Lect 3.3

# Lect 3.3 - Department of Electrical and Computer...

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Karl E. Deckart http://micro.magnet.fsu.edu/featuredmicroscopist/deckart/soap01small.html Department of Electrical and Computer Engineering ECSE 352 Electromagnetic Waves and Optics 3.3 Wave reflection at multiple interfaces References: Section 13.3 AK/ZM 3.3-2 Multilayer dielectrics • How do optical antireflection coatings work ? • How do we make a protective ousing for a radar that won’t housing for a radar that won t reflect the radar power back towards the transmitter ? How do you make a stealth aircraft ? hy do we see colours on top of Why do we see colours on top of a film of oil in a puddle ? ©AGK/ZM ECSE 352 3.3-3 ©AGK/ZM ECSE 352 3.3-4

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Blue morpho butterfly ©AGK/ZM ECSE 352 3.3-5 Learning outcomes After taking this class you should be able to: • Define the wave impedance of the total field • Explain the way in which the concept of wave pedance relates to the ehaviour f waves at impedance relates to the behaviour of waves at multilayer dielectrics • Calculate the reflection and transmission coefficients for a two layer dielectric • Describe the conditions required for high and low eflectance for a two layer dielectric reflectance for a two layer dielectric • Explain the principles of a 1/4 wave dielectric antireflection coating ©AGK/ZM ECSE 352 3.3-6 Contents • Examples of multilayer dielectrics • Definition of wave impedance • Solution for two-layer dielectric • Concept of impedance transformation • Antireflection coatings ©AGK/ZM ECSE 352 3.3-7 Review: Waves incident on an interface 1 x E + η 2 η 1 E ++ 21 x x EE τ = 11 x x −+ 1. Incident, reflected and transmitted waves 2 1 ,2 η ηη Γ= = Total field in region 1: () 1 1 1 0 xT x x jz E Ee e β φ + + =+ Γ ©AGK/ZM ECSE 352 3.3-8 2. Total wave amplitude in each medium ( ) 10 x
Multiple dielectric • Multiple reflections-transmissions ime harmonic waves st one d Time harmonic waves Æ just one reflected wave, one transmitted wave • What is total transmitted energy ? E 1 + E 2 + • What is total reflected energy ? How does this vary with layer η η η E 1 - Hw yw y thickness, properties ? 11 −+ EE Γ = ? 2 3 1 ©AGK/ZM ECSE 352 3.3-9 21 τ ++ = τ =? Z L Z 2 Z 1 Total field approach η 1 η 2 Dielectric 2 Dielectric 1 Dielectric 3 η 3 x Reflected wave H - Transmitted H 2 - E 1 - 1 a nr wave E 3 + E 2 - a n - E 1 + - a i Incident wave E 2 + a + H 3 + a nt ©AGK/ZM ECSE 352 3.3-10 z H 1 ni H 2 + n z =0 = d Total field approach η η 2 Dielectric 2 Dielectric 1 Dielectric 3 η 3 τ eff Effective transmittance at =d Γ eff Reflected wave H - Transmitted zd E 1 - 1 a nr wave E 3 + E 1 + - a i Incident wave H 3 + a nt Γ 3 ©AGK/ZM ECSE 352 3.3-11 z H 1 ni z =0 z = d 23 Calculate Field in Region 2 η 1 η 2 Dielectric 2 Dielectric 1 Dielectric 3 η 3 E 2 + E 2 - E 3 + =0 =d + + = 2 2 2 E E E 2 η + Γ = 20 23 20 E E 2 3 3 23 + = Γ ( ) ( ) ( ) ( ) ( ) [ ] d z j d z j E z x Γ + = 2 23 2 20 2 exp exp β a E E 20 p p ©AGK/ZM ECSE 352 3.3-12 ( ) ( ) ( ) ( ) ( ) [ ] d z j d z j z y Γ = 2 23 2 2 2 exp exp a H

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Total wave impedance • Define the total wave impedance , Z • This is the ratio of E to H at any point
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## This note was uploaded on 02/14/2011 for the course ECSE 352 taught by Professor Mi during the Fall '10 term at McGill.

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Lect 3.3 - Department of Electrical and Computer...

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