本研究探討電磁波斜射進入兩種不同介質內部，電磁波的折射與反射在介質表面以及介質內部所造成的影響。
電磁波的計算可由馬克斯威爾方程式得知。欲得馬克斯威爾方程式的解，可分成兩種情況，一種是將μ、ε、σ視為常數，另一種則是將μ、ε、σ視為變數。若令μ、ε、σ為常數，可使得馬克斯威爾方程式轉換為無源的波方程式，再利用D`Alembertian方程式、Helmhotz方程式[1]簡化方程式，拉普拉斯轉換(ILHI`s)[2]或是傅立葉轉換(FFT)[3]計算求得其解。
若μ、ε、σ不為常數，就可以將馬克斯威爾方程式簡化為有源的波方程式，設定吸收邊界條件、網格，利用有限元素分析，即可求得其解，進而模擬電磁波的作用。
再利用ILHI`s [4]得到暫態平面波斜射進入不同介質的結果，並且用此結果，將兩種解法互相加以驗證。

The problem is effect of electromagnetic wave. When electromagnetic wave obliquely transmitted through two different medias ,electromagnetic wave undergoes reflection and refraction at the interface and inside the media. Computation of electromagnetic wave is well known by Maxwell`s equation. There are two cases solving questions. One is constant of μ、ε、σ.Another is variable of μ、ε、σ. In case one, use D`Alembertian equation and Helmholtz equation transforming Maxwell`s equation. And solve by ILHI`s(incomplete Lips-chitz-Hankel integrals) and FFT(fast Fourier transform). In case two,if μ、ε、σ are variables ,we can simplify Maxwell`s equation. It is similar to wave equation with source. We use Finite Element Method(FEM) getting Numerical solution by setting absorbing boundary and mesh. Using results by ILHI`s would get exact solution obliquely incident on two medias. Proof numerical solution by exact solution.

摘要 i
Abstract ii
目錄 iii
符號說明 v
圖次 vi
第一章 緒論 1
1-1前言 1
1-2研究動機及目的 3
1-3文獻回顧 4
第二章 理論分析 5
2-1 Maxwell equation 5
2-2電磁波的分類 7
2-3 μ、ε、σ為常數(無源的波方程式) 9
2-4 μ、ε、σ不為常數(有源的波方程式) 13
2-4-1 統御方程式 13
2-4-2吸收邊界條件 15
2-4-3 邊界設定以及網格設定 18
2-4-4 μ、ε、σ條件設定 20
第三章 實驗方法以及驗證成果 22
3-1 入射條件與初始條件設定 22
3-2 驗證成果 24
3-2-1吸收邊界條件 24
3-2-2 有源的波方程式與無源的波方程式的驗證 27
第四章結論與未來展望 32
參考文獻 34
附錄一(摘錄自Handbook of Mathematical Functions with Formulas,Graphs,and Mathematical Tables中 的 Table25.4) 36
附錄二(摘錄自An accurate and efficient analysis for transient plane waves obliquely incident on a conductive half space (TM case) ) 37

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