Fields%20and%20Waves%20I

1
Fields and Waves I

• Lecture 22
• Wave Polarization
• K. A. Connor
• Electrical, Computer, and Systems Engineering
  Department
• Rensselaer Polytechnic Institute, Troy, NY

2
These Slides Were Prepared by Prof. Kenneth A.
Connor Using Original Materials Written Mostly by
the Following

• Kenneth A. Connor ECSE Department, Rensselaer
  Polytechnic Institute, Troy, NY
• J. Darryl Michael GE Global Research Center,
  Niskayuna, NY
• Thomas P. Crowley National Institute of
  Standards and Technology, Boulder, CO
• Sheppard J. Salon ECSE Department, Rensselaer
  Polytechnic Institute, Troy, NY
• Lale Ergene ITU Informatics Institute,
  Istanbul, Turkey
• Jeffrey Braunstein Chung-Ang University, Seoul,
  Korea

Materials from other sources are referenced where
they are used. Those listed as Ulaby are figures
from Ulabys textbook.
3
Polarization
http//www.bungie.org/archives/news-Oct_02.html
http//www.3dglassesonline.com/how-do-3d-glasses-w
ork/
http//www.maximumeyewear.com/productfolder/milita
ry-glasses/polarized-glasses.html
4
Overview

• EM Waves in Lossless Media
• Wave Equation
• General Solution (similarity to Transmission
  Lines)
• Lossless vs lossy materials (complex
  permittivity)
• Energy and Power
• EM Waves in Lossy Media
• Skin Depth
• Approximate wave parameters
• Low Loss Dielectrics
• Good Conductors
• Power and Power Deposition
• Microwave Heating
• Wave Polarization
• Reflection and Transmission at Normal Incidence
• Plane Waves at Oblique Incidence

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Wave Polarization

describes the shape and locus of tip of the
vector at a given point in space as a function of
time
The locus of , may have three different
polarization states depends on conditions

• Linear
• Circular
• Elliptical

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Wave Polarization
Laser light is polarized (can check a laser
pointer)
http//www.mic-d.com/java/argonionlaser/index.html

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Wave Polarization
Antennas usually have a dominant polarization.
Antenna design must take this into account.
Polarized light can illuminate or clarify
objects in ways that non-polarized light cannot.
Propagation through most media and scattering of
waves can significantly affect polarization.
Thus, polarized light can be very effective in
the characterization of materials and physical
objects. Polarization is the basis of one method
for 3D photography. Polarization losses can be a
significant issue is optical communications. Polar
ization direction is one option for the
representation of ones and zeros for optical
computing. The list goes on
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Wave Polarization
Encarta
9
Polarization

• For a z-propagating wave, there are two possible
  directions of
• Direction of is called as polarization
• They are two independent solutions for the wave
  equation
• Linear combinations make all possibilities

Missing Image Reference
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Polarization
a uniform plane wave traveling in the z
direction may have x and y components
Complex amplitudes
The phase difference between the complex
amplitudes of x and y components of electric
field can be defines with angle d
Ex0ax Ey0ayejd
ax,ay are the magnitudes of Ex0 and Ey0
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Polarization
The phasor of electric field
The corresponding instantaneous field
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Intensity and Inclination Angle
The intensity of
The inclination angle ?
generally they both are function of t and z
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Linear Polarization
E
z
B
Can make any angle from the horizontal and
vertical waves
Missing Image Reference
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Linear Polarization
A wave is said to be linearly polarized if
and Are in phase
(d0) or out of phase (dp)
In phase
Out of phase
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Linear Polarization (out of phase)
Ulaby
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Linear Polarization
Looking up from z
x-polarized or horizontal polarized ay0
?0 or 180
y-polarized or vertical polarized ax0
?90 or -90
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Circular Polarization

