Download - Waves, Light & Quanta
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Waves, Light & QuantaTim Freegarde
Web Gallery of Art; National Gallery, London
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Sinusoidal waves
kztrtxy sin,
• simple harmonic motion
• circular motion
,r kzt where
kztrkztr sin,cos
z
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Sinusoidal waves
0tt
0tt at ,
• wavenumber
2k
x
y
000 sin, tkxytxy
• spectroscopists’
1~ wavenumb
er
00~2sin txy
002sin txy • wavelength
kxtytxy sin, 0
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Sinusoidal waves
0xx
0xx at ,
• angular frequency
2
t
y
000 sin, kxtytxy
• frequency
1 00 2sin kxty
002sin kxty • period
kxtytxy sin, 0
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Birefringence• asymmetry in crystal
structure causes two different refractive indices
• opposite polarizations follow different paths through crystal
• birefringence, double refraction
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Optical polarization
• for any wavevector, there are two field components
• light is a transverse wave: perpendicular to E k
• any wave may be written as a superposition of the two polarizations
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Linear dichroism• conductivity of wire grid depends
upon field polarization• electric fields perpendicular to the
wires are transmitted
WIRE GRID POLARIZER
• fields parallel to the wires are absorbed
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Malus’ law
WIRE GRID POLARIZER
• amplitude transmission
cos
• intensity transmission
2cos
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Linear dichroism• crystals may similarly show
absorption which depends upon linear polarization• absorption also depends upon wavelength• polarization therefore determines crystal colour
TOURMALINE
• pleochroism, dichroism, trichroism
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Polarization in nature• the European cuttlefish also has
polarization-sensitive vision• … and can change its colour and
polarization!
MAN’S VIEW CUTTLEFISH VIEW (red = horizontal polarization)
CUTTLEFISH (sepia officinalis)
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Circular dichroism• absorption may also depend
upon circular polarization• the scarab beetle has
polarization-sensitive vision, which it uses for navigation
• the beetle’s own colour depends upon the circular polarization SCARAB BEETLE LEFT CIRCULAR
POLARIZED LIGHT
RIGHT CIRCULAR
POLARIZED LIGHT
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Optical activity (circular birefringence)
l-limonene(orange)
r-limonene(lemon)
CH2
CH3
HCH3 CH2
CH3
HCH3
CHIRAL MOLECULES
• optical activity is birefringence for circular polarizations
• an asymmetry between right and left allows opposing circular polarizations to have differing refractive indices• optical activity rotates the polarization plane of linearly polarized light• may be observed in vapours, liquids and solids
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Categories of optical polarization
• linear (plane) polarization• non-equal components in phase
• circular polarization• equal components 90° out of
phase• elliptical polarization
• all other cases
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Polarizing components
POLARIZER(filter/
separator)
LINEAR CIRCULAR
WAVEPLATE
(retarder)yx
yx TT
RL
RL TT
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Waveplates (retarders)
WAVEPLATE
• at normal incidence, a birefringent material retards one polarization relative to the other• linearly polarized light becomes elliptically polarized
le 02
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Polarization notation
• circular polarization• right- or left-handed rotation
when looking towards source
• linear (plane) polarization• parallel or perpendicular to
plane of incidence
RCP plane of incidence
perpendicular
parallel
• traces out opposite (right- or left-) handed thread
• plane of incidence contains wavevector and normal to surface
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Polarization by scattering
cdoswell.com/tips3.htm
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Brewster’s angle
ir
ri sincos
isin1
itan
• reflected light fully (s-) polarized
i r
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Brewster’s angle
www.paddling.net/sameboat/archives/sameboat496.html
ii
r
r
itan• reflected light fully (s-) polarized
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Malus’ law
WIRE GRID POLARIZER
• amplitude transmission
cos
• intensity transmission
2cos
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sin,cos iea
Characterizing the optical polarization
• wavevector insufficient to define electromagnetic wave• we must additionally define the polarization vector
k
yx aa ,ax
yz
sin,cosa• e.g. linear polarization at
angle
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Jones vector calculus• if the polarization state may be
represented by a Jones vector
• then the action of an optical element may be described by a matrix
yx aa ,a
2221
1211
aaaa
A
y
x
y
x
aa
aaaa
aa
2221
1211
JONES MATRIX
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Jones vector calculus
y
x
y
x
aa
aaaa
aa
2221
1211
JONES MATRIX
0001
1A transmission by horizontal polarizer
y
x
ii
A
exp00exp
2retardation by
waveplate
cossinsincos
3A projection onto rotated axes
• if the polarization state may be represented by a Jones vector
• then the action of an optical element may be described by a matrix
2221
1211
aaaa
A
yx aa ,a
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Birefringence• asymmetry in crystal
structure causes two different refractive indices
• opposite polarizations follow different paths through crystal
• birefringence, double refraction
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38.5º
Linear polarizers (analyzers)
e-ray
o-ray
e-ray
o-ray
s-ray
p-ray
• birefringence results in different angles of refraction and total internal reflection• many different designs, offering different geometries and acceptance angles
• a similar function results from multiple reflection
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Waveplates (retarders)
WAVEPLATE
• at normal incidence, a birefringent material retards one polarization relative to the other• linearly polarized light becomes elliptically polarized
le 02
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Compensators
adjust
fixed
variable
• a variable waveplate uses two wedges to provide a variable thickness of birefringent crystal
• a further crystal, oriented with the fast and slow axes interchanged, allows the retardation to be adjusted around zero SOLEIL
COMPENSATOR• with a single, fixed first section, this is a ‘single order’ (or ‘zero order’) waveplate for small constant retardation
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Electromagnetic waves• light is a transverse wave: perpendicular to E k
zxE
yBx
y
z
x
y
• Faraday
• Ampère
SBsE d.d.t
SEJsB d.d. 00 t yB
SEsB d.d. 00 t
xE
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Dielectrics
z
• atomic electrons move in response to electric field• resulting atomic dipole radiates field which adds to original
• Faraday
• Ampère
SBsE d.d.t
SEJsB d.d. 00 t
SEJsB d.d. 00 tr