Electromagnetic Vortices. Группа авторов

Uniform circular array (UCA) Refs. [33, 62,102–109] RF OAM Photo credit: [102] Holographic gratings Refs. [110–113] Optical and RF OAM Photo credit: [110] Reflectarray antennas Refs. [5,114–117] RF OAM Photo credit: [114]

Appendix 1.A OAM Far-field Calculation

The aperture field of an OAM‐carrying linearly polarized field with a cylindrically symmetric distribution E(ρ′) can be written as:

(1.A.1)

Table 1.2 Chronicle of milestones regarding OAM.

Reference	Year	Main contribution
[1]	1909	Theoretically studied angular momentum of circularly polarized waves
[2]	1936	Experimentally studied the SAM of light and demonstrated that SAM can cause the rotation of a mechanical system
[3]	1992	Recognized that light beams with an azimuthal phase dependence of ejlϕ carrying OAM
[17]	2004	Conducted the first experiment on OAM free‐space optical communications
[76]	2006	Reported the generation of an OAM‐carrying optical vortex in optical fibers
[62]	2007	Numerically showed that OAM can be used in the radio frequency domain
[23]	2012	Performed the first experimental test of encoding multiple channels on the same radio frequency through OAM
[80]	2013	Conducted the first OAM‐MDM experiment suggesting that OAM could provide an additional degree of freedom for data multiplexing in future fiber networks
[5]	2018	Suggested a potential application that takes advantage of the OAM cone‐shaped pattern in the far‐field

Figure 1.A.1 Schematic of the generation of OAM aperture field.

where ρ′ and ϕ′ are the radial and azimuthal coordinates in the cylindrical coordinate system; a is the transverse extend of the aperture field of the beam; l is the OAM order. A schematic of the generation of the OAM aperture field is shown in Figure 1.A.1. Typically, the input beam from the feed is a Gaussian‐type beam with a tapered amplitude distribution. The beam waist w_g, i.e. the half‐width of the normalized aperture field amplitude at 1/e, is directly related to the OAM antenna aperture diameter D, as shown in Figure 1.A.1. For example, the equivalent beam waist in Ref. [5] was w_g = 0.415D for a −12 dB taper illumination. Higher taper illumination would lead to a smaller equivalent beam waist. The role of the OAM antenna (helicoidal reflector in Figure 1.A.1) is to create the desired exit‐aperture amplitude and phase distribution at the infinite exit‐aperture plane. A common model for the aperture field of an OAM antenna is the Laguerre–Gaussian distribution Eq. (1.3).

      The equivalent magnetic current density is calculated from [122, eq. 6‐129b]:

      (1.A.2)

      The radiation integrals can be written as [122, eqs. 6‐125c, 6‐125d]:

      (1.A.3)

      (1.A.4)

      Using the integral identity [5, eq. (5)]:

      (1.A.5)

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