VLE 3 Wave optics
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Fresnel-Huygens-Principle
Fresnel-Huygens-Principle: Every non shielded point of a wave front is a source of secondary fundamental waves, which frequency has the same frequency as the primary wave. In every later point the optic field is the overlay of this secondary fundamental waves (with consideration of amplitudes and phases).
source: http://www.mbaselt.de, 24.10.2008
51
Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Calculation with the Huygens-principle
Incident plane wave
Medium 1
Boundary
Medium 2
Refracted wave
The refraction angle is a function of the velocity of the secondary waves. This is a function of the refractive index of medium 2.
52
Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Calculation with the Huygens-principle , Calculation
c1t AB sin 1
c2t AB sin 2
c1 |
|
sin 1 |
|
n2 |
||
c |
2 |
|
sin |
2 |
|
n |
|
|
|
1 |
|||
Snell‘s Law
53
Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Calculation with the Huygens-principle
Incident plane wave |
Reflected wave |
|
Fundamental waves
source: http://de.wikipedia.org, 21.08.2009
54
Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
7.Fresnel-Diffraction basic principles
55
Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Fresnel diffraction at a aperture (1)
Example: Diffraction at a aperture
The maximal optical path difference is: max AP BP
With: max AB
If |
AB |
, then also max |
. |
56
Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Fresnel diffraction at an aperture (2)
Because all waves have the same phase, they interfere at point P constructive,
but with a different magnitude
With a small aperture in comparison to the wavelength the wave propagates in a big area behind the aperture
The smaller the aperture, the more similar the diffracted wave is to a spherical wave (point source)
With AB there is only constructive interference in a small angular spectrum behind 
the aperture
With even bigger angles there is partly destructive interference
With constructive and destructive interference a diffraction pattern is generated
57
Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Diffraction pattern (1)
Diffraction patterns are dependent from the diffraction geometry. Here round geometry:
Diffraction pattern
Diffraction geometry
58
Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Diffraction pattern (2)
Quadratic diffraction geometry:
Diffraction pattern
Diffraction geometry
59
Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
8. Fraunhofer-Diffraction
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Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany