350lect16 - 16 Reection and transmission TE mode Last...

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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 di ff erently than the incident wave on the re- flecting surface. This is caused by the di ff er- ence of the reflection coe ffi - 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 j ω 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 < 0 from medium 2 in the region x > 0 . 1
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A plane-TEM wave incident onto the interface from medium 1 is as- signed a wavevector k i = k 1 x cos θ 1 + ˆ z sin θ 1 ) by taking ˆ y to be orthogonal to k i (see margin). 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 k i k r k t θ 2 θ 1 x z E i k 1 cos θ 1 k 1 sin θ 1 k 2 sin θ 2 Medium 1 Medium 2 θ 1 This makes the xz -plane the “plane of incidence” and θ 1 the “angle of incidence”, and, furthermore,
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