| 基于辛几何理论求解电磁波在二维非均匀媒质中的传播与焦散问题 |
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| 引用本文： | 赵瑾,吴先良,付彪,李世雄.基于辛几何理论求解电磁波在二维非均匀媒质中的传播与焦散问题[J].安徽大学学报(自然科学版),2001,25(4):50-55. |
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| 作者姓名： | 赵瑾 吴先良 付彪 李世雄 |
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| 作者单位： | 1. 电子工程与信息科学系,
2. 数学系, |
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| 基金项目： | 国家自然科学基金;69971001; |
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| 摘 要： | 利用辛几何的高频近似理论的新方法 ,求解电磁波在一电参数缓变的二维非均匀媒质中的传播与焦散问题。通过辛空间上的坐标变换 ,使电磁波传播中的焦散问题转化为非焦散的问题 ,并结合几何光学的方法 ,求得了包括焦散区在内的高频近似解。解决了几何光学法无法在焦散区求解的问题。计算结果与有限元法所得结果基本吻合。本方法还可以推广到复杂的二维及三维的情况
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| 关 键 词： | 辛几何理论 高频近似法 焦散 |
| 文章编号： | 1000-2162(2001)04-0050-06 |
Solving the propagation and caustics of electromagnetic w ave in two-dimension inhomogeneous media based on symplectic geometric t heory |
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| ZHAO jin ,WU Xian-ling ,FU,Biao ,LI Shi-xiong.Solving the propagation and caustics of electromagnetic w ave in two-dimension inhomogeneous media based on symplectic geometric t heory[J].Journal of Anhui University(Natural Sciences),2001,25(4):50-55. |
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| Authors: | ZHAO jin WU Xian-ling FU Biao LI Shi-xiong |
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| Institution: | ZHAO jin 1,WU Xian-ling 1,FU,Biao 1,LI Shi-xiong 2 |
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| Abstract: | A new symplectic geometrical high-frequency approximation method for solving the propagation of electromagnetic wave in the two-dimension inhomogeneous media is used in this paper. The propagating caustic problem of electromagnetic wave is translated into non-caustic problem by the coordinate transform on the symplectic space. The high-frequency approximation solution that includes the caustic region is obtained with the method combining the geometrical optics. The drawback that the solution in the caustic region can't be obtained with geometrical optics is overcome by this method. Compared with those obtained by finite elements methods, the results are proved as satisfactory as well. |
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| Keywords: | symplectic geometrical theory high-frequency approximation caustics |
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