Page 222 - Maxwell House

202 ANTENNA BASICS

Furthermore, OAM “… arises because there is an azimuthal component of the Poynting’s vector
at each point on the wavefront and non-zero resultant when integrated over the beam cross-
section” [26]. We have pointed out at this occurrence in Section 3.1.8 of Chapter 3 analyzing
the force twisting photons and observed that the propagating EM wave (5.7) should hold non-
zero E- or H-field component in the radial direction. As a result, the wavefront of each mode
with ≠ 0 is defined as the surface − = is twisted taking the shape of
Archimedes screw (simply put, corkscrew or spiral-staircase) as Figure 3.1.9 in Chapter 3
demonstrates. Simple antennas depicted in Figure 5.1.5 and reprinted from the patent [27] are
the natural microwave radiators of twisted waves.

(−) with all components of the same frequency
Suppose the signal ∑ 0 (, )
is transmitted to some
correspondent. Evidently,
on the receiving site every
single component
(, ) of this signal
0
can be decoded by applying
the spatial inverse Fourier
transform resembling
(1.82) in Chapter 1.
Consequently, the
enhanced-factor of channel
information capacity
increases proportional to
the number of wave modes
that are encoded and
decoded in a given
frequency range.
Regrettably, EM field
structures corresponding to
(5.7) are much more
complicated than the
Gaussian beam (m = 0)
Figure 5.1.5 Antennas with auger polarization transformer illustrated in Figure 4.3.5
of Chapter 4. This is due to
the fact that the solutions of wave equation

2
1 0 0 0 1 0 0
2
� � + − 2 = � � − 2 − 0 = 0
2
that takes into consideration the azimuthal variations of higher mode Gaussian beams, are
described by Hermite and Laguerre polynomials as well as Bessel functions.