| 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 |
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| 引用本文： | 佘守宪.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[J].光学学报,2003,23(7):09-814. |
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| 作者姓名： | 佘守宪 |
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| 作者单位： | 北方交通大学物理系,北京,100044 |
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| 基金项目： | 北方交通大学科技论文基金资助课题 |
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| 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4种折射率分布的计算公式。
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| 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 |
| 收稿时间： | 2002/7/29 |
Rigorous Solution of Eigenvalue Equations for Guided Modes in Inhomogeneous Optical Waveguides by Cole-Hopf Transformation |
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| She Shouxian.Rigorous Solution of Eigenvalue Equations for Guided Modes in Inhomogeneous Optical Waveguides by Cole-Hopf Transformation[J].Acta Optica Sinica,2003,23(7):09-814. |
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| Authors: | She Shouxian |
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| Abstract: | Using Cole Hopf transformation, eigenvalue equations for guided modes in inhomogentous 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. |
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| Keywords: | inhomogeneous waveguides propagation constants modal field Cole Hopf transformation Riccati equation |
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