• A wave is said to be circularly polarized if
• the magnitudes of and
  are equal and
• The phase difference is dp/2

d-p/2
dp/2
Ulaby
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Elliptical Polarization
Generally ax?ay?0 and d?0. the tip of
traces an elliptical path in x-y plane
rotation angle, ? -p/2?p/2 Ellipticity angle,
? -p/4?p/4
Ulaby
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Polarization states
The wave is traveling out of the slide
Ulaby
20
http//www.mic-d.com/curriculum/lightandcolor/pola
rizedlight.html
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Example 1 Polarization
Consider a wave travelling in the z direction
whose electric field is given by Describe the
polarization (e.g. linear, right circular, etc.)
and on an xy plot sketch the locus of
over a cycle for the following cases. a)
b)
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Example 1
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Polarization
Polarization Applet from Winston Chan (formerly
at Iowa) http//home3.netcarrier.com/chan/
The relationship between circular, linear and
elliptical polarization is discussed by Alkwin
Slenczka (University of Regensburg)
http//www-dick.chemie.uni-regensburg.de/research_
slenczka/polspe.html
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Polarization
Linear polarized light is separable as coherent
superposition of two linearly polarized waves. As
shown in the figure to the right both waves (red
and green amplitude) are polarized perpendicular
with respect to each other and of identical
amplitude.
Alkwin Slenczka
25
Polarization
In addition, linear polarized light is separable
into two circularly polarized waves of opposite
sense of rotation (red and green amplitude) of
identical amplitude.
Alkwin Slenczka
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Polarization
Birefringence, which causes a phase shift between
the two linearly polarized components, changes
linear into circular polarization (a). Linear
dichroism, however, which changes the respective
amplitude differently, simply rotates the plane
of polarization (b). Both effects together change
linear polarized light into elliptically
polarized light with main axis rotated with
respect to the original plane of polarization
(c).
Alkwin Slenczka
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Polarization
In contrast, birefringence of circularly
polarized components creates a rotation of plane
of polarization (d) while circular dichroism in
this case changes linear polarization into
elliptical (e). Both effects together create
elliptically polarized light with main axis
rotated with respect to the original plane of
polarization (f).
Alkwin Slenczka
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Polarized Light from Olympus
Naturally occurring light is randomly polarized.
That is, it is equally probable for the electric
field to be in any direction. A polarizing filter
can select a particular polarization of light.
http//www.mic-d.com/curriculum/lightandcolor/pol
arizedlight.html
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Polarized Light from Olympus
As we shall see in a future lecture, reflection
of light at oblique incidence (any angle other
than normal to the surface) will produce somewhat
polarized light. A Brewsters Angle, the
reflected light will be totally polarized.
http//www.mic-d.com/curriculum/lightandcolor/pol
arizedlight.html
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Polarized Light from Olympus
Sunglasses with polarizing lenses are made to
block light that is reflected from highly
reflective surfaces and, thus, can greatly reduce
the effects of glare.
http//www.mic-d.com/curriculum/lightandcolor/pol
arizedlight.html
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Polarized Light from Olympus
http//www.mic-d.com/curriculum/lightandcolor/pol
arizedlight.html
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Polarized Light from Olympus
An excellent example of the basic application of
liquid crystals to display devices can be found
in the seven-segment liquid crystal numerical
display (illustrated in Figure 9). Here, the
liquid crystalline phase is sandwiched between
two glass plates that have electrodes attached
similar to those depicted in the illustration. In
Figure 9, the glass plates are configured with
seven black electrodes that can be individually
charged (these electrodes are transparent to
light in real devices). Light passing through
polarizer 1 is polarized in the vertical
direction and, when no current is applied to the
electrodes, the liquid crystalline phase induces
a 90 degree "twist" of the light that enables it
to pass through polarizer 2, which is polarized
horizontally and is oriented perpendicular to
polarizer 1. This light can then form one of the
seven segments on the display.
When current is applied to the electrodes, the
liquid crystalline phase aligns with the current
and loses the cholesteric spiral pattern. Light
passing through a charged electrode is not
twisted and is blocked by polarizer 2. By
coordinating the voltage on the seven positive
and negative electrodes, the display is capable
of rendering the numbers 0 through 9. In this
example the upper right and lower left electrodes
are charged and block light passing through them,
allowing formation of the number "2" by the
display device (seen reversed in the figure).
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Photography with a Polarizing Filter
http//www.tifaq.com/images/
http//www.cs.mtu.edu/shene/DigiCam/User-Guide/fi
lter/polarizer.html
http//www.canfieldsci.com/photography/polarizer.s
html
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Photography with a Polarizing Filter
http//www.cs.mtu.edu/shene/DigiCam/User-Guide/fi
lter/polarizer.html
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Photography with a Polarizing Filter
http//www.cs.mtu.edu/shene/DigiCam/User-Guide/fi
lter/polarizer.html
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Photography with a Polarizing Filter
http//www.cs.mtu.edu/shene/DigiCam/User-Guide/fi
lter/polarizer.html
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Nikon Polarized Light
Polarized Light Microscopy Can distinguish
between isotropic and anisotropic materials. The
technique exploits optical properties of
anisotropy to reveal detailed information about
the structure and composition of materials, which
are invaluable for identification and diagnostic
purposes.
http//www.microscopyu.com/articles/polarized/pola
rizedintro.html
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Nikon Polarized Light
Isotropic materials, which include gases,
liquids, unstressed glasses and cubic crystals,
demonstrate the same optical properties in all
directions. They have only one refractive index
and no restriction on the vibration direction of
light passing through them. Anisotropic
materials, in contrast, which include 90 percent
of all solid substances, have optical properties
that vary with the orientation of incident light
with the crystallographic axes. They demonstrate
a range of refractive indices depending both on
the propagation direction of light through the
substance and on the vibrational plane
coordinates. More importantly, anisotropic
materials act as beam splitters and divide light
rays into two parts. The technique of polarizing
microscopy exploits the interference of the split
light rays, as they are re-united along the same
optical path to extract information about these
materials.
http//www.microscopyu.com/articles/polarized/pola
rizedintro.html
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Nikon Polarized Light
http//www.microscopyu.com/articles/polarized/pola
rizedintro.html
40
Nikon Polarized Light
http//www.microscopyu.com/tutorials/java/polarize
d/polarizerrotation/index.html
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Birefringence
The incoming ray of light is broken into two rays
(whose polarization is at 90 degrees to each
other and whose velocities through the material
is different--hence birefringence) that travel
through and exit the crystal.
http//webphysics.davidson.edu/alumni/MiLee/JLab/C
rystallography_WWW/birefringence.htm
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Stress Birefringence
http//www.oberlin.edu/physics/catalog/demonstrati
ons/optics/birefringence.html
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Birefringence on Plastic Boxes
http//www.engl.paraselene.de/html/birefringence_o
n_plastic_boxes.html
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Birefringence on Plastic Film
http//www.engl.paraselene.de/html/birefringence_o
n_plastic_film.html
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Quantitative analysis of the colors observed in
birefringent samples is usually accomplished by
consulting a Michel-Levy chart. The polarization
colors visualized can be correlated with the
actual retardation, thickness, and birefringence
of the specimen.
Olympus
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3D Photography
http//www.stereoscopy.com/library/waack-ch-5.html

