1. Last time: optical properties of spring-like oscillating dipoles: dielectric (or insulator)

2. Optical properties of a conductor
Why do metals reflect so well?
If there’s no damping, how to they respond to a steady E-field? A
What will their motion be in a light field?

3. Optical properties of a conductor
We can start with the math done for dielectric (insulator): A
…and modify for free electrons:

4. Optical properties of a conductor
Case of very little damping g<<w: A
For w< wp , check the sign of
Which must be nonzero? n
b) k

5. Complex index, dielectric constant, k
g=0
n, k A
What does n = 0 mean here?
For dielectric, k creates absorption.
For metal, k creates strong reflection

6. n,k for metal. Plasma frequency divides two regimes
g=wp/10
g=0
n, k A
Which frequencies are transmitted well?
Which are reflected well?

7. 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
105

8. Reflectance vs. Wavelength
Plasma frequency of silver

9. Poynting Vector energy density in a vacuum
Its magnitude is the intensity: Power/area
What equation in this course does this look like?
So S is an energy flow vector: energy/area/time

10. S or intensity
For a plane wave in index n, derive the time average intensity
From Maxwell Eqns
In an isotropic material, all the vectors are perpendicular.

11. Directions of vectors The following are always true:!
(definition and Maxwell eqn for plane wave)
Which vector pair is not guaranteed to be perpendicular?
E, S
E, k
E, B
S, B
B, k

12. Preview of a birefringent crystal

13. Complex index, dielectric constant, k

14. Complex index, dielectric constant, k
P. Near a resonance frequency, materials with atomic dipoles might have for example n = 2 and k = 3
When the wave has moved into the material by a distance of one vacuum wavelength, by what factor is the wave amplitude reduced?
a) exp(-2p)
b) exp(-3p)
b) exp(-4p)
d) exp(-6p)
P4. What is the phase change of the
wave after traveling this distance? A

15. P2. Clear, colorless glass has no resonances and little absorption in the visible, but does have them in the UV, which is at a higher w.
Hence in clear glass, index n has ______ curvature vs w for visible light.
positive
negative
Know the shape of these curves! Close your eyes and sketch and label both curves.

16. Hint: what would these curves look like in the limit of N  0?
P3. If we increase the density of a gas (N), index n
a) increases for all w
b) decreases for all w
c) increases with density below resonance, decreases above
d) decreases with density below resonance, increases above
Hint: what would these curves look like in the limit of N  0?

17. Common optical glass indices vs wavelength

18. P6. In a glass that absorbs green light
the index , imaginary index k is greatest for ______ (same choices)
yellow
green
blue
P4. In a glass that absorbs green light best, the real index n is probably greatest for ______ light.
yellow
green
blue