Perspectives on advances in high-capacity, free-space communications using multiplexing of orbital-angular-momentum beams

Beams carrying orbital-angular-momentum (OAM) have gained much interest due to their unique amplitude and phase structures. In terms of communication systems, each of the multiple independent data-carrying beams can have a different OAM value and be orthogonal to all other beams. This paper will describe the use of multiplexing and the simultaneous transmission of multiple OAM beams for enhancing the capacity of communication systems. We will highlight the key advances and technical challenges in the areas of (a) free-space and fiber communication links, (b) mitigation of modal coupling and channel crosstalk effects, (c) classical and quantum systems, and (d) optical and radio frequency beam multiplexing. © 2021 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0031230., s


I. INTRODUCTION AND OVERVIEW
In 1992, Allen et al. 1 reported that orbital angular momentum (OAM) can be carried by an optical vortex beam. This beam has a unique spatial structure such that its amplitude has a ring-like doughnut profile and the phase front "twists" in a helical fashion as it propagates. The number of 2π phase changes in the azimuthal direction represents the OAM mode order, and beams with different OAM values can be orthogonal to each other (Fig. 1). Such structured beams are a subset of the Laguerre-Gaussian (LG lp ) modal basis set in free space, which has two modal indices: (1) l represents the number of 2π phase shifts in the azimuthal direction and the size of the ring grows with l and (2) p + 1 represents the number of concentric amplitude rings. 2,3 This orthogonality enables multiple independent optical beams to be multiplexed, spatially co-propagate, and be demultiplexed-all with minimal inherent crosstalk. 1,3,4 This orthogonality is crucially beneficial for a communications system. It implies that multiple independent data-carrying optical beams can be multiplexed and simultaneously transmitted in either free-space or fiber, thereby multiplying the system's data capacity by the total number of beams (Fig. 2). Moreover, since all the beams are in the same frequency band, the system's spectral efficiency (i.e., bits/s/Hz) is also increased. These multiplexed orthogonal OAM beams are a form of mode-division multiplexing (MDM), which itself is a subset of space-division multiplexing (SDM). [5][6][7] MDM shares similarities with wavelength-division multiplexing (WDM) in which multiple independent data-carrying optical beams of different wavelengths can be multiplexed and simultaneously transmitted. WDM revolutionized optical communication systems and is ubiquitously deployed worldwide. Importantly, MDM is generally compatible with and can complement WDM such that each of the many wavelengths can contain many orthogonal structured beams and thus dramatically increase data capacity. 7,9,10 The field of OAM-based optical communications (i) is considered young and rich with scientific and technical challenges, (ii) is promising for technological advances and applications, and (iii) has produced much research worldwide such that the number of publications per year has grown significantly. 11 Capacities, distances, and numbers of data channels have all increased, and approaches for mitigating degrading effects have produced encouraging results. 4,11,12 In this paper, we discuss the evolution of several sub-fields in OAM-based optical communications. We describe advances and perspectives on different aspects of this field, including (a) free-space optical (FSO) communication links; (b) modal coupling effects and channel crosstalk mitigation techniques; (c) airborne and underwater systems; (d) quantum communications; (e) radio-frequency, millimeter-wave (mm-wave), and THz links; and (f) fiber-based systems. We note that this article will generally assume OAM multiplexed "free-space classical" optical communications as the basic default system, and separate subsections will be dedicated to the topics that deviate from this system (e.g., quantum, radio frequencies, or fiber). The intent of this article is to give a flavor of the advances as well as the growing interest in this field. To explore more about this, see the references at the end.
