I don't have a classical textbook
with me, but without here goes:
every real antenna establishes E and H vectors
around it when the energy in the feeder reaches
the antenna structure. Conventionally, we think
of the E field, because the H field is directly
related to it, but 90 degrrees apart in space.
Due to the way the current flows on the surface
of the conductive elements making up the antenna,
most of the E field will be oriented in one
vector direction relative to a fixed set of
orthogonal co-ordinates, on earth taken to be
the horizon. If the direction is parallel to
the earth's horizon, conventionally we define
this as horizontal polarization, and of course
if vertical to the horizon, vertical polarization.
If current can be pursuaded by design of the
structure to follow a particular curved path,
then circular polarization results, and this
is right hand or left hand depending on which
sense the curved path follows.
b) and c)
In the desciption above, I deliberately said
"most of the E field", because the flow of current
will establish E field in both the hozizontal
plane and the vertical plane simultaneously.
The ratio of these two vector magnitudes in
dB is the cross-polarization level. In a circular
polarized antenna with perfect circularity,
this will be zero dB, because the E field level
that can be measured is the same in the horizontal
as well as the vertical plane. If you imagine
a fat dipole, however, with the elements horizontal,
most of the E field vector will be horizontal.
However, some current will flow across the cylinder,
around the curved direction, and thus it will
set up a vertical E field. Let us assume this
level is -15dB compared to the horizontal level.
If an ideal horizontally polarized antenna were
to be used as a far field source, with no vertical
polarization, the level of energy received in
the fat dipole is taken as 0dB when they are
both in the same plane. If now the perfect antenna
is rotated to the vertical, the level received
should fall to zero, but will actually fall
to -15dB. This is the cross polar discrimination.
In my book, it is also the cross-polar isolation,
but purists might disagree and argue the point.
Essentially, cross polar discrimination shows
the ability of an antenna to separate, in the
above example by rotating it, or discriminate,
the pure vertical from the pure horizontal polarization
of a received signal.
At bottom, life is
Sucking in and blowing out.