161_1_Lecture_3

161_1_Lecture_3 - EE161 Electromagnetic Waves Fall, 2010...

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EE161 Electromagnetic Waves all 2010 Fall, 2010 Instructor: Dr. Shenheng Xu Electrical Engineering Dept., UCLA gg p , © Prof. Y. Ethan Wang
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Lecture 3 • General Plane Wave Solutions • Field Direction and Wave Propagation Direction • Polarization of the Wave
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General Plane Wave Solutions ' ) ' ( ~ jkz Ae z E As aforementioned, an uniform plane wave traveling along z’ axis, has an expression: gg , p y z Z’ One can rotate the Cartesian coordinates arbitrarily, with certain span angles and : y, p g The coordinate transform defines: cos sin sin cos sin ' z y x z x z y x jk jkz Ae Ae E ) cos sin sin cos sin ( ' ~ Therefore, a plane wave that is traveling toward an arbitrary direction is given by: jkz jky jkx Ae cos sin sin cos sin z jk y jk x jk z y x Ae (Linear phase variation in regard to x, y, z axes)
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Plane Wave Solutions in Vector Form 2 2 2 2 z y x k k k k ave number z k Wave number cos sin k k x y k z cos sin sin k k k k z y k y (   are the propagation angle) x k x ) ( ) , , ( ~ z k y k x k j x z y x Ae z y x E General solution of E field, (x- component) r k n k z k y k x k z y x ˆ ˆ ˆ ˆ k Wave number vector: Position vector: z z y y x x ˆ ˆ ˆ r Propagation direction bservation direction Observation direction
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Plane Wave Solutions in Vector Form k r k j Phase variation of the wave follows the factor of ) ( z k y k x k j z y x g r e e e.g. Phase changes slower when k and r re not pointing to the same direction! are not pointing to the same direction!
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This note was uploaded on 02/09/2011 for the course EE 161 taught by Professor Huffaker during the Spring '08 term at UCLA.

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161_1_Lecture_3 - EE161 Electromagnetic Waves Fall, 2010...

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