More Polarization

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More Polarization
Prof. Rick Trebino, Georgia Tech

• Polarization rotators
• Wave plates
• Rhombs
• Compensators
• Circular polarizers
• Reflection polarization
• Scattering polarization
• Polarization Spectroscopy

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Wave plates
x
Wave plate
z
Optic axis
y

• When a beam propagates through a birefringent
  medium, one polarization sees more phase delay
  than the other.
• This changes the relative phase of the x and y
  fields, and hence changes the polarization.

45 Polarization
-45 Polarization
Polarization state

Input

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 by 90?. 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 polarization experiences half of a wavelength
more phase delay than the other.

• If the incident polarization is 45 to the
  principal axes, then the output polarization is
  rotated by 90 to -45.

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Wave plates and input polarization
Remember that our wave plate analysis assumes 45
input polarization relative to its principal
axes. This means that either the input
polarization is oriented at 45, or the wave
plate is.
0 or 90 Polarizer
45 Polarizer
Wave plate w/ axes at 0 or 90
Wave plate w/ axes at 45
If a HWP, this yields 90 or 0 polarization. If
a QWP, this yields circular polarization.
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How NOT to use a wave plate
If the input polarization is parallel to the wave
plate principal axes, no polarization rotation
occurs!
0 or 90 Polarizer
45 Polarizer
Wave plate w/ axes at 0 or 90
Wave plate w/ axes at 45
This arrangement can, however, be useful. In
high-power lasers, we desire to keep the laser
from lasing and then abruptly allow it to do so.
In this case, we switch between this and the
previous case.
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Thickness of wave plates
When a wave plate has less than 2p relative phase
delay, we say its a zero-order wave plate.
Unfortunately, they tend to be very thin. Solve
for d to find the thickness of a zero-order
quarter-wave plate
Using green light at 500 nm and quartz, whose
refractive indices are ne no 1.5534 1.5443
0.0091, we find
d 13.7 mm
This is so thin that it is very fragile and very
difficult to manufacture.
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Multi-order wave plates
A multi-order wave plate has more than 2p
relative phase delay. We can design a
twentieth-order quarter-wave plate with 20¼ waves
of relative phase delay, instead of just ¼
d 1.1 mm
This is thicker, but its now 81 times more
wavelength dependent! Its also temperature
dependent due to ns dependence on temperature.
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A thick zero-order wave plate
The first plate is cut with fast and slow axes
opposite to those of the second one. The Jones
vector becomes

Optic axes
Input beam
Output beam
d1
d2
Now, as long as d1 d2 is equal to the thickness
of the thin zero-order wave plate, this optic
behaves like the really thin one! This is ideal.
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The Babinet Compensator rotates polarization by
an arbitrary amount.
Top wedge is cut with fast and slow axes opposite
to those of bottom wedge.
Optic axes
Output beam
Input beam
Slide one wedge with respect to the
other, changing d1 and/or d2.
d2
In practice, the two wedges are contacted.
Top wedge
Bottom wedge
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Polarization Mode Dispersion plagues broadband
optical-fiber communications.
Imagine just a tiny bit of birefringence, Dn, but
over a distance of 1000 km
If l 1.5 mm, then Dn 10-12 can rotate the
polarization by 90º!
Newer fiber-optic systems detect only one
polarization and so dont see light whose
polarization has been rotated to the other.
Worse, as the temperature changes, the
birefringence changes, too.
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A Lyot Filter is a wave plate between polarizers.
Lyot filters
Because the wave-plate polarization rotation
varies with wavelength, placing one between
polarizers yields wavelength-dependent
transmission.
Polarizer
Polarizer
Waveplate
Placing several Lyot filters (with factor-of-2
different-thickness wave-plates) in a row yields
a narrowband filter, which transmits only a
narrow range of wavelengths.
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Circular polarizers

• A circular polarizer makes circularly polarized
  light by first linearly polarizing it and then
  rotating it to circular. This involves a linear
  polarizer followed by a quarter wave plate

Unpolarized input light
45 Polarizer
QWP
Circularly polarized light
45 polarized light
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The Fresnel rhomb uses total-internal-reflection
phase shifts to rotate polarization

• After two internal reflections, input 45
  polarization rotates to
• circular polarization.

54.6
Circular polarization
45 polarization
Elliptical polarization
Unlike polarization rotation in a wave plate,
this polarization rotation is nearly wavelength
independent.
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Polarization Spectroscopy
Typical molecule
Birefringence!
The 45-polarized Pump pulse re-orients
molecules, which induces some birefringence into
the medium, which then acts like a wave plate for
the Probe pulse until the molecules re-orient
back to their initial random distribution.
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Depolarization by reflection or transmission

• Suppose that 45 polarization is incident on an
  interface, which has different parallel (x) and
  perpendicular (y) reflection coefficients.

Incident light fields
y
Incidentpolarization
x
Reflected light fields
Unless light is purely parallel or
perpendicularly polarized (or incident at 0),
polarization rotation will occur in reflection
(or transmission).
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Fresnel Reflection and Depolarization

• Fresnel reflections are a common cause of
  polarization rotation.
• The ratio of polarization-component strengths
  will change on transmission through or reflection
  off an interface.

This effect is particularly strong near
Brewster's angle.
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Cruddy stuff depolarizes

• Cruddy stuff is very non-uniform a series of
  interfaces at random angles.

Crossed polarizers with a piece of wax paper in
between.
Human tissue completely depolarizes light in the
visible, IR, and UV.
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The atmosphere depolarizes light slightly.
Odd-angle interfaces between regions of warm and
cool air cause air to slightly depolarize light.
Star
Cooler regions of air (with higher refractive
index)
Droplets of water (i.e., clouds) completely
depolarize light.
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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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Polarizers are very useful in photography.
Without a polarizer
With a polarizer
The effect of a polarizer is probably the one
filter effect that you cant reproduce later
using Photoshop!
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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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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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Brewster's Angle Revisited
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