Linear and Circular Polarization
Date: April 28, 2011
What is the difference between linear polarization and circular polarization?
Linear polarization is simpler, to our way of thinking.
It can be expressed as the product of one transverse e-field vector and one sine wave in time.
Circular polarization is the superposition (sum in 3D space) of two linear polarizations,
with the e-field vectors orthogonal to each other as well as to the direction of travel,
and the sine-waves 90 degrees out of phase in time.
It is just as if the E-field 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 sine-wave plot does.
You can see that if a medium absorbed Y-axis lin.-pol. waves, but passed Z-axis polarized waves
(as the typical polarized does) , then the circular-polarized wave
would be trimmed back to being only a linear-polarized 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 elliptical-polarized wave can also be expressed as
the sum of a circular-polarized wave and a linear-polarized wave,
both of the same frequency and direction.
Suppose the direction of travel is X-axis.
My chosen linear-pol. wave might have its electric-field vector
anywhere in the Y-Z plane, orthogonal to the direction of travel (wave-vector).
Suppose it's aligned with the Y-axis.
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
E_circ = y^ * sin(w*t) + z^ * cos(w*t)
E_circ = y^ * sin(w*t) - z^ * cos(w*t)
One is left-hand polarized, the other is right-hand 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 time-phase difference is correct.)
Strangely enough, photons themselves can be circular- or linear- polarized.
Both circular and linear are equally valid basis-sets 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.
Electro-Magnetic 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 Electro-Magnetic wave is defined by the orientation of
the Electrical component of the Electron-Magnetic 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
Electro-Magnetic wave is said to be horizontally polarized.
Linearly polarized Electro-Magnetic waves do not change orientation as they
propagate through space.
Circularly polarized Electro-Magnetic 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, Electro-Magnetic 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.
Here is another reference for you (and be sure to click on the animate
Click here to return to the Physics Archives
Update: June 2012