Reflection & Transmission of EM Waves

Outline

Reading – Shen and Kong – Ch. 4

• 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.

3. In a double-slit experiment, as you decrease the space between the slits, the interference peaks decrease proportionally.

Propagation direction

Coherent light

Barrier with double slits

constructive interference

destructive interference

detector screen

2

Waves in Materials

Index of refraction

ω

k = (n − jκ )c

2κω 4πκα = =

c λ

Absorption coefficient

3

Incident and Transmitted Waves

Incident Wave

Normal Incidence

Transmitted Wave

same amplitudes incident wave

Medium 1 Medium 2

�E

�H

transmitted wave

reflected wave

4

EM Wave Reflection

Thin Film Interference

Dielectric Reflection Metal Reflection

Cell Phone Reflection AM Radio Reflection

Image by Ali Smiles :) http:/www.flickr.com/photos/77682540@N00/2789338547/

Image in the Public Domain

on flickr

Metal Reflection

© Kyle Hounsell. All rights reserved. This content is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/fairuse.

5

Incident and Transmitted Waves

Incident Wave Known

Reflected Wave

Normal Incidence

Transmitted Wave

Define reflection coefficient as

Define transmission coefficient as

incident wave

Medium 2

�H

�E

Medium 1

transmitted wave reflected wave

6

Key Takeaways

•  Define the reflection coefficient as

•  Define the transmission coefficient as

2

7

Normal is discontinuous at a surface charge.

E-Field Boundary Conditions

Tangential is continuous at a surface.

Known

nEA⊥

EB⊥

δ

A

ρs+ + + + + +

surface

area

surface

L

nC

EB‖

EA‖

δ

8

H-Field Boundary Conditions

Tangential is discontinuous at a surface current .

Normal is continuous at a surface.

surface

area

δ

A nμoHA⊥

μoHB⊥

nδ�K

L

CHA‖

HB‖

9

Incident EM Waves at Boundaries

Incident Wave Known

�Ei = xEioe

−jk1z

1 1� �Hi = zη

× Ei y= ˆ Eie−jk1z

1 η o1

Normal Incidence incident wave

Medium 2

�H

�E

Medium 1

10

Reflected EM Waves at Boundaries

Reflected Wave Unknown DEFINE REFLECTION COEFFICIENT AS

�E = xEre+jk1zr o

1 Er� (−z)× �Hr = ˆ E = −y o e+jk1

r ˆ z

η1 η1

Normal Incidence

Medium 2

�H�E

Medium 1

reflected wave

11

Transmitted EM Waves at Boundaries

Transmitted Wave Unknown DEFINE TRANSMISSION COEFFICIENT AS

�Er = xEtoe

−jk2z

1 Et� �Ht = z

η× Et y= ˆ o e−jk2z

2 η2

Normal Incidence

transmitted wave

Medium 2

�H

�E

Medium 1

12

Reflection & Transmission of EM Waves at Boundaries

� � �E1 = Ei + E � �r E2 = Et

Medium 1 Medium 2

� � �H1 = Hi +Hr � �H2 = Hr

Medium 1 Medium 2

13

Reflection of EM Waves at Boundaries

� �E1(z=0) = E2(z=0)

� �H1(z=0) = H2(z=0)

η =

√μ

ε

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

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

Normal Incidence incident wave

Medium 1 Medium 2

�H

transmitted wave

�E

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

2

2

nn

Consider nearly-lossless optical materials. For typμ1 ≈ μ2 ≈ μ0.

μ μ−2 1

ε ε − ε= ≈ 2 1 ε

r 1 =2 −n 1

μ μ2 1 +ε ε+ 1 2 +n1

ε ε2 1

Result μ1 ≈ μ2 μ1 ≈ μ2

ical dielectrics,

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

18

Reflection of EM Waves at Boun

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

assuming μ1 = μ2 = μ0

daries

What is different in the two reflected waves ? Which side is air and which side is glass ?

REMEMBER:

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.

19

Why does metal reflect light?

© Kyle Hounsell. All rights reserved. This content is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/fairuse.

20

Microscopic Lorentz Oscillator Model

21

T-A-R-T

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

Refl

ecti

on %

T A R T

T A R T

0

10

20

30

40

50

60

70

22

Standing wave pattern of the H-field

Standing wave pattern of the E-field

Reflection of a Normally Incident EM Wave from a Perfect Conductor

Incident wave

reflected wave

kz = −2π kz = −π

kz = −3π/2 kz = −π/2

�Ei = xEoe−jkz

�Hi = y

(Eo

ηo

)e−jkz

23

Microscopic Lorentz Oscillator Model … for FREE ELECTRONS IN METALS

ε r,ε

i

Drude Model for metals

εi

εr

εr

ωωp

0.1

0.2

0.3

0.4

0.5

-5

-10

-20

-25

-30 pω

n

κ

γ/2

n,κ

n1

2

3

4

5

6

ω

T R

24

Reflectivity of Silver

pω

n

κ

γ/2

n,κ

n1

2

3

4

5

6

pωωω

100

80

60

40

20

Refl

ecti

on(%

) T R T R

25

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

Thin Film Interference

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

water

oil

Incident light

Constructive interference

air

27

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