Optical properties of a conductor
Why do metals reflect so well?
Modification for conductor: free electrons, so
o2  0
qe
qe
i  k r t 
i  k r t 
r r  r 
Eo e
 r r 
Eo e
me
me
A
2
o
For bound charges, the spring limits the displacement r
What limits r for free charges? At what frequency is the
motion the largest?
Optical properties of a conductor
We can start with of dielectric (insulator):
2
q
2
1
eN
 n  i   1      1  m   2   2  i
e o
oA
…and modify for conductor:  2  0
o
 n  i 
2
 1      1 
p
2
i  
2
 p2
qe2 N

me o
Optical properties of a conductor
Case of very little damping <<:
 n  i 
2
 1
 p2
2
n2  2in   2  1 
2in  0 ?
p2
2
A
One must be zero, one nonzero.
 p2
For < p , check the sign of 1  2 .

Which must be nonzero?
a) n
b) 
n,k for metal. Plasma frequency divides two regimes
=0
n, 
=p/10
=p/10
n, 
A
 n  i 
2
 1
p
2
i   2
Which frequencies are transmitted well?
Which are reflected well?
Typical plasma frequencies
p
metals
density N (m-3)
1028
(Hz)
1016
semicond. (pure)
1024
1014
semicond. (doped),
fusion expts
1020
1012
ionosphere
(60 to 450 km)
1011
107
interplanetary space
107
105
2
q
2
eN
p 
me o
Reflectance vs. Wavelength
Plasma frequency of silver
Poynting Vector
energy density in a vacuum
S  E
B
u field
  0 E 2 B2


 2
20




Its magnitude is the intensity: Power/area
o

S  
u field  umedium
t


What equation in this course does this look like?
So S is an energy flow vector: energy/area/time
S or intensity
For a plane wave in index n, derive the time average intensity
S  E
B
o
Bo 
k  Eo

From Maxwell Eqns
In an isotropic material, all the vectors are perpendicular.
I time  avg

2
n o c
n o c
2
2

Eo 
Eo x  Eo y  Eo z
2
2
2
nc

Bo
2 o
2

Directions of vectors
The following are always true:!
(definition and basic MaxEqn for plane wave)
S  E
B
o
Bo 
k  Eo

Which vector pair is not guaranteed to be perpendicular?
a) E, S
b) E, k
c) E, B
d) S, B
e) B, k
Preview of a birefringent crystal
Review
P.
f ( x, t)  f ( x  ct)is a solution to
It is also a solution to ____:
1)
3
2)
a)
b)
c)
d)
2
1  2 f ( x, t)
f ( x, t)  2
0
2
2
x
c
t

1  3 f ( x, t)
f ( x, t)  3
0
3
3
x
c
t
4
1  4 f ( x, t)
f ( x, t)  4
0
4
4
x
c
t
eqn 1
eqn 2
both
neither
Contrast: E/M wave properties in seawater
Seawater has free charges,
But unlike metals, it has very strong damping >>
(radio waves moving ions in seawater )
Must keep  small so  will be small!
 n  i 
2
 1      1 
 p2
i   2
A
ZEVS, THE RUSSIAN 82 Hz ELF TRANSMITTER
US is experimenting with 2 Hz transmitters!