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# Class Note for ECE 6340 with Professor Jackson at UH 2

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COURSE
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TYPE
Class Notes
PAGES
14
WORDS
KARMA
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This 14 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
Critical Angle Assume lossless materials nz39 Vluz39rgz39w 2172 n2 lt I ll quot2 Snell s law 6 sin 1 sin n1 sm i 2n2 sm 9t r i quot2 Critical Angle At the critical angle si1r1 61 1 Q 90 Critical Angle cont 9t 2 sin 1 sin 61 ky 2k1 sian gt k1 sin c 2 k2 sin tc 2 k2 so ky gtk2 Critical Angle cont power flow III II quot region 2 II k2 2ky2lt ja g2yky Critical Angle cont I l Determine the transmitted angle 9t 1116 1sm6 i quot2 n sinxjysinxcoshyjcosxsinhy lsin6i gt 0 n2 Use y0 or xi7T2 not possible must use sngn sinxz sin l gt0 icoshyz sin i gt0 n2 n2 Critical Angle cont n coshy lsm 9l n2 gt y i cosh 51m n2 n irjcosh1 1s1n6l n2 Er J jy Hence 9t 2 E A Critical Angle cont 2 ijcosh 1 sin6i 2 112 Choose sign to obtain correct value for kl2 kz2 2k2 cos 6t 2 k2 cosx jy 2 k2 cosxcoshy jsinxsinh y jk2 sinh y j k2 sinhicosh 1 ism 61 quot2 The sign is chosen to obtain a decaying wave Critical Angle cont Hence Notes The critical angle applies to any polarization A critical angle exists only when going from a higher to a lower density medium 721 gt 722 Practical note When dealing with inhomogeneous plane waves complex angles it is usually easier to avoid working with angles and use the separation equation instead kzz jlky2 k22 TMZ Brewster Angle E Brewster Angle cont 7M 7M Perfect match Z 01 Z 02 kzl kZZ 081 082 2 2 2 cl 0sz k2 k1 sm 9b 91 92 12 1 sin2 6 22 12 sin2 6b 2 2 81 82 Brewster Angle cont Assume 1 uQ 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 82 2 2 82 81 81 82 sin2 6b Brewster Angle cont Hence For nonmagnetic media only the TMZ polarization has a Brewster angle A Brewster angle exists for any material contrast ratio 5111 9th Brewster Angle cont n 8 lsm 6b 1 311161 quot2 82 92 VQVqQ 81 81482 Hence ECE 6340 Intermediate EM Waves Fall 2008 Prof David R Jackson Dept of ECE Notes 19

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