waveguide - Guided Waves boundary conditions waves in...

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guided waves Electromagnetic Waves and Optics 1 Guided Waves • boundary conditions • waves in confined geometries • wave guides • optical fibers guided waves Electromagnetic Waves and Optics 2 Wave Guides (Light Pipes) controlled energy transport – boundary reflections direct wave – not simple ray optics if size ≈λ microwaves: metal pipes visible/near IR: glass fibers – total internal reflection
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guided waves Electromagnetic Waves and Optics 3 Boundary Conditions 2 1 2 1 0 n n t t B B S d B E E S d B t l d E = = = = ∫∫ ∫∫ r r r r r r at boundary, Maxwell’s Equations require continuity of – tangential E field –n o rm a l B f i e l d 2 t E 1 1 , µ ε 1 E 2 2 , 2 E 2 t E 1 t E 1 t E 2 n B 1 n B 1 B 1 n B 2 n B 2 B guided waves Electromagnetic Waves and Optics 4 Rectangular Wave Guide assume perfect conductor: E t = 0 (neglects skin depth) try free space solution? try TEM solution? – close: alter B direction? () t kz i t kz i e c E j B e E i E ω = = / ˆ ˆ 0 0 r r Î violates boundary conditions (unless E 0 = 0) ( ) ()() 0 0 0 0 = = = = = = = = a x E x E b y E y E y y x x t kz i t kz i e y x B j B e y x E i E = = , ˆ , ˆ r r Î violates Maxwell’s Eqs. t B j y E k z E j t B E y x x = = × ˆ ˆ ˆ r r r x y a b
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guided waves Electromagnetic Waves and Optics 5 Rectangular Wave Guide try TE solution •M a x w e l l s E q s .
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waveguide - Guided Waves boundary conditions waves in...

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