Peter O. Brackett wrote:
. . .
It is commonly understood that polarization of electromagnetic waves may
be either linear or circular.

Then some education is in order. Electromagnetic waves are elliptically
polarized. The two extreme special cases of this are linear and circular
(with axial ratio of zero -- or infinite depending on your choice of
definition -- and one respectively). There are an infinite number of
other possible elliptical polarizations with different axial ratios.

Linear Polarization (LP):

Of course waves that are linearly polarized may have any arbitrary
orientation angle (theta) with respect to a reference frame such as the
earth's surface. For example most common linear amateur antennas
produce and/or respond to waves of linear polarization, and these
antennas produce either either horizonally or vertically polarized waves
depending upon the orientation of the (linear) antenna with respect to
the earth's surface (ground).

Of course linear polarization can have any orientation, not just
vertical or horizontal. And even those terms lose meaning when away from
the Earth. However, it's often convenient to mathematically separate
waves into two superposed components of horizontal and vertical
polarization.

As examples; a 1/2 wave length dipole for 10 meters hung at 30 feet
between two trees of equal height produces a largely horizonally
polarized wave and, a 2 meter 1/4 wave dipole mounted in the center of
the roof of an automobile produces a largely vertically polarized wave.

The polarization of the dipole signal will be purely horizontal only
directly broadside. The signal off the ends are purely vertically
polarized, and in other directions neither horizontal nor vertical.

Of course as electromagnetic waves are propagated throughout an
environment are never purely orientated and usually contain an ensemble
of many orientations, because the waves are reflected from the ground,
trees, buildings, mountains, bridges, moving vehicles, and sometimes
propogated through moving and anisotropic media such as the ionosphere,
etc... and so the multiple reflection surfaces at various angles to the
earth's surface and/or refractions and Faraday rotations will conspire
to "mix up" the original orientation of the E vector of a purely linear
transmitted wave and usually produces a quite mixed polarization at
distance from an emitting antenna.

By "mixed" polarization, I assume you mean a single polarization which
is neither horizontal nor vertical and can be described as a "mixture"
of a purely horizontal and a purely vertical wave.

Malus' Law {I = Io [cos(theta)]^^2} describes the response of a linearly
polarized receiving antenna to waves arriving at a polarization angle
theta relative to the receiving antenna's preferred orientation. i.e a
horizontally polarized antenna will produce maximum response to
horizontally polarized waves and a minimum response (zero) to a
vertically polarized wave and vice versa.

Of course in practice, because of the multipath reflections and
refractions the 'cross response' is never exactly zero or maximum as
predicted by Malus Law.

It's also difficult to get the polarizations of the antennas exactly right.

Just the same it is preferable to have the orientation of a receiving
antenna 'aligned' with that of a particular transmitting antenna. In
the HF region it is difficult for hams to "rotate" the orientation of
their receiving antennas to maximize signal pickup based upon
polarization, and so most hams are forced to take whatever response
their relatively fixed antennas produce to the relatively unknown
orientation of received waves.

There's no advantage at HF of having the antenna orientations the same
if the path is via the ionosphere.

In military or commercial installations, where money and space may not
be an issue, either electronically or mechanically derived spatial
antenna polarization diversity can be utilized to maximize received
signal strength based upon arriving polarization. Polarization
diversity receivers...

Circular Polarization (CP):

. . .

Again Malus Law applies, in an easily applied modified form and so...
RHCP receiving antennas respond to RHCP waves and LHCP receiving
antennas respond to LHCP waves. A purely RHCP antenna will produce zero
response to an LHCP wave, etc...

Interesting. Can you work an example for us? I'm curious as to what you
use for theta in the "law's" equation.

An interesting effect happens upon reflection of CP waves. An RHCP wave
reflected from a perfectly reflecting surface returns (is echoed) as a
LHCP wave!

Only if it strikes the surface directly head-on. Otherwise you get an
elliptically polarized wave. The axial ratio depends on the angle of
incidence and, if the reflector isn't perfectly conducting, on the
impedance of the surface.

CP propagation is often used in Satellite communications where a
satellite may use both RHCP and LHCP transmitting antennas on the same
frequency for communicating independently with two different ground
stations using R and L CP antennas on the same frequency. CP frequency
diversity doubles channel capacity!

I think you mean that polarization (not frequency) diversity doubles
channel capacity.

Yet another common form of CP antenna uses crossed linear antennas fed
with a 90 degree (Pi/2) phase difference excitation.

As far as I know all currently known CP antennas such as axial mode
helixes and crossed 90 degree linear arrays produce CP waves where the
angular velocity of rotation is one revolution per cycle of the RF
carrier, or in other words one radian of circular rotation for each
radian of frequency transmitted. In other words most well known CP
antennas produce ONLY synchronous CP, where the angular velocity of
rotation of the E vector is synchronized exactly with the frequency of
the wave being transmitted.

That is, in fact, the definition of circular or elliptical polarization.

I believe that the well known and understood situation of purely
synchronous CP is NOT necessesarily the only form of CP.

It's the only one which fits the definition. If you choose to rotate the
polarization at some other rate, you should call it something else.

Warning... The following may be an invention!

Consider the case of a linear antenna, say a dipole, fed from a feed
line over rotating slip rings, such that the antenna can be rotated
while it is transmitting.

Now transmit on that dipole antenna whilst mechanically spinning it
clockwise [RHCP?] (with a mechanical motor of some kind).

The dipole antenna is linear and thuse emits linear polariztion, except
it is mechanically spinning, and so the E vector emanating from the
antenna will be rotating with respect to its direction of travel.

In this case the angular velocity of the motor that spins the linear
antenna need not be synchronous with the frequency being radiated.

For example we could mechanically spin the antenna at 330 rpm while
transmitting a carrier of 1 GHz.

This would most certainly produce circular polarization. For is not the
E vector spinning at 330 revs!

Sorry, it doesn't. An unavoidable side effect of the synchronicity
change is that the amplitude of the E field still changes at a 1 GHz
rate, going through a complete cycle from max to zero to max to zero to
max each nanosecond. A circularly polarized wave doesn't change
amplitude with time. A non-circular elliptical wave changes amplitude
but not fully to zero each cycle.

Circularly polarized waves have many characteristics and particular
relationships to linearly polarized waves. The waves you're producing
don't have some of these characteristics, like the constant amplitude.
Your method doesn't produce circularly polarized waves even though the
polarization does indeed change with time.

In fact the astute newsreader may note that we need not use a motor to
rotate the antenna. In fact, I can propose several ways of
"electronically" rotating the linear antenna at any arbitrary angular
velocity, not necessarily synchronous with the transmitted frequency and
so produce a so-called non-synchronous CP at any desired rate of rotation.

Clearly, according to Malus Law, the maximum response to the
non-synchronous CP received waves from this 'rotating' antenna
contraption would be from a similarily rotating receiving antenna!

Question?

What would be the response of an axial mode helix antenna or say crossed
90 degree fed dipoles or any other "synchronous" CP antenna to such a
non-synchronous wave produces by a rotating antenna?

Because a circularly polarized antenna responds equally well to all
orientations of linear polarization, the normal helix wouldn't be aware
of the polarization rotation -- unless the polarization rotation was
fast enough to be nearly synchronous.

Would the response of a syncrhronous axial mode helix be less than that
of a sympathetically rotating receiving antenna?

No.

What?

Thoughts, comments?

Sorry, I didn't find it "mind-blowing".

-- Pete K1PO
-- Indialantic By-the-Sea, FL

Roy Lewallen, W7EL