pc20312 wave optics section 3: interference. interference fringes i 1 + i 2 image adapted from...
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PC20312 Wave Optics
Section 3:
Interference
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Interference fringes
212 II
212 III1 + I2
Image adapted from Wikipedia
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Temporal coherence
Phase relationship changes over a characteristic time
1
cCoherence time:Image adapted from Wikipedia
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Spatial coherence
Wave with infinite temporal and spatial coherence
Wave with infinite temporal coherence but finite spatial
coherence
Wave with finite temporal and spatial coherence
A pinhole isolates part of the wavefront and thus
increases spatial coherence. Coherence
length is unaffected.
Images adapted from Wikipedia
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Types of interference
Wavefront division
e.g. Young’s slits
Amplitude division
e.g. Michelson interferometer
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Thomas Young
Thomas Young (1773-1829)
• “The Last Man Who Knew Everything “
• Learned 13 languages by age 14
• Comparative study of 400 languages
• Translated the Rosetta stone
• PhD in physics & medical doctor
• Young’s slits
• Young’s modulus
• Founded physiological optics:
• colour vision
• astigmatism
• accommodation of the eye
• Seminal work on haemodynamics
• Secretary to the Board of Longitude
• Superintendent of the HM Nautical Almanac Office. Image from Wikipedia
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Young’s slits 1
Poor spatial coherence
Good spatial coherence
Single slit isolates part of wavefront
Double slits act as two coherent
sources
To distant screen
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Young’s slits 1Young’s original diagram presented to Royal Society in 1803
Image from Wikipedia
http://www.acoustics.salford.ac.uk/feschools/waves/diffract3.htm
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Young’s slits 3
a
y
r2
r1
r
s
s >> a
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Lloyd’s mirror
i
y
r1
l1l2
Phase change on reflection
source
image of source
r2 = l1+l2
t
Rev. Humphrey Lloyd (1800-1881) Trinity College Dublin
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Multiple slits
S0
S3
S4
S5
S6
S1
S2
a
r
2r
3r
s>>a
P
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Interference pattern for multiple slits
Inte
nsity
, I
N=10N=3N=5
ka2
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Michelson Interferometer
Albert Abraham Michelson (1852-1931)
d1
d2
beamsplitter
Mirror, M1
Mirror, M2
compensator plate
lens
screen
light source
d = 2(d1- d2)
Image from Wikipedia
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The compensator plate
Without compensator:
• Unequal paths thru glass
• path length diff. = f()
With compensator:
• Equal paths thru glass
path length diff. f()
Rays to M1 pass thru BS once
Rays to M2 pass thru BS three
times
NB nglass= f()
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Equivalent diagram for Michelson interferometer
source plane M1 plane M2 plane
d
d cos()
S S1 S2
Images of S in M1 and M2
lens
f
focal plane
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Fringe patterns
Sodium lamp
Images from http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/michel.html#c1
White light
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Fourier Transform Spectroscopy
d1
d2
beamsplitter
compensator plate
lens
detector
Movable mirror
0 2 4 6 8 10 12 140
0.5
1
1.5
2
d
I(d) monochromatic
d
I(d) polychromatic
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Thin films
nt nini
BD
C
A
s
source
lens
i
t
A
C
D
i
i
A
C
B st
t
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Thin film applications
Dichroic mirrors – high reflectivity for narrow bandwidth only Anti-reflection coatings –
reduces glare from lenses
Images from Wikipedia
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Thin films in nature
Oil on water – oil layer thickness varies giving a rainbow effect in white light
Soap bubbles – thickness and angle of film varies to give rainbow
The ‘Tapetum lucidum’ is found behind the retina of many animals (not humans) – it enhances night vision
The tapetum lucidium in a
calf’s eye
Images from Wikipedia and Google Image
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Multibeam interference
Er
s
source
Et0
Et1
Et3
Et2
Et5
Et4
Er0
Er1
Er3
Er2
Er5
Er4
Er6
lenslens
Et
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Stokes’ relations
Sir George Gabriel Stokes (1819-1903)
r2E+ttE
E rE
tE
E rE
tE
rE
tErtE+trE
A) B)
C) • B) is time-reverse of A)
• Comparing B) and C):
r2 + tt=1
r = -r
Images from Wikipedia
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The Airy function
Sir George Biddell Airy (1801-1892)
Finesse, F = Free Spectral Range, Resolution,
Image from Wikipedia
0 1 2 3 4 5 6 7 8 9 100
0.2
0.4
0.6
0.8
1
Frequency
Tra
nsm
issi
on
F=2F=10F=50
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RRF
12
Image from Wikipedia
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Fabry-Pérot Etalons 1
Potrait images from http://www-obs.cnrs-mrs.fr/tricent/astronomes/fabry.htm &Wikipedia
Charles Fabry (1867-1945)
Alfred Pérot (1863-1925)
s
r
source
lens
f2 highly reflecting parallel surfaces
Outer surfaces are non-parallel
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0
500
1000
1500
2000
2500
3000
3500
4000
4500
0 5 10 15 20 25 30
Frequency (GHz)
Inte
nsi
ty (
Arb
. u
nit
s)
FSR
Images from Google image Data from D. Binks PhD thesis
Fabry-Pérot Etalons 2