PC20312 Wave Optics
Section 2:
Polarization
Polarization states
linear
circular
elliptical
Image from Wikipedia
Linear and circular polarization
http://physics-animations.com/Physics/AVI/ellf.avi
Dipole radiation
E
Optical E-field…
…drives oscillating
dipoles in the medium…
http://www-antenna.ee.titech.ac.jp
www.harvard.edu/~efortin/thesis/html/EMR_light.shtml
/~hira/hobby/edu/em/dipole2/dipole2.html
…which radiate in all
directions except parallel to E.
http://physics.usask.ca/~hirose/ep225/radiation.htm
Polarization by reflection
Ei
Er
Et
• E perpendicular to plane of incidence
Er
Ei
Et
• E parallel to plane of incidence
• “s-polarised”
• “p-polarised”
• Emission always max in direction of Er
• Emission amplitude varies with
direction of Er
Click here for a web-based animation of Brewster’s angle
Brewster’s angle, B
P-polarised light
Ei
Er=0
ni
B
t
nt
Et
 nt 
 B  tan  
 ni 
1
Sir David Brewster 1781-1868
Polarization by scattering
Ein vertical  no vertical scattering
Ein horiz.  no horiz. scattering
polarised
For unpolarised incident light
the scattered light is:
Completely polarised in
vertical  horiz directions
partially polarised
unpolarised
Partially polarised in
intermediate directions
Animation from http://www-antenna.ee.titech.ac.jp/~hira/hobby/edu/em/smalldipole/force.gif
Polarized light in nature
Unfiltered image
Image seen through polarising filter
Image from Wikipedia
Polaroid
E-field component
aligned with long
axis of molecule is
absorbed
E

E cos
E sin
E cos
Polaroid sheet
eg aligned PVA molecules
PVA structure from http://wwwchem.csustan.edu/CHEM2000/EXP2/bkg.htm
Malus’ Law
I    I 0 cos 2  
Etienne-Louis Malus
1775-1812
http://physics-animations.com/Physics/AVI/polariz.avi
Anisotropic Materials
P  E
Ey
 
D   0 1   E   0 E
Ex
Py
Px
 x

  0
0

0
y
0
0

0
 z 
For calcite:
 x   y  no2
Calcite CaCO3
 z  ne2
no = 1.658 & ne=1.486 (at =590 nm)
Image from Wikipedia
Birefringence
Optic Axis
z
k x  k sin  cos 
Eo
k
k y  k sin  sin 
k z  k cos 
Eo


• Eo perpendicular to k & optic axis
Ee
• Ee perpendicular to Eo
y
x
Double Refraction
Optic
Axis
unpolarised light
e-ray
o-ray
For calcite, typical angle between
beams ~6
Image from Wikipedia
Polarizing Beamsplitter
calcite
unpolarised light
e-ray
polarised light
o-ray
transparent glue
polarised light
Photo from http://www.lightmachinery.com
Optic Axis points towards you
Waveplates
Optic
Axis
z
no>ne : Optic Axis is ‘fast’
y
x
ne>no : Optic Axis is ‘slow’
d
In this diagram, is the optic axis slow or fast?
Photo from http://www.lightmachinery.com
The Faraday Effect
Image from
http://en.wikipedia.org/wiki/Faraday_effect
Material
V (rad.T-1.m-1)
Glass
9.210-4
Water
3.8 10-4
Air
1.8 10-7
Quartz
4.8 10-4
Terbium
Gallium Garnet
-40
Faraday Isolator
E
P1
P1
45
B
45
B
E
P2
P2