Reflection & Transmission of EM Waves

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1 Reflection & Transmission of EM Waves Reading Shen and Kong Ch. 4 Outline Everyday Reflection Reflection & Transmission (Normal Incidence) Reflected & Transmitted Power Optical Materials, Perfect Conductors, Metals 1

2 TRUE or FALSE 1. Destructive interference occurs when two waves are offset by a phase of ½πm, or half a wavelength. 2. The intensity of a plane wave oscillates in time. This means it is always constructively and destructively interfering with itself. 3. In a double-slit experiment, as you decrease the space between the slits, the interference peaks decrease proportionally. Coherent light destructive interference detector screen Propagation direction Barrier with double slits constructive interference 2

This means it is always constructively and destructively interfering with itself. 3.

3 Waves in Materials ω k = (n jκ ) c Index of refraction Absorption coefficient 2κω α = = c 4πκ λ 3

$refraction Absorption$

4 Incident and Transmitted Waves same amplitudes H E incident wave Normal Incidence reflected wave transmitted wave Incident Wave Medium 1 Medium 2 Transmitted Wave 4

5 EM Wave Reflection Metal Reflection Thin Film Interference Dielectric Reflection Image in the Public Domain Metal Reflection Kyle Hounsell. All rights reserved. This content is excluded from our Creative Commons license. For more information, see Image by Ali Smiles :) on flickr Cell Phone Reflection AM Radio Reflection 5

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6 Incident and Transmitted Waves E H incident wave Normal Incidence reflected wave transmitted wave Medium 1 Medium 2 Incident Wave Known Transmitted Wave Reflected Wave Define reflection coefficient as Define transmission coefficient as 6

Incident Wave Known Transmitted Wave Reflected Wave Define

7 Key Takeaways Define the reflection coefficient as Define the transmission coefficient as 2 7

8 E-Field Boundary Conditions E A E B area A δ ρ s ˆn surface Normal is discontinuous at a surface charge. E A C δ ˆn surface E B L Tangential is continuous at a surface. Known 8

9 H-Field Boundary Conditions μ o H A area A δ ˆn surface μ o H B Normal is continuous at a surface. H A K C δ ˆn H B L Tangential is discontinuous at a surface current. 9

10 Incident EM Waves at Boundaries H E incident wave Normal Incidence Medium 1 Medium 2 Incident Wave Known E i =ˆxE i oe jk 1z H i = 1 1 ẑ E i =ˆ y E i e jk 1z o η 1 η1 10

11 Reflected EM Waves at Boundaries E H Normal Incidence reflected wave Medium 1 Medium 2 Reflected Wave Unknown DEFINE REFLECTION COEFFICIENT AS E =ˆxE r e +jk 1z r o 1 E r H ( z) r = ˆ E = y o e +jk 1 r ˆ η 1 η 1 z 11

Unknown DEFINE REFLECTION COEFFICIENT AS E =ˆxE r e

12 Transmitted EM Waves at Boundaries E H Normal Incidence transmitted wave Medium 1 Medium 2 Transmitted Wave Unknown DEFINE TRANSMISSION COEFFICIENT AS E r =ˆxE t oe jk 2z H t = 1 E t ẑ E t =ˆ y o e jk 2z η 2 η 2 12

13 Reflection & Transmission of EM Waves at Boundaries E 1 = E i + E r E 2 = E t Medium1 1 Medium 2 H 1 = H i + H r H 2 = H r 13

14 Reflection of EM Waves at Boundaries E 1(z=0) = E 2(z=0) H 1(z=0) = H 2(z=0) η = μ ɛ 14

15 Reflectivity & Transmissivity of Waves Define the reflection coefficient as Define the transmission coefficient as What are the ranges for r and t? Is energy conserved? 15

16 Reflection & Transmission of EM Waves at Boundaries H E incident wave Normal Incidence transmitted wave Medium 1 Medium 2 Additional Java simulation at 16

17 Reflectivity & Transmissivity of EM Waves Note that The definitions of the reflection and transmission coefficients do generalize to the case of lossy media. For loss-less media, r and t are real: For lossy media, r and t are complex: Incident Energy = Reflected Energy + Transmitted Energy R = r 2 fraction of incident power that is reflected T = 1 R fraction of incident power that is transmitted 17

$Reflected Energy + Transmitted Energy R = r 2 fraction of incident power that is reflected T = 1 R$

18 Reflectivity of Dielectrics Consider nearly-lossless optical materials. For typical dielectrics, μ 1 μ 2 μ 0. r μ2 μ1 ε2 ε1 ε1 ε2 n n = = 1 μ μ n 2 1 ε + ε n ε ε Result μ 1 μ 2 μ 1 μ 2 Image by Will Montague photos/willmontague/ / on flickr 18

r μ2 μ1 ε2 ε1 ε1 ε2 n n = = 1 μ μ n 2 1 ε + ε n + 1 2 + 1 ε ε 2 1 2 2

19 Reflection of EM Waves at Boundaries REMEMBER: In terms of the characteristic impedances In terms of the index of refraction, assuming μ 1 = μ 2 = μ 0 What is different in the two reflected waves? Which side is air and which side is glass? Animations Dr. Dan Russell, Kettering University. All rights reserved. This content is excluded from our Creative Commons license. For more information, see 19

Which side is air and which side is glass? Animations Dr. Dan Russell, Kettering University.

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21 Microscopic Lorentz Oscillator Model 21

22 T-A-R-T T A R T Reflection % T A R T 10 0 T-A-R-T - the material has four distinct regions of optical properties: Transmissive, ω < ω 0 - γ/2, Absorptive, ω 0 - γ/2 < ω < ω 0 + γ/2 Reflective, ω 0 + γ/2 < ω < ω p Transmissive, ω > ω p 22

23 Reflection of a Normally Incident EM Wave from a Perfect Conductor E i =ˆxE o e jkz ( ) H i Eo =ŷ η o e jkz reflected wave Incident wave Standing wave pattern of the E-field kz = 2π kz = π Standing wave pattern of the H-field kz = 3π/2 kz = π/2 23

24 0.5 Microscopic Lorentz Oscillator Model for FREE ELECTRONS IN METALS γ/2 Drude Model for metals ɛr, ɛi ɛ i ω p ɛ r ω n, κ κ R T ɛ r 2 1 n n p ω ω 24

25 Reflectivity of Silver γ/ κ 80 n, κ n R T n Reflection(%) R T ω p ω ω p ω 25

26 Ice is more reflective than water 70-80% of sunlight reflected by snow 10% reflected by ocean water 20% reflected by vegetation and dark soil 26

27 Thin Film Interference Incident light Constructive interference oil air water Image by Yoko Nekonomania flickr.com/photos/nekonomania/ / on flickr 27

28 MIT OpenCourseWare Electromagnetic Energy: From Motors to Lasers Spring 2011 For information about citing these materials or our Terms of Use, visit:

Interaction of Atoms and Electromagnetic Waves

Interaction of Atoms and Electromagnetic Waves Outline - Review: Polarization and Dipoles - Lorentz Oscillator Model of an Atom - Dielectric constant and Refractive index 1 True or False? 1. The dipole