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Unformatted text preview: 25 Wave reflection and transmission In this lecture we will examine the phenomenon of planewave reflections at an interface separating two homogeneous regions where Maxwell’s equations allow for traveling TEM wave solutions. The solutions will also need to ˆ n · ( D + D ) = ρ s ˆ n · ( B + B ) = 0 ˆ n × ( E + E ) = 0 ˆ n × ( H + H ) = J s satisfy the boundary condition equations repeated in the margin. We will consider a propagation scenario in which (see margin): Region 1 Region 2 H i x y z E i E t H t H r E r 1. Region 1 where z < is occupied by a perfect dielectric with medium parameters μ 1 , 1 , and σ 1 = 0 , 2. Region 2 where z > is homogeneous with medium parameters μ 2 , 2 , and σ 2 , 3. Interface z = 0 contains no surface charge or current except possibly in σ 2 → ∞ limit which will be considered separately at the end. • In Region 1 we envision an incident planewave with linearpolarized field phasors ˜ E i = ˆ xE o e jβ 1 z and ˜ H i = ˆ y E o η 1 e jβ 1 z , where – E o is the wave amplitude due to far away source located in z → ∞ region, – η 1 = μ 1 1 and β 1 = ω √ μ 1 1 . 1 Fields above satisfy Maxwell’s equations in Region 1, but if there were no other fields in Regions 1 and 2 boundary condition equations requiring continuous tangential E and H at the z = 0 interface would be violated....
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 Spring '08
 Kim
 Trigraph, Boundary value problem, Transmission line, Γ Eo

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