopf)变换法 ,将渐变折射率波导导模的本征值方程变换为里卡提 (Riccati)方程 ,通过较简洁的数学演算导出导模的传播常量与模场分布的解析解 ,给出了平方律分布、对称爱泼斯坦 (Epstein)分布、爱泼斯坦层的平板波导与平方律分布圆光纤Using Cole-Hopf transformation, eigenvalue equations for guided modes in inhomogeneous optical waveguides are transformed to Riccati equation, and rigorous analytic solutions for propagation constants and modal field distributions are deduced in a simple and convenient way. Formulas for square-law index profile, symmetric Epstein profile, Epstein-layer model of planar guides and for parabolic profile circular optical fibers are deduced.

关 键 词：渐变折射率波导 传播常量 模场 科尔-霍普夫变换 里卡提方程 非均匀光波导 导模 本征方程 

分 类 号：TN252[电子电信—物理电子学]