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:
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 wg, 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 wg = 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)