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# exam2 - School of Electrical and Computer Engineering...

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School of Electrical and Computer Engineering, Cornell University 1 ECE 303: Electromagnetic Fields and Waves Fall 2007 Exam 2 October 23, 2007 INSTRUCTIONS: • Only work done on the blue exam booklets will be graded – do not attach your own sheets to the exam booklets under any circumstances • Every problem must be done in a separate blue booklet – so you must have 3 separate blue booklets before starting the exam • To get partial credit you must show all the relevant work • Correct answers with wrong reasoning will not get points • All questions do not carry equal points • All questions do not have the same level of difficulty DO NOT WRITE IN THIS SPACE

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School of Electrical and Computer Engineering, Cornell University 2 Problem 1 (30 points) Consider a plane wave given by: ( ) ( ) r k j o i i e z j y x j E r E r r r r . ˆ 3 ˆ 2 ˆ + + = incident from free space upon a medium whose permittivity is described by the tensor ε . The frequency of the incident wave is ω . The plane of incidence is the x-z plane. The interface is at z= 0 as shown below. a) What is the polarization of the incident wave (linear, right or left circular, right or left elliptical, etc)? Explain your answer. No points will be awarded for a correct answer but a wrong or misleading or inadequate or incomplete explanation. Now suppose that the dielectric permittivity tensor of the medium on the right is: = 3 0 0 0 3 2 0 0 0 3 o ε ε b) In which direction does the transmitted wave go? Specify using the angle of transmission t θ and give numerical value. c) Write the complete expression for the transmitted E-field ( ) r E t r r in terms of the given parameters. There should be no unknown or unspecified variables in your answer. The values of all the variables must be specified in terms of the given parameters.
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