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Unformatted text preview: ECE 222B, Winter 2010 Solution to Homework Set 3 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 are varepsilon 1 and mu in region 1, and ε 2 and μ in region 2. Both permit- tivities 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 (ˆ x + j ˆ y )exp h- j ~ β i · ~ r i , where E A is a constant and ˆ x = cos θ i ˆ x- sin θ i ˆ z. If the wave is incident upon the surface at the Brewster angle, what is the fraction of power transmitted? Solution: First, decompose the wave into two waves with perpendicular and parallel polarization. Since the angle of incidence is the Brewster angle, only the perpendicular polarization (with electric field pointing in the y direction) will be partially reflected. The parallel polarization (with field in the x-z plane) will be totally transmitted. For the perpendicular polarization, the incident electric field is ~ E i ⊥ ( x,z ) = jE A ˆ y exp h- j ~ β i · ~ r i , with reflection coefficient (equation 5-17a in the textbook)...
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