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

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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 12.3 Andrew Kirk 2005 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 2005 ECSE 352 3.3-3 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 2005 ECSE 352 3.3-4

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Contents • Examples of multilayer dielectrics • Definition of wave impedance • Solution for two-layer dielectric n p t f impdn t n s f mt in Concept of impedance transformation • Antireflection coatings ©AGK 2005 ECSE 352 3.3-5 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 2005 ECSE 352 3.3-6 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 ? ow does this vary with layer η η η E 1 - Hw yw y thickness, properties ? Γ = ? 2 3 1 ©AGK 2005 ECSE 352 3.3-7 = τ =? Z L Z 2 Z 1 Total field approach η 1 η 2 Dielectric 2 Dielectric 1 Dielectric 3 η 3 x ©AGK 2005 ECSE 352 3.3-8 z z =0 z = d
Calculate Field in Region 2 η 1 η 2 Dielectric 2 Dielectric 1 Dielectric 3 η 3 z z =0 z =d ©AGK 2005 ECSE 352 3.3-9 Total wave impedance • Define the total wave impedance , Z • This is the ratio of E to H at any point • For an unbounded medium, is given by impedance f the medium I e of the medium, I.e. = η For a z-directed, x-polarized plane wave: E ©AGK 2005 ECSE 352 3.3-10 H Wave impedance at a dielectric boundary η η 2

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