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homework5

# Engineering Electromagnetics with CD (McGraw-Hill Series in Electrical Engineering)

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EE 151 Caltech Electromagnetic Engineering Spring ‘05 Homework 5 Due Tuesday, May 10 th in class 1. Anti-reflection (AR) coating : A transparent dielectric coating is applied to a glass substrate ( ε r = 4,μ r = 1) to eliminate the reflection of a normally incident red light [ λ 0 (wavelength in free space) = 750nm]. (1) Determine the required dielectric constant and thickness of the coating. (μ r =1 ) (2) If violet light [ λ 0 = 420nm] is shone normally on the coated glass, what percentage of the incident power will be reflected? Figure 1.

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2. (Fabry-Perot Etalon) (a) Consider the Fabry-Perot Etalon below. Two identical partially reflective mirrors constitute a resonant cavity. Show that the transmittance of the plane wave A i through the etalon is: Figure 2. 3. (Metal Waveguide) Problem 14.15 and 14.16 in Hayt and Buck 7 th edition. A parallel-plate guide is partially filled with two lossless dielectrics (Figure 3) where ε r1 = 4.0, ε r2 = 2.1, and d = 1cm. At a certain frequency, it is found that the TM 1 mode propagates through the guide without suffering any reflective loss at the dielectric interface. (a) Find this frequency. (b) Is the guide operating at a
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