6.007 Lecture 29: Reflection and Transmission of EM Waves

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 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. Coherent light Propagation 3. In a double-slit direction experiment, as Barrier with you decrease the double slits space between the slits, the interference destructive constructive peaks decrease interference interference proportionally. detector screen

2 Waves in Materials ω k = (n − jκ ) c

Index of refraction

Absorption coefficient 2κω 4πκ α = = c λ

3 Incident and Transmitted Waves same amplitudes E Normal Incidence H incident wave

transmitted wave reflected wave

Medium 1 Medium 2 Incident Wave Transmitted Wave

4 EM Wave Reflection Metal Reflection Thin Film Interference

Dielectric Reflection Metal Reflection © Kyle Hounsell. All rights reserved. This content Image in the Public Domain is excluded from our Creative Commons license. For more information, see Image by Ali Smiles :) http://ocw.mit.edu/fairuse. http:/www.flickr.com/photos/ 77682540@N00/2789338547/ on flickr

Cell Phone Reflection AM Radio Reflection

5 IncidentE and Transmitted Waves incident wave H Normal Incidence

transmitted wave reflected wave

Medium 1 Medium 2

Incident Wave Known Transmitted Wave

Define reflection Reflected Wave coefficient as

Define transmission coefficient as

6 Key Takeaways

• Define the reflection coefficient as

• Define the transmission coefficient as

7 E-Field Boundary Conditions

area A nˆ EA⊥ + + + + +δ + ρs surface EB⊥ Normal is discontinuous at a surface charge.

C EA nˆ δ surface EB L Tangential is continuous at a surface.

Known

8 H-Field Boundary Conditions

area A nˆ μoHA⊥ δ surface μoHB⊥ Normal is continuous at a surface.

C nˆ HA K δ HB Tangential is discontinuous at L a surface current .

9 Incident EM Waves at Boundaries

E incident wave H Normal Incidence

Medium 1 Medium 2

Incident Wave Known

i −jk1z Ei =ˆxEoe 1 1 i −jk1z Hi = zˆ × Ei =ˆy Eoe η1 η1

10 Reflected EM Waves at Boundaries

H Normal Incidence E

reflected wave

Medium 1 Medium 2

Reflected Wave Unknown DEFINE REFLECTION COEFFICIENT AS

r +jk1z Er =ˆxEo e 1 Er o +jk1z Hr =(−z ˆ) × Er = −yˆ e η1 η1

11 Transmitted EM Waves at Boundaries E H Normal Incidence

transmitted wave

Medium 1 Medium 2

Transmitted Wave Unknown DEFINE TRANSMISSION COEFFICIENT AS

t −jk2z Er =ˆxEoe 1 Et o −jk2z Ht = zˆ × Et =ˆy e η2 η2

12 Reflection & Transmission of EM Waves at Boundaries E1 = Ei + Er E2 = Et

MediumMedium 11 Medium Medium 2 2 H1 = Hi + Hr H2 = Hr

13 Reflection of EM Waves at Boundaries E1(z=0) = E2(z=0)

H1(z=0) = H2(z=0) μ η =

14 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 Reflection & Transmission of EM Waves at Boundaries

E Normal Incidence incident wave H

transmitted wave

Medium 1 Medium 2

Additional Java simulation at http://phet.colorado.edu/new/simulations/

16 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 Reflectivity of Dielectrics

Consider nearly-lossless optical materials. For typical dielectrics,

μ1 ≈ μ2 ≈ μ0.

μμ 21− εε ε− ε n− n r = 21≈ 12 = 12 μμ εε+ n+ n 21+ 12 12 εε21

Result μ1 ≈ μ2 μ1 ≈ μ2

Image by Will Montague http://www.flickr.com/ photos/willmontague/3787127610/ on flickr

18 Reflection of EM Waves at Boundaries

REMEMBER:

In terms of the In terms of characteristic the index of impedances refraction, assuming

μ1 = μ2 = μ0

Animations © Dr. Dan Russell, Kettering University. All rights reserved. This content is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/fairuse. What is different in the two reflected waves ?

Which side is air and which side is glass ?

19 Why does metal reflect light?

20 Microscopic Lorentz Oscillator Model

21 T-A-R-T

70 T A R T 60

50 % 40

Reflection T A R T 20

T-A-R-T - the material has four distinct regions of optical properties:

• Transmissive, ω < ω0 - γ/2,

• Absorptive, ω0 - γ/2 < ω < ω0 + γ/2

• Reflective, ω0 + γ/2 < ω < ωp

• Transmissive, ω > ωp

22 i −jkz E =ˆxEoe reflected wave Reflection of a E Normally Incident H i =ˆy o e−jkz η EM Wave from a o Perfect Conductor

Incident wave

Standing wave pattern of the E-field

kz = −2πkz= −π

Standing wave pattern of the H-field

kz = −3π/2 kz = −π/2

23 Microscopic Lorentz Oscillator Model

… for FREE ELECTRONS IN METALS

Drude Model for metals γ/2 0.5 0.4 i r 0.3 6 0.2 5 κ 0.1 i 4 κ , ω r

ωp n, 3 R T -5 -10 r 2 n

-20 1 n -25 ω -30 ω p

24 Reflectivity of Silver

γ/2

100 6

5 κ 80

κ 60

n, R 3 T R T 40 2 n Reflection(%) 20 1 n ω ω ω p ω p

25 Ice is more reflective than water

10% reflected by ocean water 20% reflected by vegetation and dark soil 70-80% of sunlight reflected by snow

26 Thin Film Interference

Constructive interference Incident light

air oil

water

Image by Yoko Nekonomania http://www. flickr.com/photos/nekonomania/4827035737/ on flickr

27 MIT OpenCourseWare http://ocw.mit.edu

6.007 Electromagnetic Energy: From Motors to Lasers Spring 2011

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