Development of a full-Vector beam-propagation method for optical waveguide analysis and its application to radiation problems

用于光波导分析的全矢量光束传播方法的开发及其在辐射问题中的应用

• 批准号: 11650398
• 负责人: YAMAUCHI Junji
• 金额: $ 1.22万
• 依托单位: Hosei University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2001
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11650398/
• 关键词: Optical waveguides; Beam-propagation methods; Finite-difference methods; FDTD methods; Dielectric rod antennas; Numerical analysis; アンテナ; ファイバグレーティング; 時間領域ビーム伝搬法

The method of simulating a full-vectorial propagating beam in dielectric waveguides has been developed, and its application to radiation problems has been discussed.First, consideration is given to the improvement of the accuracy of a finite difference formula. The so-called Douglas scheme has been extended to a non-uniform grid, while maintaining the fourth-order truncation error. Furthermore, the boundary conditions at the dielectric interface are introduced, which allows the analysis of a step-index waveguide with high-index contrast. The eigenmode and the coupling length are calculated and compared with previously published results.Before, studying the radiation problems, we investigate the performance of the boundary conditions at the edge of the computational window. The perfectly matched layer achieves high absorption when the number of layers is more than 20, but it requires considerable memories. The concurrent complementary operators method gives the performance comparable to the PML with 16 layers. The most efficient calculation can be made using Higdon-type boundary condition, although the application is limited to particular problems.The radiation problems of a dielectric rod antenna are investigated using the FDTD method. The propagating beam is decomposed into surface and unguided waves. The effects of the length of the dielectric rod on the gain have been explained qualitatively and quantitatively. It is found that the gain becomes maximal, when the surface wave interferes with the unguided wave in such a way that the resultant field at the plane containing the edge of the rod extends toward the air region with the equiphase condition. The theoretical results agree well with the experimental results.

本文提出了模拟介质波导中全矢量传播光束的方法，并讨论了该方法在辐射问题中的应用。首先，考虑提高有限差分公式的精度。在保持四阶截断误差的情况下，将道格拉斯方案扩展到非均匀网格。此外，还介绍了介质界面处的边界条件，从而可以对具有高折射率对比度的阶跃折射率波导进行分析。计算了本征模和耦合长度，并与已有的结果进行了比较。在研究辐射问题之前，我们研究了计算窗口边缘边界条件的性能。当层数超过20层时，完美匹配层具有较高的吸收率，但需要相当大的内存。并发互补算子方法的性能可与16层的PML相媲美。使用higdon型边界条件可以进行最有效的计算，尽管其应用仅限于特定问题。利用时域有限差分法研究了介电杆天线的辐射问题。传播波束被分解为表面波和非导波。对介电杆长度对增益的影响作了定性和定量的解释。结果表明，当表面波与非导波干涉时，在等相条件下，包含杆边的平面上的合成场向空气区延伸时，增益达到最大。理论结果与实验结果吻合较好。

项目成果

Junji Yamauchi: "Propagating beam analysis of optical waveguides"Research Studies Press, England. 280 (2002)

Junji Yamauchi：“光波导的传播光束分析”研究出版社，英国。

J.Shibayama,T.Takahashi,J.Yamauchi,and H.Nakano: "Finite-difference time-domain beam propagation method for analysis of three-dimensional optical waveguide"Electronics Letters. vol.35,no.18. 1548-1549 (1999)

J.Shibayama、T.Takahashi、J.Yamauchi 和 H.Nakano：“用于分析三维光波导的有限差分时域光束传播方法”《电子快报》。

J.Yamauchi, T.Murata, H.Nakano: "Semi-vectorial H-field analysis of rib waveguides by a modified beam-propagation method based on the generalized Douglas scheme"Optics Letters. Vol.25,No.24. 1771-1773 (2000)

J.Yamauchi、T.Murata、H.Nakano：“通过基于广义道格拉斯方案的改进光束传播方法对肋形波导进行半矢量 H 场分析”《光学快报》。

J. Yamauchi, T. Murata, and H. Nakano: "Analysis of rib waveguides by a fourth-order accurate finite-difference beam-propagation method"IEICE Transactions. Vol.J85-C, No.4. 241-248 (2002)

J. Yamauchi、T. Murata 和 H. Nakano：“通过四阶精确有限差分光束传播方法分析肋形波导”IEICE Transactions。

T. Ando, N. Nakayama, J. Yamauchi, and H. Nakano: "Optical waveguide analysis using a Yee-lattice-based modified finite-difference formula for an arbitrary dielectric interface"IEICE Transactions. Vol.J85-C, No.6 (in press).

T. Ando、N. Nakayama、J. Yamauchi 和 H. Nakano：“使用基于 Yee-lattice 的修正有限差分公式对任意介电界面进行光波导分析”IEICE Transactions。