

Linear and Circular Polarization
Name: Rinku
Status: student
Grade: 912
Location: OH
Country: India
Date: April 28, 2011
Question:
What is the difference between linear polarization and circular polarization?
Replies:
Linear polarization is simpler, to our way of thinking.
It can be expressed as the product of one transverse efield vector and one sine wave in time.
Circular polarization is the superposition (sum in 3D space) of two linear polarizations,
with the efield vectors orthogonal to each other as well as to the direction of travel,
and the sinewaves 90 degrees out of phase in time.
It is just as if the Efield vector spins in a circle around the direction of travel
(at any one fixed point in space),
instead of bobbing +1 , 0, 1 , 0, +1, ... in a single axis, like a sinewave plot does.
You can see that if a medium absorbed Yaxis lin.pol. waves, but passed Zaxis polarized waves
(as the typical polarized does) , then the circularpolarized wave
would be trimmed back to being only a linearpolarized wave.
Elliptical polarization is like circular, except:
the vectors may not be exactly orthogonal, and
the phase difference might not be exactly 90 degrees.
I think any ellipticalpolarized wave can also be expressed as
the sum of a circularpolarized wave and a linearpolarized wave,
both of the same frequency and direction.
Suppose the direction of travel is Xaxis.
My chosen linearpol. wave might have its electricfield vector
anywhere in the YZ plane, orthogonal to the direction of travel (wavevector).
Suppose it's aligned with the Yaxis.
Linear polarization:
E_lin = y^ * sin(w*t) : or more broadly, E_lin = (A*y^ + B*z^) * sin(w*t)
"y^" being my way of saying the Y_axis vector in computer text.
"w" = 2*pi*frequency
"t" is time of course
Circular:
E_circ = y^ * sin(w*t) + z^ * cos(w*t)
or
E_circ = y^ * sin(w*t)  z^ * cos(w*t)
One is lefthand polarized, the other is righthand polarized.
I forget how to determine which sign gets which name.
You can do algebra with these and find that two orthogonal linear waves can make a circular wave,
and two circular waves left and right polarized can make a linear wave.
(if their timephase difference is correct.)
Strangely enough, photons themselves can be circular or linear polarized.
Both circular and linear are equally valid basissets for imagining everything, if you can do the math.
You can probably think up orthogonal elliptical polarizations, too, and use those for everything.
Reality doesn't seem to care which way is simpler in our math expressions.
Jim Swenson
Rinku
ElectroMagnetic waves (which include radio and light waves) have two fields
(an electric field and a magnetic field) that are oriented 90 degrees apart.
(In other words the electrical field is orthogonal to the magnetic field.)
Polarization of an ElectroMagnetic wave is defined by the orientation of
the Electrical component of the ElectronMagnetic wave.
That is, if the Electrical field is in the vertical orientation, then the
wave is said to be vertically polarized.
Conversely, if the Electrical field is oriented parallel to the horizon, the
ElectroMagnetic wave is said to be horizontally polarized.
Linearly polarized ElectroMagnetic waves do not change orientation as they
propagate through space.
Circularly polarized ElectroMagnetic waves rotate (spin) in a circular
pattern as they propagate through space.
If the transmitting and receiving antennas are of the same polarization,
there is no signal loss due to mismatched polarity.
Theoretically, if the antennas are mismatched at 90 degrees, there will be
infinite signal loss.
However as a practical matter, ElectroMagnetic waves drift in orientation
as they propagate due to changes in atmospheric density so there is always
some signal left to be picked up by the cross polarized antenna.
Here is a local experiment for you.
Take the plastic out of a pair of polarized sun glasses and put them on top
of one another
Then rotate one of them until no light passes through them. At that point
the lenses are cross (mismatched) polarized.
Here are some pictures that can help you visualize what polarization is.
http://hyperphysics.phyastr.gsu.edu/hbase/phyopt/polclas.html
Here is another reference for you (and be sure to click on the animate
link):
http://physics.info/polarization/
Sincere regards,
Mike Stewart
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Update: June 2012

