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Unformatted text preview: 25 Wave reflection and transmission In this lecture we will examine the phenomenon of plane-wave 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 plane-wave with linear-polarized 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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This note was uploaded on 06/20/2011 for the course ECE 329 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.
- Spring '08