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The basic questions one would like to
answer with respect to the optical behaviour of materials and with respect to
the simple situation as illustrated are:
- How large is the fraction R that is reflected? 1 –
R then will be going in the material.
- How large is the angle b, i.e. how large
is the refraction of the material?
- How is the light in the material absorped, i.e. how large is the absorption
coefficient?
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Of course, we want to know that as a function of
the wave length l or the frequency n = c/l, the angle a, and the two basic directions of the polarization
( |
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All the information listed above is
contained in the complex index of refraction n* as given Þ |
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Basic definition of
"normal" index of refraction n |
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Terms used for complex index of refaction n*
n = real part
k = imaginary part |
| n*2 = (n + ik)2 = e'
+ i · e'' |
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Straight forward definition of n* |
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Working out the details gives the
basic result that
- Knowing n = real part allows to answer question 1 and
2 from above via "Fresnel laws" (and "Snellius'
law", a much simpler special version).
- Knowing k = imaginary part allows to
answer question 3 Þ
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| Ex = |
exp – |
w · k · x
c |
· exp[ i · (kx
· x – w · t)] |
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Amplitude:
Exponential
decay with k |
"Running" part of
the wave |
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Knowing the dielectric function of a
dielectric material (with the imaginary part expressed as conductivity sDK), we have (simple) optics completely
covered! |
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| n2 |
= |
1
2 |
æ
ç
è |
e' |
+ |
æ
è |
e' 2 + |
sDK2
4e02w2 |
ö
ø |
½ |
ö
÷
ø |
| k2 |
= |
1
2 |
æ
ç
è |
– e' |
+ |
æ
è |
e' 2 + |
sDK2
4e02w2 |
ö
ø |
½ |
ö
÷
ø |
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If we would look at the tensor properties of
e, we would also have crystal optics (=
anisotropic behaviour; things like birefringence) covered. |
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We must, however, dig deeper for e.g. non-linear
optics ("red in - green (double frequency) out"), or new disciplines
like quantum optics. |
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© H. Föll