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Some Movies

• Aspirin 1
• Aspirin 2
• DNA

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Faraday Rotation
http//www.teachspin.com/instruments/faraday/index
.shtml
http//www.unifiedphysics.com/
   The rotation in the plane of polarization is
caused by circular birefringence and their
relationship with the magnetic field in terms of
Zeeman Effect. The rotation is given by the
following expression where is the angle
of rotation, B is the strength of the magnetic
field in Gauss, d is the length of the medium and
V is Verdet constant.
http//www.wooster.edu/physics/JrIS/Files/kash-web
article.pdf
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Faraday Rotation
The phenomenon of the Faraday effect was first
observed by Michael Faraday in 1845. He found out
that when a block of glass is subjected to a
strong magnetic field, it becomes optically
active. The effect occurs when the rotation of a
linearly polarized wave passes through a
thickness of a transparent medium. The beam
should be plane polarized, that is, it can pass
through an analyzer without attenuation only when
its axis is parallel to that of the analyzer. The
propagation of the beam of light has to be
parallel to the direction of the magnet field in
order to observe the rotation in its plane of
polarization. If the field is perpendicular to
the beam, then there is no rotation. There should
be a medium present where the beam and the
magnetic fields will interact. When non-magnetic
materials like copper, lead, tin and silver are
placed between the magnet, they cause no effect
to polarized waves.
http//www.wooster.edu/physics/JrIS/Files/kash-web
article.pdf
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Faraday Rotation
Wikipedia
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Antenna Polarization
A linear polarized antenna radiates wholly in one
plane containing the direction of propagation. 
In a circular polarized antenna, the plane of
polarization rotates in a circle making one
complete revolution during one period of the
wave.  If the rotation is clockwise looking in
the direction of propagation, the sense is called
right-hand-circular (RHC).  If the rotation is
counterclockwise, the sense is called
left-hand-circular (LHC). An antenna is said to
be vertically polarized (linear) when its
electric field is perpendicular to the Earth's
surface.  An example of a vertical antenna is a
broadcast tower for AM radio or the "whip"
antenna on an automobile.
Antenna Polarization Application NoteBy Joseph
H. Reisert
http//www.astronwireless.com/polarization.html
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Antenna Polarization