OAM multiplexing has the potential to increase the total transmission rates in optical communication systems due to its ability to multiplex and simultaneously transmit multiple data-carrying channels on different OAM beams. As each OAM beam carrying an independent data stream co-propagates with other OAM beams, the spectral efficiency of the system (i.e., bits/s/Hz) scales with the number of OAM beams utilized for multiplexing. As such, OAM beams can be carried on both orthogonal polarizations, and polarizationdivision multiplexing (PDM) can also be applied to further double the spectral efficiency of the system. The first use of OAM multiplexing for MDM communication links resulted in an FSO link that multiplexed four different OAM modes on two polarizations, with an aggregated data rate of 1.37 Tbit/s. 7 As shown in Fig. 3, on one polarization, four Gaussian beams carrying independent data channels (Data1, Data3, Data5, and Data7) were transformed into four OAM modes (OAM1, OAM2, OAM3, and OAM4) by adding different phase patterns. Conjugated phase patterns were used at the receiver to convert the OAM-carrying beams back into Gaussian beams. By utilizing PDM, four additional data channels (Data2, Data4, Data6, and Data8) were multiplexed and carried by the same OAM modes (OAM1, OAM2, OAM3, and OAM4) on the other polarization, resulting in eight independent data channels on the same wavelength. This increased the spectral efficiency of the system eightfold.
Moreover, WDM can be utilized to further increase the capacity of OAM multiplexed FSO links. The concept of combining OAMmultiplexing, PDM, and WDM for capacity enhancement is presented in Fig on a single frequency and polarization. 9,10 One demonstration of such a system combined 12 OAM modes, two polarizations, and 42 wavelengths, resulting in a total of 1008 data channels each carrying 100-Gbit/s data, to achieve an aggregated rate of 100.8 Tbit/s in the laboratory. 9 Figure 4(d) shows the observed optical spectrum of a single OAM beam (l = +10) that carries the WDM signals. 9 Another work reported a demonstration of 26-OAM mode-multiplexing over 368 WDM and polarization-multiplexed with an aggregate data rate of 1.036 Pbit/s. 10 The experimental demonstrations of OAM-multiplexed communication links in the laboratory were generally conducted over short distances of ∼1 m. In recent years, there have been several experiments that investigated the potential of using OAM beams to achieve long-distance FSO links in the field environment: [13][14][15] (i) A 120-m FSO communication link with a 400-Gbit/s data rate based on four-OAM multiplexing; each OAM beam carries 100-Gbit/s quadrature phase-shift keying (QPSK) modulated data channels. 13 (ii) A 260-m FSO data transmission link between two buildings using OAM multiplexing and 16-quadrature-amplitudemodulation (16-QAM) signals with an 80-Gbit/s aggregated bit rate. 14 The expansion of an OAM-based link over much longer distances might give rise to several challenges, including the divergence of the OAM beams, system pointing and misalignment, and atmospheric turbulence effects. Significant efforts have been made to achieve such links over longer distances. An FSO link based on the OAM encoding scheme was demonstrated over a distance of ∼143 km between two islands. 15 An OAM-based encoding scheme can be achieved by sequentially transmitting different OAM beams, each representing a data symbol, within each time slot. Compared to a binary signal, which has two possible data bit values of "0" and "1," an M-ary OAM encoding signal may have many values ranging from "0" to "M -1." The number of data bits per unit time can reach log 2 M, and thus, the data capacity in each channel can be increased. Figure 5(a) shows the link layout for sending and receiving the OAM modes in the above-mentioned 143-km link. 15 The observed patterns of four different OAM mode superpositions are shown in Figs. 5(b)-5(e). Under the relatively weak turbulence, the lobed modal structure was visible for mode superpositions with l = {−1, +1}, {−2, +2}, or {−3, +3}. In order to recover the encoded data, an artificial neural network-based pattern recognition algorithm was used to distinguish images of different OAM mode superpositions. The received mode superpositions could be identified with an accuracy of >80% up to OAM mode order l = 3, and the decoded message had an error rate of 8.33%. The results indicate that the freespace transmission of OAM modes over a 100-km-scale distance is feasible.

