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Unformatted text preview: 16 Reflection and transmission, TE mode • Last lecture we learned how to represent plane-TEM waves propagating in a direction ˆ k in terms of field phasors In 1808 Etienne-Loius Malus discovered that light re- flected from a surface at an oblique angle will in general be polarized differently than the incident wave on the re- flecting surface. This is caused by the differ- ence of the reflection coeffi- cients of TE and TM com- ponents of the incident wave as we will learn in this lec- ture. Practical implementa- tion of the phenomenon in- clude polarizers and polariz- ing filters used in optical in- struments, photography, and LCD displays. ˜ E = E o e- j k · r and ˜ H = ˆ k × ˜ E η such that η = μ , k = k ˆ k, and k = ω √ μ . Such waves are only permitted in homogeneous propagation media with constant μ and and zero σ . – The condition of zero σ can be relaxed easily — in that case the above relations would still hold if we were to replace by + σ jω as we will see later on. • In this lecture we will examine the propagation of plane-TEM waves across two distinct homogeneous media having a planar interface be- tween them. k i k r k t θ 2 θ 1 x z H i k 1 cos θ 1 k 1 sin θ 1 k 2 sin θ 2 Medium 1 Medium 2 θ 1 • With no loss of generality we can choose unit vector ˆ x be the unit- normal of the interface plane separating medium 1 in the region x < from medium 2 in the region x > . 1 • A plane-TEM wave incident onto the interface from medium 1 is as- signed a wavevector k i = k 1 (ˆ x cos θ 1 + ˆ z sin θ 1 ) by taking ˆ y to be orthogonal to k i (see margin)....
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This note was uploaded on 09/27/2011 for the course ECE 450 taught by Professor Staff during the Fall '08 term at University of Illinois, Urbana Champaign.
- Fall '08