Frustrated total internal reflection
Frustrated total internal reflection
FTIR
How does it show up in the theory?
waves at a single boundary Snell’s law, R, T
Frustrated TIR
Analogy to reflection, transmission, tunneling in QM
http://phet.colorado.edu/en/simulation/quantumtunneling
Frustrated total internal reflection for
multi-touch displays
Why do we see vivid colors in
reflection and not much in
transmission?
Double boundary
Air-Water (n=1.3)-Air film (soap film) r10  r12 
1.3  1
 0.13
1.3  1
T tot 
T max

1  F sin  
2
2
T
F 
Dd/lvac
4 R10 R12
1 
10
R
12
R
F = 0.60
F: one kind of
“finesse”

2
Air-Water (n=1.3)-Air film (soap film)
Normal incidence
Can we make a
device with greater
contrast in
transmission?
T
Dd/lvac
Air-Diamond (n=2.4)-Air film
r
10
r
2.4  1
2.4  1
T
F = 0.88
Dd/lvac
1 2

Air- Kryptonite? (n=10) -Air
r
10
r
1 2

10  1
10  1
T
F = 18
Dd/lvac
Interference ideas for why increasing r makes these peaks so sharp?
Multiple reflection view of r,t
r
r’ t’
t
Eo

1  x  x  x  ...   x 
2
3
n
n 0
ik z d
i 2kz d



tt e r r e
ik z d
tt e
1
1 x
Simple notation assume n0 = n2 so only have r,r’, t,t’
P. Derive t, the sum of all the terms on the right of the system
a) got it right b) tried
r
r’ t’
t
Eo

1  x  x  x  ...   x 
2
3
n
n 0
ik z d
i 2kz d



tt e r r e
ik z d
tt e
1
1 x
ttotal  tt e
ikd
1
i 2 kd
1  r ' r e
Calculation of r
r
r’ t’
t
Eo

1  x  x  x  ...   x 
2
3
n
n 0
ik z d
i 2kz d



tt e r r e
ik z d
tt e
1
1 x
P. Derive r, the sum of all the reflected terms on the left of the
system
a) got it right b) tried