Propagation of Optical Waves through the Boundary of Two Media

Boundary Conditions

The simplest case of wave propagation over the intersection between two media is that where the intersection surface can be assumed as flat, and the second medium perfectly conductive.

If so, for a perfectly conductive flat surface, the total electric field vector is equal to zero, that is, E = 0 [1—3,10—13]. In this case, the tangential component of electric field vanishes at the perfectly conductive flat surface, that is,

Consequently, it follows from Maxwell’s equation V X E(r) = iwH(r) (see References 14, 46) for the case of ц = 1 and B = H, at such a flat perfectly conductive surface the normal component of the magnetic field also vanishes, that is,

As also follows from Maxwell’s equations (2.1)—(2.4), the tangential component of magnetic field does not vanish because of the electric surface current. At the same time, the normal component of electric field does not vanish because of electrical charge density at the perfectly conducting surface. Hence, by introducing the Cartesian coordinate system, one can present the boundary conditions (2.18) and (2.19) at the flat perfectly conductive surface as follows:

 
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