Frustrated total internal reflection

Last time: double boundary

Last time: double boundary

Analogy to reflection, transmission, tunneling in QM

Frustrated TIR

waves at a single boundary Snell’s law, R, T

http://phet.colorado.edu/en/simulation/quantum-tunneling

Frustrated total internal reflection for multi-touch displays

Suppose we have a laser beam entering a piece of glass under special conditions so R = 0.

What is the same for both beams?a) Beam intensityb) Beam powerc) bothd) neither

R and T from r and t

2t t

i i

nT t

n

coscos

2R r

Why do we see vivid colors in reflection and not much in transmission?

Double boundary

Air-Water (n=1.3)-Air film (soap film) 1 0 1 2

1.3 10.13

1.3 1

r r

Dd/lvac

T

maxtot

21 sin2

TT

F

1 0 1 2

21 0 1 2

4

1

R RF

R R

F = 0.60

F: one kind of “finesse”

Air-Water (n=1.3)-Air film (soap film)Normal incidence

Dd/lvac

T

Can we make a device with greater contrast in transmission?

Air-Diamond (n=2.4)-Air film

Dd/lvac

T

1 0 1 2

2.4 1

2.4 1

r r

F = 0.88

Air- Kryptonite? (n=10) -Air

Dd/lvac

T

1 0 1 2

10 1

10 1

r r

F = 18

Interference ideas for why increasing r makes these peaks so sharp?

Multiple reflection view of r,t

2 3

0

1 ... n

n

x x x x

1

1 xSimple 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 systema) got it right b) tried

2z zik d i k dtt e r r e zik dtt e

t r’

Eo

t’ r

2 3

0

1 ... n

n

x x x x

1

1 x

2

1

1ikd

total i kdt tte

rre

2z zik d i k dtt e r r e zik dtt e

t r’

Eo

t’ r

2 3

0

1 ... n

n

x x x x

1

1 x

2

1

1ikd

total i kdt tte

rre

2z zik d i k dtt e r r e zik dtt e

t r’

Eo

t’ r

Calculation of r

2 3

0

1 ... n

n

x x x x

1

1 xP. Derive r, the sum of all the reflected terms on the left of the

systema) got it right b) tried

2z zik d i k dtt e r r e zik dtt e

t r’

Eo

t’ r