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composite signal suitable for transmission over a common channel. ” It means that the users
share the same medium, likewise free space, optical fiber, coaxial line, etc., to communicate.
Meantime, the frequency spectrum is currently overpopulated and scarce resource that restricts
the frequency multiplexing. The code division multiplexing utilizes frequency spectrum more
efficient letting multiple users communicate simultaneously even on the same frequencies with
minimum interference by coding each message differently (like sending messages in different
languages) and so on. Such tendency is apparent; how to pack the greatest number of signals in
the same channel avoiding or at last minimizing interference between them.

One of an actual way to achieve this goal is to vary EM wave polarization. Until recently, the
number of realizable polarization states was restricted by vertical (VLP) and horizontal (HLP)
linear polarization or two their combinations, right- and left-handed circular polarization, i.e.
RCP and LCP. We set aside this issue until the next chapter noting only that in circularly
polarized EM wave the photons gyrate in the plane normal to the direction of wave propagation
while |r| = 0 (see Figure 3.1.4), i.e. they possess not only linear but so-called Spin Angular
Momentum (SAM), as well. The critical issue is that each polarization must be recognized as
independent signals (so-called orthogonal signals, i.e. loosely speaking, they cannot “see” each
other) by antennas on receiving site of the communication system. If so, each of different
information signals carried by EM waves of VLP and HLP or RCP and LCP is apparently
recognizable. However, it is not a breakthrough because the information channel capacity is
just doubled. To get more, we should use wider
Right-Handed Left-Handed varieties of EM wave polarizations meaning to
complicate photons’ movement. Apparently, any
such manipulation should keep them in the
orthogonal state.

In 1992, physicist Les Allen and his colleagues at
Leiden University, Netherlands, pointed out that we
can develop the communication system based on
photon capability to carry the Orbital Angular
Momentum (OAM). It means that |r| > 0 in Figure
3.1.4c, i.e. a photon orbits like Earth around Sun. The
critical issue is how to transfer the required energy to
such photons. The answer is in Poynting’s vector
orientation. According to our calculations in the
Figure 3.1.9 Twisted EM beam
illustration previous section, the liner moment of EM wave is
2
defined as = / . Then the vector-product
= × / is proportional to the torque force twisting photons. Therefore, EM wave with
2
2
| × / | > 0 possesses the required OAM. Meanwhile, the vector triple product × = ×
( × ) = ( ∘ ) − ( ∘ ) that means that the propagating EM wave should hold
nonzero E- or H-field component in the radial direction. Several such OAM orthogonal twisted
beams are pictured in Figure 3.1.9. The bottom image corresponds to classical CP.

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8 S. Haykin, Communication Systems, 3 Edition, John Wiley & Sons, 1994