Reflection And Refraction of Electromagnetic Waves By a Dielectric Slab Between

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Reflection And Refraction of Electromagnetic Waves By a Dielectric Slab Between
William Selwyn
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It follows from equation (1) that all the Cartesian components of E and IT satisfy Helmholtz's equation (2) (V^ + k^) Y - 0, J J = 1, 2, 3, 2 2 where V is the Laplacian operator and k. ■ -ifon ( (p. +ioac . E ), Throughout the J J J work it is assumed that k. Has a negative imaginary part (i. E. , that the con- ductivity never vanishes) j this assumption gives a simple form for the radia- tion condition at infinity, namely that all the components vanish exponentially with large distances. It al...so ensures that all th3 integrals occurring in the analysis are convergent.
- u - On applying the method adopted by Copson it is fairly simple to obtain the following integral expressions for the Cartesian components of E and H in the region z > 0, The subscripts x, y, z in the formulas denote the component direction- (3) 3U-, ^x--3z^ ^y^ ■ az » au-j^ av^ ^z ' ax * ay ' ^- ^1^1 ^1 \' where "i " h/^1 ^x'^'^y* ^1 " ^ Ai ^ydx' and the script letters denote the values of the respective components on the plane z' =0.


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