161_1_Class3

161_1_Class3 - EE161 Electromagnetic Waves Spring, 2010...

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Unformatted text preview: EE161 Electromagnetic Waves Spring, 2010 Prof. Y. Ethan Wang Electrical Engineering Dept. UCLA Lesson 3 General Plane Wave Solutions Field Direction and Wave Propagation Direction Polarization of the Wave General Plane Wave Solutions cos sin sin cos sin ' z y x z + + = ' ) ' ( ~ jkz Ae z E = As aforementioned, an uniform plane wave traveling along z axis, has an expression: x y z Z One can rotate the Cartesian coordinates arbitrarily, with certain span angles and : The coordinate transform defines: z jk y jk x jk jkz jky jkx z y x jk jkz z y x Ae Ae Ae Ae E + + = = = = cos sin sin cos sin ) cos sin sin cos sin ( ' ~ Therefore, a plane wave that is traveling toward an arbitrary direction is given by: (Linear phase variation in regard to x, y, z axes) Plane Wave Solutions in Vector Form ) ( ) , , ( ~ z k y k x k j x z y x Ae z y x E + + = General solution of E field, (x- component) n k z k y k x k z y x = + + = k Wave number vector: Position vector: z z y y x x + + = r r k Propagation direction 2 2 2 2 z y x k k k k + + = Wave number = = = cos sin sin cos sin k k k k k k z y x ( , are the propagation angle) x y z k k x k y k z Observation direction Plane Wave Solutions in Vector Form r k r k j e Phase variation of the wave follows the factor of ) ( z k y k x k j z y x e + + e.g....
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This note was uploaded on 05/10/2010 for the course EE 190776201 taught by Professor Yuanxunethanwang during the Spring '10 term at UCLA.

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161_1_Class3 - EE161 Electromagnetic Waves Spring, 2010...

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