• Horizontally polarized (linear) antennas have
  their electric field parallel to the Earth's
  surface.  Television transmissions in the USA use
  horizontal polarization.
• A circular polarized wave radiates energy in both
  the horizontal and vertical planes and all planes
  in between.  The difference, if any, between the
  maximum and the minimum peaks as the antenna is
  rotated through all angles, is called the axial
  ratio or ellipticity and is usually specified in
  decibels (dB).  If the axial ratio is near 0 dB,
  the antenna is said to be circular polarized.  If
  the axial ratio is greater than 1-2 dB, the
  polarization is often referred to as elliptical.

Antenna Polarization Application NoteBy Joseph
H. Reisert
http//www.astronwireless.com/polarization.html
53
Antenna Polarization
In the early days of FM radio in the 88-108 MHz
spectrum, the radio stations broadcasted
horizontal polarization.  However, in the 1960's,
FM radios became popular in automobiles which
used vertical polarized receiving whip antennas. 
As a result, the FCC modified Part 73 of the
rules and regulations to allow FM stations to
broadcast RHC or elliptical polarization to
improve reception to vertical receiving antennas
as long as the horizontal component was dominant.
Antenna Polarization Application NoteBy Joseph
H. Reisert
http//www.astronwireless.com/polarization.html
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Antenna Polarization
Circular polarization is most often use on
satellite communications.  This is particularly
desired since the polarization of a linear
polarized radio wave may be rotated as the signal
passes through any anomalies (such as Faraday
rotation) in the ionosphere.  Furthermore, due to
the position of the Earth with respect to the
satellite, geometric differences may vary
especially if the satellite appears to move with
respect to the fixed Earth bound station. 
Circular polarization will keep the signal
constant regardless of these anomalies.
Antenna Polarization Application NoteBy Joseph
H. Reisert
http//www.astronwireless.com/polarization.html
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Antenna Polarization
Why is a TV signal horizontally polarized?
Because man-made noise is predominantly
vertically polarized.
Do the transmitting and receiving antennas need
to have the same polarization?
Yes.
http//www.hp.com/rnd/pdf_html/antenna.htm
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Antennas
In the next course Fields and Waves II we
spend a good deal of time on antennas. The
simplest antenna is the Hertzian dipole, which
looks like the following figure with the antenna
axis aligned with the z direction in spherical
coordinates.
Transmission Line
Ulaby
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Antennas
The electric field around the Hertzian dipole
note the vertical polarization
Ulaby
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Antennas
Power is radiated horizontally, which is a good
thing since this means that such antennas can
easily communicate with one another on the
surface of the earth. The range in angle is more
than sufficient to handle the small elevation
changes that characterize the earths surface.
Ulaby
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Antennas Half Wave Dipole vs Quarter Wave
Monopole
http//en.wikipedia.org/wiki/FileHalf_E28093_W
ave_Dipole.jpg
http//www.ahsystems.com/catalog/SAS-551.php
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Antennas Half Wave Dipole vs Quarter Wave
Monopole
Ulaby
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Antennas Half Wave Dipole vs Quarter Wave
Monopole
Ulaby
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Stamps and Money
http//th.physik.uni-frankfurt.de/jr/physstamps.h
tml
63
http//th.physik.uni-frankfurt.de/jr/physstamps.h
tml
Stamps and Money
http//www2.physics.umd.edu/redish/Money/