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# set3 - ECE 222B Winter 2010 Homework Set 3 Due Tuesday...

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ECE 222B, Winter 2010 Homework Set 3: Due Tuesday, February 2nd. 1. A plane wave in medium 1 is incident on an interface (at z=0) with medium 2 with an angle of incidence θ i . (See Figure 5-2 in Balanis for the geometry of the problem). The permittivity and permeability is ε 1 and μ 0 in region 1, and ε 2 and μ 0 in region 2. Both permittivities are real (ideal media). The incident wave is circularly polarized and the incident electric field can be written as -→ E i ( x, z ) = E A ( b x 0 + j b y ) exp h - j -→ β i · -→ r i , where E A is a constant and b x 0 = cos θ i b x - sin θ i b z. If the wave is incident upon the surface at the Brewster angle, what is the fraction of power transmitted? 2. (15 points) Assume that you are given an idealized plasma such that the effective permittivity is ² = ² 0 " 1 - ω 2 p ω 2 # where ω p is a constant called the plasma frequency. You may assume that μ = μ 0 . (a) Assume that you are given a TEM wave propagating in the z direction such that ~ E = E 0 exp [ - jβz ] ˆ x . Express β as a function of ω .

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