reflection & transmission of em waves · pdf filedestructive interference occurs when two...
TRANSCRIPT
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
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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.
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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
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Key Takeaways
• Define the reflection coefficient as
• Define the transmission coefficient as
2
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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
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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‖
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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
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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
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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
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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
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Reflection of EM Waves at Boundaries
� �E1(z=0) = E2(z=0)
� �H1(z=0) = H2(z=0)
η =
√μ
ε
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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?
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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
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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
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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
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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.
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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
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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
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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
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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
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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
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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
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Thin Film Interference
Image by Yoko Nekonomania http://www. flickr.com/photos/nekonomania/4827035737/ on flickr
water
oil
Incident light
Constructive interference
air
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