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Fields and Waves I
Lecture 22
Wave Polarization
K. A. Connor
Electrical, Computer, and Systems Engineering Department
Rensselaer Polytechnic Institute, Troy, NY
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 Ulaby’s textbook.
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Polarization
http://www.bungie.org/archives/news-Oct_02.html
http://www.3dglassesonline.com/how-do-3d-glasses-work/
http://www.maximumeyewear.com/productfolder/military-glasses/polarized-glasses.html
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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 E vector at a given
point in space as a function of time

The locus of E , 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 nonpolarized 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.
Polarization 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
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Polarization
•For a +z-propagating
wave, there are two 
possible directions of E

•Direction of E 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
~
~
~
E ( z)  E x ( z)a x  E y ( z)a y
~
E ( z)  ( E x 0 a x  E y 0 a y )e  jkz
Complex amplitudes
The phase difference between the complex amplitudes of x
and y components of electric field can be defines with angle δ
Ex0=ax
Ey0=ayejδ
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ax,ay are the magnitudes of Ex0 and Ey0
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Polarization
The phasor of electric field
~
E ( z)  (a x a x  a y a y e j )e  jkz
The corresponding instantaneous field

~
E ( z, t )  Re E ( z)e jt

E ( z, t )  a x a x cos(t  kz)  a y a y cos(t  kz   )

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
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Intensity and Inclination Angle

The intensity of E ( z , t )

E ( z, t )  E x2 ( z, t )  E y2 ( z, t )



1/ 2
 a x cos (t  kz)  a y cos (t  kz   )
2
2
2
2

The inclination angle ψ
 E y ( z, t ) 

 ( z, t )  tan 
 E x ( z, t ) 
1
generally they both are function of t and z
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1/ 2
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
E x ( z, t ) and E y ( z, t )
Are in phase (δ=0) or out of phase (δ=π)

E (0, t )  (a x a x  a y a y ) cost

E (0, t )  (a x a x  a y a y ) cost
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In phase
Out of phase
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Linear Polarization (out of phase)


2
2
E (0, t )  a x  a y

1/ 2
cost
  ay 
  tan 

 ax 
1
Ulaby
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Linear Polarization
Looking up from +z
x-polarized or horizontal polarized
ay=0
ψ=0° or 180°
y-polarized or vertical polarized
ax=0
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ψ=90° or -90°
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Circular Polarization
A wave is said to be circularly polarized if
~
E x ( z) and E~y ( z)
•the magnitudes of
•The phase difference is δ=±π/2
are equal and
δ=-π/2
δ=π/2
Ulaby
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Elliptical Polarization

Generally ax≠ay≠0 and δ≠0. the tip of E traces an
elliptical path in x-y plane
rotation angle, γ
-π/2≤γ≤π/2
Ellipticity angle, χ
  a 
1
  
tan   
R
 a 
-π/4≤χ≤π/4
Ulaby
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Polarization states
The wave is traveling out of the slide
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Ulaby
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http://www.mic-d.com/curriculum/lightandcolor/polarizedlight.html
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Example 1 – Polarization
Consider a wave travelling in the z direction whose electric field is

given by
E ( z, t )  3cos(t  z)a x  C cos(t  z  )a y
Describe the polarization (e.g.
 linear, right circular, etc.) and on an xy
plot sketch the locus of E ( z , t ) over a cycle for the following cases.
,   0o
a)
C  4V
b)
C  3V m ,   45o
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m
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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.uniregensburg.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
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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/polarizedlight.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 Brewster’s Angle, the reflected light will
be totally polarized.
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*http://www.mic-d.com/curriculum/lightandcolor/polarizedlight.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/polarizedlight.html
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Polarized Light from Olympus
*http://www.mic-d.com/curriculum/lightandcolor/polarizedlight.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 sevensegment 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.
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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/~s
hene/DigiCam/UserGuide/filter/polarizer.html
http://www.canfieldsci.com/photography/polarizer.shtml
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Photography with a Polarizing Filter
http://www.cs.mtu.edu/~shene/DigiCam/User-Guide/filter/polarizer.html
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Photography with a Polarizing Filter
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http://www.cs.mtu.edu/~shene/DigiCam/User-Guide/filter/polarizer.html
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Photography with a Polarizing Filter
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http://www.cs.mtu.edu/~shene/DigiCam/User-Guide/filter/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/polarizedintro.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/polarizedintro.html
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Nikon – Polarized Light
http://www.microscopyu.com/articles/polarized/polarizedintro.html
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Nikon – Polarized Light
http://www.microscopyu.com/tutorials/java/polarized/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/Crystallography_WWW/birefringence.htm
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Stress Birefringence
http://www.oberlin.edu/physics/catalog/demonstrations/optics/birefringence.html
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Birefringence on Plastic Boxes
http://www.engl.paraselene.de/html/birefringence_on_plastic_boxes.html
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Birefringence on Plastic Film
http://www.engl.paraselene.de/html/birefringence_on_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.unifiedphysics.com/
http://www.teachspin.com/instruments/faraday/index.shtml
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:
  VBd
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-webarticle.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-webarticle.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 Note
By Joseph H. Reisert
24 May 2017
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 Note
By Joseph H. Reisert
24 May 2017
http://www.astronwireless.com/polarization.html
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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 Note
By Joseph H. Reisert
24 May 2017
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 Note
By Joseph H. Reisert
24 May 2017
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 earth’s
surface.
Ulaby
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Antennas – Half Wave Dipole vs Quarter Wave Monopole
http://en.wikipedia.org/wiki/File:Half_%E2%80%93_Wave_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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http://th.physik.uni-frankfurt.de/~jr/physstamps.html
Stamps and Money
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http://th.physik.uni-frankfurt.de/~jr/physstamps.html
Stamps and Money
24 May 2017
http://www2.physics.umd.edu/~redish/Money/
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