VLE 3 Wave optics
.pdf
Examples for interference (1)
Example:
1 = 2, = 0 |
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→ amplification |
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2,5 |
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ψ1 |
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2 |
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ψ2 |
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1,5 |
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ψres |
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0,5 |
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-1 |
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-1,5 |
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-2 |
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-2,5 |
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31
Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Examples for interference (2)
Example:
1 = 2, = |
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→ cancellation |
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1,5 |
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ψ1 |
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ψ2 |
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ψres |
0,5 |
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-1 |
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-1,5 |
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32
Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Examples for interference (3)
Example
1 = 2, = 2 /3 → phase shift with same amplitude |
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1,5 |
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ψ1 |
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ψ2 |
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ψres |
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0,5 |
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-1 |
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-1,5 |
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33
Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Examples for interference (4)
Example:
1 = 2 2 |
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→ beat |
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2 |
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ψ1 |
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1,5 |
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ψ2 |
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ψres |
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1 |
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0,5 |
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-1 |
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-1,5 |
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34
Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Examples for interference (5)
source: www.mseu.de, 07.10.09
35
Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Superposition of two waves
Superposition of two waves with the same wavelength
→- /4 < < + /4: constructive interference
→/4 < < 3 /4: destructive interference
→3 /4 < < 5 /4: constructive interference, etc. Intensity of the resulting superposition at 1 = 2:
→I I1 I2 2
I1 I2 cos
→Maximal intensity at cos = 1, thus at = 0, ±2 , ±4 , etc.
→Completely destructive interference at cos = -1, also bei = ± , ±3 , etc.
When two waves are superposed with the same amplitudes I1 = I2 = I0:
→ I0 |
2I0 1 cos 4I0 |
cos2 |
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Imax 4I0 and Imin |
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→ Intensity is quadrupled with doubled amplitude
36
Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
5. Interference for measurement instrumentation
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Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Coherence
Coherence denotes, that there is a distinct phase relation between two waves. It is the condition for interference.
There is a distinction between temporal and spatial coherence. To get interference, there must be temporal and spatial coherence.
Temporally and spatially |
Only spatially |
Only temporally |
coherent |
coherent |
coherent |
time axis |
Source: http://de.wikipedia.org, 14.10.2008 |
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38
Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Coherence length
Coherence length is the distance from a coherent source to a point where a wave maintains a specified degree of coherence. Within this distance, the wave in question is most similar to a perfect sinusoidal wave. The significance is that wave interference will be strong within a coherence length of the source, but not beyond it.
high
and
low
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coherence lengths |
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Source: http://de.wikipedia.org, 14.10.2008 |
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Coherence lengths for different light sources:
Light source |
Coherence length |
Sun light |
Few µm |
Thermal light sources |
Up to approx. 500 mm |
Laser |
Up to several km |
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39 |
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Prof. M. Schmidt |
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Institute of Photonic Technologies, Univ. Erlangen, Germany |
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Wave front and amplitude distribution
Generation of two coherent waves: wavefront and amplitude split
Wave front distribution |
Amplitude distribution |
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Coherent
partial beam Double slit 
Point source
Plane wave
Incoming 
Coherent beam
cylinder waves
Beam spliter
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Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany