Lecture 9
7.7 TIR cont.
7.8 Metals
8 Geometric Optics
The evanescent wave
•
Without a transmitted wave we have
problem
•
The boundary condition cannot be fulfilled
•
We need a transmitted wave which does
not carry energy across the boundary
(on average)
E
t
=
E
ot
e
"
#
y
e
i k
t
x
n
i
n
t
sin
$
i
"
%
t
&
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(
(
)
*
+
+
"
=
k
t
#
n
i
n
t
$
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(
)
2
sin
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1
Let’s go back to the reflection and refraction problem
What happens if a the gap is very small such that the
eveanescent wave reaches another medium ?
Frustrated total internal refection
Prism
Coupler
•
As we have seen in both descriptions for
the waveguide only certain modes will be
guided effectively
•
The modes have different wave vectors in
xdirection
•
If we want to couple light into a waveguide
using the evanescent wave only certain
angle of incidence will work
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Coupling light into a waveguide
(light ray picture)
Waveguide (fiber)
Can we couple light directly from the top ?
No, because effective
incoupling can only be
achieved for directions
which result in total
internal reflection in the
fiber. This means the
angle in air is larger
than 90
o
!
p
!
n
n
p
sin
"
p
=
n
f
sin
"
n
n
p
n
f
k
x
=
"
=
k
f
n
f
sin
#
n
Constructive
interference
"
=
k
f
n
p
sin
#
p
We adjust the angle
!
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 Fall '04
 DIEROLF
 Reflection And Refraction, Geometrical optics, free electrons, plasma frequency, evanescent wave

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