Page 221 - Maxwell House

Chapter 5 201

magnitude of red and green projections at the starting point G). The red side and green bottom
solid lines illustrate the component harmonic variations along the ( − )-axis. Evidently, it
converts into LP when = 0 and into CP if the two LP amplitudes are equal and shifted in
phase = ±/2. Therefore, both LP and CP are just the special cases of elliptic polarization.
It is clear that this statement can be inversed: any LP or CP wave may be represented as a
superposition of two elliptically polarize waves or any elliptical polarized wave may be
represented of as a sum of two CP of unequal magnitude.

In a typical case, the polarization ellipse shown in Figure 5.1.4 in purple may be expressed in
term of its major a-axis and minor b-axis (the same manner as in geometry), i.e. the parameter
called the axial ratio = / < 1, and the tilt of the major axis with respect to the -axis.
The final expressions are not complicated but quite cumbersome. Note that in general, the axial
ratio can be conveniently expressed in [dB] as = −20 log ( ). Evidently,
⁄
10
= ∞ for LP antennas since one of the ellipse axis is zero while = 0 dB for ideal
CP antennas since a = b. Nevertheless, an antenna continues to be classified as having CP while
< 2 – 3dB.
5.1.2 Co- and Cross-Polarization

The polarization that is identical to be transmitted and then received is called Co-Pol, and its
orthogonal one is called Cross-Pol or short X-Pol. For example, if the vertical LP is designated
as Co-Pol the horizontal (H) LP is X-Pol and vice versa. The same goes for the duo RHCP &
LHCP. Theoretically, antennas developed for one polarization in a pair must not emit or peak
up the signal of opposite polarization, but nothing in this world is perfect. The value of Cross
Polarization Discrimination (XPD) defines as the ability of an antenna to reject the X-Pol
signal. In case of LP, this parameter depends on the polarization ellipticity and is defined in
[dB] as = 20log ((1 + ) (1 − )⁄ ) where 0 ≤ ≤ 1. In general, the cross
10
polarization discrimination varies from 3-10 dB for relatively simple antennas and up to 40 -
60 dB for more sophisticated ones. Note in conclusion that EM waves can change their
polarization under the influence of turbulence in the atmosphere and ionosphere, reflection from
the objects like the earth’s surface, buildings, trees, clouds, mountains, and many other
obstacles. This effect is called depolarization.
5.1.3 Twisted EM Waves

We briefly touched on the polarization of EM field phenomenon related to the orbital angular
momentum (OAM) of photons (look back at Figure 3.1.4c and 3.1.9) in Chapter 3. Scientists
learned quite recently how to generate and control OAM thereby significantly extending the
variety of orthogonal, i.e. independent and thus recognizable, EM wave polarizations [25].
Loosely speaking, we can imagine that photons are slightly delayed in their periodical rotation
and acquire some azimuthal varying phase that can be written in phasor form as exp()
where = 0, ±1, ±2, … . This phase varies from zero to 2π in the plane perpendicular to the
propagation direction. If such speculation is near truth, we can expect that Maxwell’s equations

should provide not only the solution as in (4.67) but more general one depending on transversal
azimuthal coordinate 0 ≤ ≤ 2

(, ) = (, ) (−) (5.7)
0