Modern Optics II – Polarization of light
Special topics course in IAMS
Lecture speaker: Wang-Yau Cheng
2006/4
Outline
🡪 Polarization vs. dipole oscillation
Concepts of induced dipole moment
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Higher harmonic radiation
Neutral atoms
Interact with EM wave
Scattering by molecules is not spherically�symmetric. It has a "dipole pattern."
The field emitted by an oscillating dipole excited by a vertically
polarized light wave:
Directions of scat-
tered light E-field
No light is emitted along
direction of oscillation!
Directions of scat-
tered light E-field
Direction of light excitation
E-field and electron oscillation
Emitted intensity pattern
Dipole Emission Pattern from an Antenna
The pattern is somewhat distorted by the earth and nearby objects.
Analogous to a molecule emitting light, an antenna emits a dipole pattern at much lower frequency and longer wavelength:
Linear polarization
Left hand circular polarization
Right hand circular polarization
For stimulation emission process, all the dipoles will be coherently induced and the radiation will go with certain polarization
Note that χ could be a tensor
Interact with EM wave
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Optical Activity
Unlike birefringence, optical activity maintains a linear polarization
throughout. The rotation angle is proportional to the distance.
Right-handed quartz
🡪Ways to change the polarization status
Wave plates
When a beam propagates through a birefringent medium, one
polarization experiences more phase delay than the other.
If both polarizations are present, this has the effect of changing
relative phase of the x and y fields, and hence rotating the polarization.
Input:
Polarization state:
Output:
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Wave plates (continued)
Wave plate output polarization state:
A quarter-wave plate creates circular polarization, and a half-wave plate rotates linear polarization to its orthogonal state.
We can add an additional 2mπ without changing the polarization, so the polarization cycles through this evolution as d increases further.
“Quarter-wave plate”
“Half-wave plate”
(45-degree input polarization)
Half-Wave Plate
If the incident polarization is 45° to the principal axes, then the�output polarization is rotated by 90°.�
If the incident polarization is parallel to one of the principal axes of the plate, then no polarization rotation occurs.
When a beam propagates through a half-wave plate, one polarization�experiences half of a wavelength more phase delay than the other.
Jones Matrices for standard components
Multiplying Jones Matrices
Crossed polarizers:
x
y
z
x-pol
y-pol
so no light leaks through.
Uncrossed polarizers
(slightly):
rotated
x-pol
y-pol
So Iout ≈ ε2 Iin,x
up
down
Steering mirrors
CRYSTAL QUARTZ WAVEPLATES
Phase shifts in reflection (glass to air)
nt < ni
Interesting phase above the critical angle
180° phase shift
for angles below
Brewster's angle;
0° for larger angles
0° 30° 60° 90°
Incidence angle
0° 30° 60° 90°
Incidence angle
π
0
π
0
┴
||
Total Internal Reflection occurs just as the�transmitted beam grazes the surface.
Note that the irradiance of the transmitted beam goes to zero as it
grazes the surface.
Total internal reflection is 100% efficient.
quarter wave Fresnel rhomb retarder
Winding fiber
The Faraday Effect
A magnetic field can induce optical activity.
The Faraday effect allows control over the polarization rotation.
🡪 Ways to purify the polarization
Phase shifts in reflection (air to glass)
ni < nt
180° phase shift
for all angles
180° phase shift
for angles below
Brewster's angle;
0° for larger angles
0° 30° 60° 90°
Incidence angle
0° 30° 60° 90°
Incidence angle
π
0
π
0
┴
||
Phase shifts in reflection (glass to air)
nt < ni
Interesting phase above the critical angle
180° phase shift
for angles below
Brewster's angle;
0° for larger angles
0° 30° 60° 90°
Incidence angle
0° 30° 60° 90°
Incidence angle
π
0
π
0
┴
||
Glare is horizontally polarized
Puddle reflection viewed
through polarizer that
transmits only horizontally
polarized light
Puddle reflection viewed
through polarizer that
transmits only vertically
polarized light
Light reflected
into our eyes
from the puddle
reflects at about
Brewster's Angle.
