VLE 3 Wave optics
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Optics and optical technologies
Lecture part 03:
Wave optics
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Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Additional literature
•E. Hecht: Optik. Oldenburg Verlag
•F. Pedrotti; L. Pedrotti: Optik für Ingenieure. Springer Verlag. 2005 (www.springerlink.com)
•B. Saleh: Grundlagen der Photonik. Wiley VCH. 2008
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Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Overview
1.Basics of wave motion
2.Three dimensional wave description
3.Electro magnetic waves
4.Superposition, interference
5.Interference for measurement instrumentation
6.Fresnel-Huygens-Principle
7.Diffraction basics
8.Fresnelund Fraunhofer-diffraction
9.Double slit and grating
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Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
1. Basics of wave motion
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Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Types of waves
Transverse waves
Propagation direction
Oscillation direction
e.g. Water waves
source: www.gymnasium-parsberg.de, 07.10.09
Longitudinal wave
Propagation direction
source: www.baunetzwissen.de, 07.10.09
Oscillation direction e.g. Sound waves
source: http://leifi.physik.uni-muenchen.de, 07.10.09
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Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Waves (1)
In general: |
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A wave is a moving |
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v = 1 m/s |
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Distortion |
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t=0s |
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t=1s |
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2,5 |
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t=2s |
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Assumption: moves with constant |
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t=3s |
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Speed in direction |
(x,t) |
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f x,t |
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One dimensional wave function: |
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(x, t) f (x t) |
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x |
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Example: x 3 / 10x2 |
1 f x |
x, t 3 / 10 x t 2 |
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Moving of the wave in positive x-direction: |
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→Representation in the diagram for = 1 m/s at different points in time, shape of the wave does not change
→For (x+ t) the wave would move in negative x-direction.
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Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Waves (2)
Representation as a differential equation:
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→ One-dimensional wave equation |
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t2 |
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Harmonic wave: Sine - / cosine function
x,t f x t Asin k x t
with A – Amplitude, k – wavenumber
→ Solution of the wave equation
Waves are periodic in time and space.
The periodicity in space is called wavelength
→ x,t x ,t
This means for a harmonic wave that the argument changes by 2
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sin k x |
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sin k x |
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sin k x |
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Hence it follows: |
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k 2 |
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with k being called wave number |
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Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Waves (3)
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x/ |
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(x) = A sin (2 |
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(*A) |
0,5 |
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0 |
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-0,5 0 |
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= 2 |
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(* ) |
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The argument of the sine-function is called phase φ.
At = 0, , 2 , 3 , … (x) = 0
→ also: (x) = 0 at = 0, /2, , 3 /2, …
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Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Waves (4)
Temporal period
→x,t x,t
→sin k x t sin k x t sin k x t 2
With its: : |
k or2 |
The period is equal to the time The inverse is the frequency
→1
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per wave
Further derived quantities: angular velocity
2 
2 wave number
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Equivalent representation of a harmonic wave: |
Asin kx t |
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Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Waves (5)
Phase angle: |
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Asin kx |
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kx t
→ at x,t t 0,x 0 0,0 0
General case: x,t Asin kx t
with – original phase (phase constant)
→ x,t kx t
Change of the phase over time:
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→ is equal to the angular velocity |
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t x |
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Chang of the phase over distance:
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→ is equal to the wavenumber k |
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x t |
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Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany