312ps6 - PROBLEM SET 6 ECE 312 Autumn Quarter 2010...

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PROBLEM SET 6 ECE 312 Autumn Quarter 2010 Assigned: November 3rd Due: November 10th in class Instructor: Joel Johnson Problem 1 A 3 GHz plane wave E ˜ i 3 x ˆ 2 y ˆ –4 z ˆ () e jA 4 x 3 z + = V/m is obliquely incident from free space onto a planar boundary at z 0 = with a dielectric medium. (a) Find the angle of incidence θ i . (b) Find A . (c) Write the perpendicular polarized component of E ˜ i . (d) Write the parallel polarized component of E ˜ i . (e) Find the incident magnetic field H ˜ i . Problem 2 A fiber optic cable operates by using the total internal reflection of light to keep light waves inside the cable. Consider a cable made of spun glass, ε 2.2 ε 0 = , μμ 0 = , σ 0 = , which is sur- rounded by free space. We will model this problem as a 4.2 10 14 × Hz wave incident in the x-z plane (as in the book) from the glass medium onto a planar boundary with free space. (a) What is the critical angle for this configuration? (b) For a plane wave incident at 50 degrees, calculate θ t sin and θ t cos . How far outside the cable do the free space fields attenuate to 1/e of their value at the boundary?
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312ps6 - PROBLEM SET 6 ECE 312 Autumn Quarter 2010...

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