EEE 537 L7 Waveguide Theory Based on Wave Optics

EEE 537 L7 Waveguide Theory Based on Wave Optics -...

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Waveguide Theory Based on Wave Optics • Waveguides were discussed in terms of geometric optics r ray optics (Snell’s law total reflection etc) or ray optics (Snell s law, total reflection etc) • Geometric or ray optics fails to describe certain optical henomena (interference, diffraction, polarization, etc) phenomena (interference, diffraction, polarization, etc) • More rigorous description is wave optics, or physical optics (under what conditions is geometric optics valid?) • In wave optics, waveguides are dealt with by solving Maxwell’s equations directly with appropriate boundary nditions conditions EEE537 Fall 2010 C.Z. Ning, ECEE ASU 1
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Planar Waveguide: Polarization Constrains General solution of the field in a 2D waveguide with propagation direction along z ] z) - i( ω [ e ) y x, ( β t xp E E = ] z) - i( ω [ e ) y x, ( t xp H H = β : propagation constant for propagating wave with given free space wavelength: π c 2 2 ow do you determine ω λ k 0 = = EEE537 Fall 2010 C.Z. Ning, ECEE ASU Part of task of waveguide theory: solve wave equation with boundary conditions! How do you determine ? 2
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For a slab waveguide uniform in y: 0 = y x z n r2 n r1 TE Wave: x y H E μω β = n r2 Maxwell equations factorized to two blocks: Special Case: Free Space y z x E i x H H i εω = ) ( , , z y x H E H If in addition, 0 = x z y H i x E = 0 H 0 x E z y = = x y εωΕ βΗ = TM Wave: H y ) 0 ( , , y x E H y z x ιμωΗ x Ε ιβΕ = + 0 E 0 x z = = ) ( , , z y x E H E ) 0 ( H E EEE537 Fall 2010 C.Z. Ning, ECEE ASU z y ιωεΕ x Η = , , y x TEM Waves (no guiding!) 3
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Wave Equations in a Slab Wave Guide ithout loss) (without loss) TE Mode x x 0 2 2 2 = + ) ( ) ( ) ( x E x E y β εμ ω z n r1 n r2 n r1 2 x y n r n r2 n r2 TM Mode 0 2 2 2 2 = + (x) )H β εμ ( ω x (x) H y y EEE537 Fall 2010 C.Z. Ning, ECEE ASU 4
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TE Mode 0 2 2 2 2 = + ) ( ) ( ) ( x E n k x E y r 2 0 y β x π ε μ ω 2 0 0 0 = = k 0 r k n = με λ EEE537 Fall 2010 C.Z. Ning, ECEE ASU 5
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Properties of Modes at ω (n r1 >n r2 ): r1 0 r2 0 n k n k 0 < < < β Case 1: 1 2 2 2 2 ) all regions 0 2 1 0 2 < = ) β n (k (x) E x (x) E ,r r y y
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This note was uploaded on 01/02/2012 for the course ECE 537 taught by Professor Czning during the Fall '10 term at ASU.

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EEE 537 L7 Waveguide Theory Based on Wave Optics -...

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