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450fall09hw9 - ECE 450 Homework 9 Due Tue 5 PM 1 A uniform...

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Unformatted text preview: ECE 450 Homework 9 Due: Tue, Oct 27, 2009, 5 PM 1. A uniform, time-harmonic plane wave with TM polarized electric field phasor ˜ E i = ˆ x- ˆ z √ 2 e- j 2 π x + z √ 2 V m propagating in glass is impinging obliquely upon a planar glass-air interface at x = 0 plane. The magnetic permeability of the glass is that of free space and its relative electric permittivity is 2.25. a) What are the wavenumber k 1 and frequency ω of the incident wave in the glass? b) What is the angle of incidence θ 1 and what is the critical angle θ c in this reflection problem? Explain why an evanescent wave will be produced in the half-space x > (occupied by air) in terms of angles θ 1 and θ c . c) Using Snell’s law, determine cos θ 2 where θ 2 is the angle of the transmitted wave (assumed to be bounded everywhere in x > half-space). Discuss why θ 2 is complex valued and your choice of the sign of cos θ 2 d) Obtain the numerical value of the reflection coefficients Γ ....
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