Announcements 2/17/12
Prayer
 Monday is holiday
 Tues is virtual Monday—we have class!
 Reading assignment for Tuesday
a. Remove section 7.1 (we’re covering it
today)
b. Keep section 7.2
c. Add Colton Fourier series/transforms
handout (I will hand it out now)

Reading Quiz

The technique of finding the complex index of
refraction, n and k, from polarization changes in
reflectance is called:
a. circularometry
b. ellipsometry
c. hyperbolometry
d. linearometry
e. parabolometry
Ellipsometry
starts linear,
angle 
3
linear polarizer,
angle 
1
2
Wikipedia
does
something
 cos2 

 sin  cos 
sin  cos   rp

2
sin   0
http://www.gaertnerscientific.com
/ellipsometers/l116sf.htm
0  cos  


rs  sin  
Ellipsometry, cont.
 cos2 

 sin  cos 
sin  cos   rp

sin 2   0
0  cos  
 sin  
rs 

Two measurements, two unknowns
 deduce rs and rp
if multilayers:
 deduce n and k
lots of measurements!
On to Chapter 7!
Poynting vector review
Poynting vector for a sum of plane waves
Two Different Velocities



What happens if a wave pulse is sent through a
dispersive medium? Nondispersive?
Dispersive wave example:
a. f(x,t) = cos(x-4t) + cos(2 (x-5t))
– What is “v”?
– What is v for w=4? What is v for w=10?
What does that wave look like as time progresses?
(next slide)
Mathematica
0.1 seconds
0.7 seconds
What if the two
velocities had
been the same?
1.3 seconds
Time Evolution of Dispersive Pulse
Credit: Dr. Durfee
Peak
moves at
about 13
m/s (on
my office
computer)
Wave moving in time
Note:
frequencies
are infinitely
close together
|Amplitude|2 for each
frequency component
Phase and Group Velocity
Credit: Dr. Durfee
Window is moving
along with the
peak of the pulse
vp 
wave
kave
 velocity of "wiggles"
12.5 m/s
dw
vg 
dk
 velocity of "envelope" (peak)
evaluatedat kave
13 m/s
From Wikipedia

Example where vphase > vgroup
http://en.wikipedia.org/wiki/Group_velocity
One of my contributions to Wikipedia

Example where vphase is negative!
http://en.wikipedia.org/wiki/Group_velocity
More movies
Start on Fourier handout, if time