On Sat, 17 Jul 2004 14:26:54 -0700, Roy Lewallen wrote:

J. Harvey wrote:

One of my assumptions is that the RHCP and LHCP can operate in
complete isolation of each other. . .

Some time ago, I stated that at any point in space there's a single
field, and that we can split it into various components to suit our
analytical needs. But the way we choose to split it or, conversely, the
way it was created (from a single source or polarization, or multiple
ones) doesn't alter the nature of the field in any way. I'm not sure if
what I said was simply disbelieved or whether it was ignored -- the end
result is the same.

The total field you get from simultaneous RHCP and LHCP waves is simple
to see by using the index finger of each hand to represent the
instantaneous orientation of the E field from each of two waves. Point
the index finger of your left hand downward and the index finger of your
right hand upward, knuckle-to-knuckle, so the fingers make a vertical
line extending from one fingertip to the other. The left index finger
will represent the LHCP wave and the right index finger the RHCP wave.
At the beginning instant that we're illustrating, they're out of phase
and sum to zero. So the field at that point and that time is zero.

Now rotate your left finger 45 degrees CCW and the right finger 45
degrees CW, to represent how the fields are oriented 1/8 period later or
1/8 wavelength away. If you add the two finger "vectors", you find the
result is a field that's horizontal, pointing to the left, and 1.414
times the length of one finger. Rotate the fingers another 45 degrees,
the left finger CCW and the right one CW. Now they're both pointing to
the left, and the sum is a horizontal field with magnitude equal to 2
fingers. If you continue this process, you'll find that the sum of the
two fields is always horizontal, and it oscillates between zero and two
fingers in instantaneous amplitude. It is, in fact, exactly the same as
and entirely indistinguishable from a horizontally polarized wave coming
from, say, a dipole. You can reach the same conclusion mathematically
from the equations I posted a few weeks ago.

If you run the same experiment beginning with the fingers in phase --
both pointing upwards -- you'll get a purely vertically polarized wave.
And with other starting phase angles, you'll get linearly polarized
waves of other orientations.

No magical energy distruction or disappearing takes place -- it's all
accounted for. And you can receive it just fine with a dipole.

Roy Lewallen, W7EL

You're absolutely right, Roy, I confess I shot without aiming properly. It's
been many years since I worked with CP, and I now remember going through the
same exercise that you presented above with the same result, a
linearly-polarized wave. Thanks for the refresher course.

Walt, W2DU