Modern Optics II

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Modern Optics II Polarization of light

• Special topics course in IAMS
• Lecture speaker Wang-Yau Cheng
• 2006/4

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Outline

• Wave properties of light
• Polarization of light
• Coherence of light
• Special issues on quantum optics

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• Polarization of light
• ? Polarization vs. dipole oscillation
• Ways to change the polarization status
• Ways to purify the polarization
• Polarization in light scattering

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Concepts of induced dipole moment
Interact with EM wave
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Scattering by molecules is not sphericallysymmetr
ic. 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
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Dipole Emission Pattern from an Antenna
Analogous to a molecule emitting light, an
antenna emits a dipole pattern at much lower
frequency and longer wavelength
The pattern is somewhat distorted by the earth
and nearby objects.
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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
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Note that c 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.

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Right-handed quartz
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• Polarization of light
• Polarization vs. dipole oscillation
• ?Ways to change the polarization status
• Ways to purify the polarization
• Polarization in light scattering

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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

(45-degree input polarization)
Quarter-wave plate
Half-wave plate
A quarter-wave plate creates circular
polarization, and a half-wave plate rotates
linear polarization to its orthogonal state. We
can add an additional 2mp without changing the
polarization, so the polarization cycles through
this evolution as d increases further.
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Half-Wave Plate
When a beam propagates through a half-wave plate,
one polarizationexperiences half of a wavelength
more phase delay than the other.

• If the incident polarization is 45 to the
  principal axes, then theoutput 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.

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Jones Matrices for standard components
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Multiplying Jones Matrices

• Crossed polarizers

so no light leaks through.
Uncrossed polarizers (slightly)
So Iout e2 Iin,x
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Steering mirrors
up
down
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CRYSTAL QUARTZ WAVEPLATES 
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Phase shifts in reflection (glass to air)

• nt lt ni

Interesting phase above the critical angle
180 phase shift for angles below Brewster's
angle 0 for larger angles
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Total Internal Reflection occurs just as
thetransmitted 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.
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quarter wave Fresnel rhomb retarder
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Winding fiber
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The Faraday Effect

• A magnetic field can induce optical activity.

The Faraday effect allows control over the
polarization rotation.
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• Polarization of light
• Polarization vs. dipole oscillation
• Ways to change the polarization status
• ? Ways to purify the polarization
• Polarization in light scattering

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Phase shifts in reflection (air to glass)

• ni lt nt

180 phase shift for all angles
180 phase shift for angles below Brewster's
angle 0 for larger angles
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Phase shifts in reflection (glass to air)

• nt lt ni

Interesting phase above the critical angle
180 phase shift for angles below Brewster's
angle 0 for larger angles
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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.
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Brewster's Angle
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 qi qt
90. So Thus,

• A complex trigonometric calcu-lation reveals
  that the reflection
• coefficient for parallel-polarized
• light goes to zero for Brewster's
• angle incidence, tan(qi) nt / ni

qi
qi
ni
nt
qi qt 90
qt
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BREWSTER ANGLE
Extinction 510-5
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Piles of plates
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BROAD BAND POLARIZING CUBES
The extinction of transmitted -p component is at
least 1 part in 500
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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 510-5
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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 110-4
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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 110-5
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MAGNESIUM FLUORIDE ROCHON
extinction ratio of at least  10-3
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.
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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.
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Polarizer used in camera
The extinction of transmitted -p component is at
least 1 part in 200
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• Polarization of light
• Polarization vs. dipole oscillation
• Ways to change the polarization status
• Ways to purify the polarization
• ? Polarization in light scattering

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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
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Scattering of unpolarized light

• Again, no light is scattered along the input
  field direction,
• i.e. with k parallel to Einput.

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Scattering in the Earth's atmosphere leads to
interesting polarization properties of skylight.
Sun's rays
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Skylight is polarized if the sun is to your side.
Right-angle scattering is polarized
This polarizer transmits horizontal
polarization (of which there is very little).
Polarizer transmitting vertical polarization

• Multiple scattering yields some light of the
  other polarization.
• In clouds, much multiple scattering occurs, and
  light there is
• unpolarized.

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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.