Electromagnetic Vortices. Группа авторов

Figure 1.17 and Refs. [75, 86, 87]).

Figure 1.16 Intensity profiles of LP modes and OAM modes. The constituent eigenmodes and the propagation constants β of each mode are noted below each LP and OAM mode. Unlike OAM modes, LP modes (i) have distinct propagation constants leading to walk‐off and (ii) share common eigenmodes and are inherently coupled resulting in crosstalk.

1.4 OAM Generation Methods

The history of OAM dates back in 1992, when Allen et al. showed that helically phased beams with a phase term e^jlϕ carry OAM [3]. Since then, research efforts have focused on the generation of OAM beams. Figure 1.18 shows the analogy between the generation principle of OAM and conventional beams. In a conventional antenna system, a device (such as reflectors [22] and lenses [88]) is used to transform an input wavefront (for example, a spherical wavefront in Figure 1.18) into a planar wavefront, to achieve a highly directive beam in the far‐field. In analogy with the conventional antenna system, an OAM system employs an OAM device to transform the input wavefront into a spiral wavefront. Figure 1.19 shows a representative example where the wavefront‐transformation devices are a parabolic reflector [22] and a helicoidal reflector antenna [23], corresponding to the conventional and OAM cases, respectively. The conventional reflector antenna attempts to achieve a uniform phase in the exit aperture, whereas the helicoidal reflector aims to achieve the OAM vortex phase.

Figure 1.17 (a) Cross‐section of a 19‐ring multi‐OAM multi‐ring fiber. (b) Refractive index profile of a single ring. (c) Intensity and phase distributions of HE₃₁ related OAM mode in a single ring.

      Source: Li and Wang [75] © 2014 Springer Nature.

Figure 1.18 Analogy between conventional and OAM generation principle.

The generation of OAM‐carrying beams necessitates the design of antennas that can generate the vortex aperture phase and spiral wavefront that are associated with OAM beams. Some representative designs that have been developed for this purpose are shown in Table 1.1. The spiral phase plate (SPP) has one planar and one spiral surface with a step discontinuity, and the thickness increases as the azimuth angle increases [13, 19,89–91]. The original shape of the conventional parabolic reflector is modified to form a ‘helicoidal reflector’ [23] that converts the field generated by a feed into an OAM‐carrying field [92–94]. A stepped spiral reflecting surface is a discrete approximation of the helicoidal reflector [101]. Planar SPPs, transmitarray [95–100], and reflectarray antennas [5,114–117] employ elements that are distributed in planar surfaces; these elements compensate the phase delay associated with incident waves from different paths emitted from the feed and generate the desired vortex phase distribution. The uniform circular array (UCA) consists of elements that are uniformly distributed on the circumference of a circle. The array elements are fed with an input signal with the same amplitude but with a successive phase delay from element to element such that after a full turn the phase has been incremented by 2πl, where l is the OAM mode number [33, 62,102–109]. The transmittance functions of holographic gratings can also be designed to generate OAM beams [110–113]. Other generation methods include cylindrical lenses [3], spatial light modulators [9], q plates [118], dielectric resonators [119], traveling‐wave circular loops [120], and metasurfaces [121]. The previous designs can generate single‐mode OAM beams, superposition of OAM modes, i.e., mixed‐mode OAM beams [5, 95], and mode‐reconfigurable OAM beams [102, 121].

Figure 1.19 Comparison between the generation method of conventional antennas with directive far‐field patterns and OAM antennas: the case of reflector antennas.

1.5 Summary and Perspectives

This chapter has provided a comprehensive overview of OAM beams. We analyzed the fundamental properties of OAM beams and contrasted them with conventional beams. In addition, an appendix is provided to summarize the fundamental mathematical details when the OAM concept is used for potential antenna applications. We discussed emerging applications of OAM in free‐space optical and RF communications as well as in fiber communications, highlighting potentials, and technical challenges. A comprehensive list of relevant references is included. We also summarized the generation methods of optical and RF OAM. Analogies regarding the fundamental properties, antenna communication links, and generation methods between OAM and conventional beams have been provided. More details on various aspects of OAM are discussed in various chapters of this book. We conclude by providing Table 1.2, which summarizes the theoretical and experimental milestones regarding OAM in chronological order. OAM is a field with short history of less than 30 years that has come a long way so far, and we are excited to see the future advancements of OAM.

Table 1.1 OAM generation methods and fabricated prototypes.

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Generation method	Prototype photo
Spiral phase plate (SPP) Refs.: [13, 19,89–91] Optical and RF OAM		Photo credit: [90]
Helicoidal reflector antenna and reflector antenna systems Refs. [23,92–94] RF OAM		Photo credit: [23]
Planar spiral phase plate and transmitarray antenna Refs. [95–100] RF OAM		Photo credit: [95]
Stepped spiral reflecting surface Ref. [101] RF OAM