Electromagnetic Vortices. Группа авторов

OAM‐DM, polarization‐division multiplexing, and wavelength‐division multiplexing is shown in Figure 1.14. OAM‐DM can be combined with other multiplexing schemes, such as time, polarization, and wavelength multiplexing, to satisfy the ever‐growing need for transmission capacity.

      The possibility of using OAM‐DM extends beyond optical frequencies. Thidé et al. [62] were the first to numerically show that antenna arrays can generate OAM beams in radio frequencies and highlight the potential of OAM communications in the lower frequencies. The first experimental test of encoding multiple channels on the same radio frequency using OAM was performed by Tamburini et al. [23]. Subsequently, several OAM‐DM experiments have been performed in the radio frequency domain. In [63], an OAM‐DM 10 m microwave link operated at 10 GHz with four OAM modes was experimentally demonstrated to quadruple the spectral efficiency while keeping a low‐receiver computational complexity. The antenna aperture size was 0.6 m, which corresponds to a far‐field distance of 2D²/λ = 24 m and the 10 m link cannot be considered a far‐field link. In [64], a 32 Gbit s⁻¹ mm‐wave link was demonstrated over 2.5 m at a carrier frequency of 28 GHz with a spectral efficiency of 16 bit s⁻¹ Hz⁻¹ using four independent OAM beams on each of the two orthogonal polarizations. The receiving and transmitting antenna aperture had circular apertures with diameters of 30 cm, which correspond to a far‐field distance of 2D²/λ = 16.8 m and the 2.5 m link cannot be considered a far‐field link. As discussed in Section 1.3, the adoption of OAM in far‐field wireless radio frequency (RF) communications is still an open problem.

      1.3.2.2 Optical Fiber Communications

      Optical fibers have been successfully integrated into communication systems, offering the advantages of large bandwidth, low loss and cost, and immunity to electromagnetic interference [65]. The conventional optical fiber is known as single‐mode fiber (SMF) and includes a core surrounded by a transparent cladding material with a lower index of refraction; the attenuation is typically 0.2 dB/km at 1550 nm and the core radius does not exceed 10 μm [53]. Up to now, the increasing demand for high‐speed data transfer in optical networks has been covered by the conventional SMF. The growing demand for network capacity is expected to continue in the future. According to Ref. [66], the annual global data center traffic will reach 20.6 Zettabytes (zB) – or 20.6 × 10²¹ bytes – (1.7 zB per month) by the end of 2021, up from 6.8 zB per year (568 exabytes per month) in 2016.

Figure 1.14 A schematic illustrating the concept of three‐dimensional multiplexing to increase the multiplexed data channels by combing (a) OAM‐DM, (b) polarization‐division multiplexing, and (c) wavelength‐division multiplexing.

      Source: Huang et al. [60] © 2014 Optical Society of America.

In an attempt to meet the everlasting demand for network capacity, alternative methods have been developed to increase the spectral efficiency of optical networks. The problem is that the conventional SMF has its inherent capacity limits; therefore, researchers have focused on innovative ways to increase the data‐carrying capacity of a single optical fiber. SDM using multi‐core fibers (MCFs), multi‐mode fibers (MMFs), and their combination has been considered to overcome the capacity crunch of conventional SMFs [67, 68]. A schematic of different types of optical fibers is shown in Figure 1.15 [65]. In an MCF, multiple cores share the same cladding and act as an independent data carriers; thereby, the spectral efficiency scales by the number of the cores. Unlike MCFs, MMFs have a single core that is larger than the conventional SMF, usually around 50 μm in radius. MMFs can support multiple spatial orthogonal modes each carrying distinct data and acting as a separate communication channel, thus increasing the spectral efficiency of optical fibers. The latter special case of SDM is known as MDM [67].

Figure 1.15 A schematic representation of different types of optical fibers.

The most popular spatial modes for fiber MDM are the linearly polarized (LP) modes. LP modes are the superposition of the fiber eigenmodes transverse electric (TE), transverse magnetic (TM), and hybrid modes of HE and EH type [65]. LP modes are the solution of the scalar Maxwell’s equations and propagate under the weakly guiding approximation, which is valid when the refractive indices of the core and the cladding are very close (within 1%) [69]. The intensity profiles of LP modes together with the constituent eigenmodes and the corresponding propagation constants β are shown in Figure 1.16a–d. The constituent eigenmodes of each LP mode have different propagation constants leading to walk‐off and mode distortion. LP modes also share common eigenmodes and thus are inherently coupled during propagation leading to crosstalk. To overcome the problem of mode‐coupling, MMFs rely on digital signal processing (DSP) algorithms based either on adaptive optics feedback or complex multiple‐input multiple‐output (MIMO) methodologies [32, 70].

      To avoid inter‐modal coupling and MIMO DSP complexity in MMFs, OAM modes have been proposed as an alternative modal basis set [69]. The electric field of OAM modes in fibers can be expressed in terms of HE and EH hybrid modes as [71, 72]:

      (1.16)

      The intensity profiles of OAM modes, the constituent eigenmodes, and the corresponding propagation constants β are shown in Figure 1.16e–h. Unlike LP modes, OAM modes are formed by the superposition of a single eigenmode type with even and odd symmetry [73]. That is, OAM modes are inherently de‐coupled resulting in low crosstalk, and the constituent eigenmodes with even and odd symmetry share the same propagation constant leading to a reduced walk‐off effect compared to LP modes [74]. As a result, OAM has the potential to increase the spectral efficiency of optical fiber communications while obviating complex DSP algorithms.

OAM‐based fiber communications is a new field of research with a short history. The first paper to report the generation of an OAM‐carrying optical vortex in a fiber was published in 2006 [76]. Bozinovic et al. reported the stable propagation of OAM modes in a new class of optical fibers, called vortex fibers [77, 78]. The vortex fiber of [78] maintained a mode purity of 97% after a propagating distance of 20 m at a wavelength of 1550 nm under bends and twists. The same group demonstrated the successful transmission of OAM states through a 0.9 km vortex fiber. In 2012, a 1.1 km long vortex fiber was presented [79]. A year later, the same 1.1 km vortex fiber was used to achieve 400 Gbit s⁻¹ data transmission using four OAM modes at a single wavelength of 1550 nm, and 1.6 Tbit s⁻¹ using two OAM modes over 10 wavelengths around 1550 nm with a low‐complexity DSP coherent detection method [80]. The experiment of [80] suggested that OAM could provide an additional degree of freedom for data multiplexing in future fiber networks using OAM‐MDM that does not require complex DSP [81]. At present, research efforts focus on the design of fibers that can support multiple OAM modes, both MMFs (see,