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Class Note for ECE 6340 with Professor Jackson at UH 2


Class Note for ECE 6340 with Professor Jackson at UH 2

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This 13 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 18 views.

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Date Created: 02/06/15
ECE 6340 mntermediate EM Waves Fall 2006 Prof Donald R Wilton ECE Dept Notes 19 Based on Notes by Prof David R Jackson Critical Angle Assume lossless materials quot139 Vluz39rgzw 1212 n2 lt 721 n2 Snell s law 39 39 6 sin1 sin n1 sm 91 n2 sm Q t n2 Critical Angle At the critical angle at 90 Sing 1 quot2 722 lt 1 21 quot2 Critical Angle cont 9t 2 sin 1 i sin 61 n2 91 gt 90 3 6t 2 complex kyzk1 sian gt k1 sin c 2 k2 so ky gt 2 Critical Angle cont ky gt k2 kZZ j ky2 k22 ja powerflow I region 2 Critical Angle cont I l Determine the angle at 1116 1sm6 i quot2 Let er x Use o o n smx jy 2 sm x cosh y j cos x smh y 1 sm 91 n2 7139 Hence Ht y 2 n cosh y lsm n2 Critical Angle cont y i cosh 1 sinQ quot2 i cosh1 sin 61 n2 7 Hence 6 E W i 0 Choose sign to obtain correct value for kz2 kz2 2k2 cos 6t 2 k2 cosx jy 2 k2 cosxcoshy j sinxsinh y jk2 sinhy The sign is jk2 sinh i cosh 1 153101 Chosen to obtain a n2 decaying wave Critical Angle cont Hence The critical angle applies to any polarization A critical angle exists only when going from a higher to a lower contrast medium n1 gt n2 TM rewster Angle TM TM ZOI ZOZ Brewster Angle cont 7M 7M Perfect match Z01 Z2 kzl kZZ a 81 a 82 2 2 2 100365 zxkz k1 sm 9b 91 92 12 1 sin2 6b 22 12 sin2 6b 2 2 81 82 Brewster Angle cont Assume 1 2 2 2 1 sm QbZEZ glsm Qb 2 81 82 2 2 2 2 2 52 52 sm Qb glgz gl sm 6b 82 82 81 Z 82 2 2 82 81 81 82 2 sm 67b Brewster Angle cont a sm b 2 81 82 8182 J5 9b l o For nonmagnetic media only the TMz polarization has a Brewster angle Hence A Brewster angle exists for any material contrast ratio Brewster Angle cont 8 sm 9 sm 9b 1 sm 9b quot2 5 Hence


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