a why do metals reflect so well? optical properties of a conductor modification for conductor: for...
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A
Why do metals reflect so well?
Optical properties of a conductor
Modification for conductor: 2 0o
2 e e
e e
i k r t i k r t
o o o
q qr r r E e r r E e
m m
For bound charges, the spring limits the displacement r
What limits r for free charges?
displacement r for bound, unbound charges
0 0.5 1 1.5 2 2.5-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5x 10
-6
(1016 rad/sec)
disp
lace
men
t xo
magnitude
real
imaginary
A
Optical properties of a conductor
2
2
2 2
11 1 e
e o o
q Nn i
m i
First, start with (opposite case!) of dielectric: (insulator)
Modification for conductor:
2
2
21 1 pn i
i
2 0o
Typical plasma frequencies density N (m-3) (Hz)
metals 1028 1016
semicond. (pure) 1024 1014
semicond. (doped), fusion expts
1020 1012
ionosphere (60 to 450 km)
1011 107
interplanetary space
107 105
p
22 ep
e o
q N
m
A
Optical properties of a conductor
2
2
21 pn i
Case of very little damping << :g w
22 2
22 1 pn in
For < w wp , check the sign of . Which must be nonzero?
a) n b) k
2 0in ?2
21 p
A
Optical properties of a conductor
Since wo 0, can we simply shift n( ), ( )?w k w
n,k for metal. Plasma frequency divides two regimes
A
g=wp/10
g=0n, k
g=wp/10
n, k
Which frequencies are transmitted well?Which are reflected well?
Reflectance vs. Wavelength
Plasma frequency of silver
Poynting Vectorenergy density in a vacuum
field mediumS u ut
2 20
02 2fieldE B
u
o
BS E
What equation does this look like?
Its magnitude is the intensity: Power/area
So S is an energy flow vector: energy/area/time
Directions of vectors
o
BS E
o
o
k EB
S, irradiance, intensity
o
BS E
For a plane wave in index n, derive the time average intensity
oo
k EB
22 2 2
2
2 2
2
o otime avg o ox o y o z
oo
n c n cI E E E E
ncB
o
BS E
o
o
k EB
The following are always true (definition and basic MaxEqn for plane wave)
Which vector pair is not guaranteed to be perpendicular? a) E, Sb) E, kc) E, Bd) S, Ee) B, k
Preview:
P. is a solution to
It is also a solution to ____:1)
2)
a) eqn 1b) eqn 2c) bothd) neither
Wave equation
f x t f x ct ( , ) ( )2 2
2 2 2
10
f x tf x t
x c t
( , )
( , )
3 3
3 3 3
10
f x tf x t
x c t
( , )
( , )
4 4
4 4 4
10
f x tf x t
x c t
( , )
( , )