So parallel
(i.e., vertical)
polarization sees
zero reflection.
Polarizer sunglasses transmit only vertically polarized light.
Brewster's Angle
A complex trigonometric calcu-�lation reveals that the reflection
coefficient for parallel-polarized
light goes to zero for Brewster's
angle incidence, tan(θi) = nt / ni
When the reflected beam makes a
right angle with the transmitted beam,
and the polarization is parallel, then
no scattering can occur, due to the
scattered dipole emission pattern.
But our right-angle assumption
implies that θi + θt = 90°. So:
Thus,
ni
nt
θi
θi
θt
θi +θt = 90°
BREWSTER ANGLE
Extinction 5*10-5
Piles of plates
The extinction of transmitted -p component is at least 1 part in 500
BROAD BAND POLARIZING CUBES
GLAN THOMPSON
The Glan Thompson polarizer is made of two calcite prisms cemented together. Two types of Glan Thompsons are available. One is the standard form and the other is the long form. Their length to aperture ratios are 2.5 : 1 and 3.0 : 1 respectively. Glan Thompsons tend to have higher extinction ratio than air spaced polarizers. In the ultra violet spectrum, their transmission is limited by absorption in calcite as well as the cement layer. These polarizers can be used from about 350 to 2300 nm.
Extinction 5*10-5
GLAN TAYLOR
The Glan Taylor prism polarizer is made of two calcite prisms which are assembled with an air space . It has a length to aperture ratio of approximately 1.0 which makes it a relatively thin polarizer. It is made of UV selected calcite. A 10 mm thick calcite plate having 50% or more transmission at 250 nm is considered UV selected. The spectral range of this polarizer is from 250-2300 nm. Below 250 nm, transmission cutoff wavelength varies from crystal to crystal.
Extinction 1*10-4
CALCITE WOLLASTON
Calcite Wollaston prism polarizer is made of two prisms of calcite which are cemented together. The two output beams in a Wollaston polarizer exit with unequal beam deviation ( asymmetry ) which is given in the table below. The beam separation angle is dependent on wavelength. Useable range of this polarizer is from 350 nm to 2300 nm.
Extinction 1*10-5
MAGNESIUM FLUORIDE ROCHON
The magnesium fluoride Rochon polarizer is made of two prisms of single crystal magnesium fluoride which are optically contacted. This polarizer can be used over the spectral range of 140 to 6000 nm and has an extinction ratio of at least 10-3.
extinction ratio of at least 10-3
CALCITE BEAM DISPLACER
A calcite Beam Displacer splits the input unpolarized beam of light into two orthogonally polarized components which exit parallel to each other. The ordinary polarization transmits straight through while the extraordinary transmits through the crystal making approximately 6 degree angle with the straight through beam and emerges parallel to it. The beam displacement varies slightly with wavelength. Non standard beam displacers are available by special order.
Polarizer used in camera
The extinction of transmitted -p component is at least 1 part in 200
🡪 Polarization in light scattering
Scattering of polarized light
No light is scattered along the input field direction, i.e. with k parallel to E.
Vertically polarized
input light
Horizontally polarized
input light
Scattering of unpolarized light
Again, no light is scattered along the input field direction,
i.e. with k parallel to Einput.
Scattering in the Earth's atmosphere leads to interesting polarization properties of skylight.
Sun's rays
Skylight is polarized if the sun is to your side.
Multiple scattering yields some light of the other polarization.
In clouds, much multiple scattering occurs, and light there is
unpolarized.
Right-angle scattering
is polarized
Polarizer transmitting vertical polarization
This polarizer transmits
horizontal polarization
(of which there is very little).
Polarization Spectroscopy
The 45°-polarized “Pump” pulse reorients molecules, which induces some birefringence into the medium, which then acts like a wave plate until the molecules re-orient back to their initial random distribution.