EEE 537 L5 Wave Propagation Across Interfaces

EEE 537 L5 Wave Propagation Across Interfaces - Wave...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
ave Propagation Across Wave Propagation Across Interfaces EEE537 2010 Fall C.Z. Ning ECEE ASU 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Boundary Conditions ˆ ˆ r r s D D n σ = ) ( ˆ 2 1 r r medium 1 1 D r S Δ ∫∫ = S V dV S d D ρ r r r r n 0 ) ( 2 1 = B B n medium 2 2 D r 0 Δ h = S S d B 0 Normal component of D and B are continuous th i f h d it ( ) h s Δ = lim Using the integral form of the two curl equations, one can prove following boundary conditions: if there is no surface charge density medium 1 1 E r 1 H r W Δ = CS s d t B l d E r r r r 0 ) ( ˆ 2 1 = × E E n r r n ˆ medium 2 2 E r 2 H r 0 Δ h + = s d t D J l d H r r r r r s J H H n = × ) ( ˆ 2 1 r r n ˆ : Surface normal Tangential component of E and H are continuous if there is no surface current density EEE537 2010 Fall C.Z. Ning ECEE ASU 2
Background image of page 2
Wave Propagation Across Medium Interface: TE Waves ransverse electric Ε) ave: A C s ˆ n ˆ r Transverse electric (ΤΕ) wave: The electric field is in the z - direction. (s-polarization) α + = cos ˆ sin ˆ 1 1 1 k y k x k r r r r k i r k i r r r r + = 1 1 Ce Ae E z cos sin 1 1 1 k y k x k = I: B r k i = 2 Be E z β cos ˆ sin ˆ 2 2 2 k y k x k = r II: ( ) z E z E ˆ = r ( ) t i z z e E E ω = sin ' sin sin 2 1 1 Be Ce Ae x ik x ik x ik = + Tangential continuity at y=0 : Since this relation has to hold for all x, following two conditions must hold (understand?) ' = 2 2 2 n sin r n k = = = ε aw of EEE537 2010 Fall C.Z. Ning ECEE ASU sin sin 2 1 k k = 1 1 1 sin r n k Law of reflection Snell’s Law B C A = + x=0 in particular, 3
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Fresnel Formula for TE Waves • To determine the amplitudes, we need one more equation, provided by the 0 0 εμ μ = = k and H B continuity of tangential component of H ( ) 2 1 μ= × = E i H r r ω 0 Recall ? ω H has both x (tangential) and y (normal) components, we need only x-components } Ce Ae { e cos H cos cos sin 0 1 x 1 1 1 α ε y ik y ik x ik + = I: k β cos sin 0 2 x 2 2 Be e cos H y ik x ik = s s 2 1 II: 1 (2.33) B s cos C A or B cos ) C A ( cos 2 0 0 = = + Tangential continuity at y=0: EEE537 2010 Fall C.Z. Ning ECEE ASU cos 1 B C A = + 4
Background image of page 4
Fresnel Formula for TE Waves B ] cos sin cos sin 1 [ B ] cos cos 1 [ 2 1 2 α β ε + + = A B ] cos
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 01/02/2012 for the course ECE 537 taught by Professor Czning during the Fall '10 term at ASU.

Page1 / 20

EEE 537 L5 Wave Propagation Across Interfaces - Wave...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online