B. Two-dimensional modal basis sets
Although there has been significant interest in OAM as a modal basis set for MDM communications, what is the rationale for choosing OAM over other types of modes? On a fundamental level, MDM requires that you can efficiently combine and separate different modes, so almost any complete orthogonal basis set could work. Indeed, many different types of modes were demonstrated in freespace and fiber, including Hermite-Gaussian (HG), LG, and linearly polarized (LP) modes. 5,7,[16][17][18][19][20] In discussions with Boyd and Padgett, 21 two practical issues seemed to emerge as reasons that one "might" prefer OAM modes (as a subset of LG modes) to other modal basis sets: (i) OAM modes are round, and free-space optical components are readily available in round form. (ii) It is important to maintain interchannel orthogonality and minimize crosstalk. This can be accomplished by fully capturing the specific parameter that defines the modal orthogonality. For a case in which different channels can be defined by different OAM l values, the channel and mode can be fully determined by azimuthally capturing a full 360 ○ circle no matter the size of the round aperture. 22,23 Structured beams from a modal basis set can generally be described by two modal indices such that the beam can be fully described by these coordinates. For example, LG modes have l  (azimuthal) and p (radial) components, whereas HG beams have n (horizontal) and m (vertical) components. OAM modes are a subset of a full LG modal basis set, which can be characterized by two indices: the radial index p and the azimuthal index l, as shown in Fig. 6. The electrical field of an LG beam can be represented by 2,18 LG ℓ,p (r, ϕ, l, p, where ω 0 is the beam waist, LP |l| p is the generated Laguerre polynomials, and (r, ϕ) is the cylindrical coordinate. However, the vast majority of publications on MDM-based FSO communications FIG. 6. Intensity and phase profiles of LG beams with non-zero radial index p and azimuthal index l. The values of p + 1 and l represent the number of rings in the intensity profile for the non-zero l value and the number of 2π phase changes along the azimuthal direction in the phase profile.
LG beams with different pairs of indices (l, p) are orthogonal to each other. 24  utilized only a change in a single modal index. Specifically, each beam commonly had a different l value but the same p = 0 value. 7,8,10,13,15,25 LG beams with different p values can also be utilized in MDM FSO links. For example, there has been an experimental demonstration of a 200-Gbit/s MDM link based on the multiplexing of LG modes with the same l value but different p values. 18 It should be noted that these works utilized one-dimensional modal basis sets, which means that they only varied one of the two modal indices (l, p). While this one-dimensional system can accommodate many orthogonal beams, a system designer could also use the other beam modal index in order to possibly achieve a larger twodimensional set of data channels. This two-dimensional approach was shown experimentally for LG and HG beams. 17,18 It is important to note that a significant challenge is the sufficient capture of the beam at the receiver aperture to ensure accurate phase recovery and orthogonality along both indices. 18 Theoretically, LG beams with different pairs of indices (l, p) are orthogonal to each other. Therefore, extending the one-dimensional modal basis sets (e.g., LG beams with only l or p index changing) to two-dimensional ones (e.g., LG beams with both l and p indices changing) could provide a larger two-dimensional modal space for orthogonal data-carrying channels and increase the transmission capacity of a communication link. A fourfold multiplexing of LG modes was experimentally demonstrated to achieve a 400-Gbit/s communication link. 17 In this experiment, a twodimensional LG modal set was used and both modal indices (l, p) were varied. In addition, four HG modes were utilized to achieve such a four-channel MDM link [ Fig. 7(a)], and the effects of aperture size as well as lateral and rotational misalignments on the crosstalk performance were also investigated. 17 Due to different symmetric properties of LG modes and HG modes, they might present different crosstalk performances under different misalignments in the MDM link. It was found that (1) a limited-size aperture at the receiver causes power loss for both LG and HG beams, (2) a lateral misalignment between the transmitter and receiver causes crosstalk for LG beams, while HG beams with a zero m or n index are more tolerant to lateral misalignment due to the axial symmetry, and (3) a rotational misalignment causes crosstalk for HG beams but does not tend to influence LG modes due to their circular symmetry, as shown in Fig. 7(b).

III. BASIC CHALLENGES AND EFFECTS FOR OAM-BASED MDM COMMUNICATION SYSTEM
A key issue in almost any MDM communication system is dealing with intermodal power coupling and deleterious inter-datachannel crosstalk. There are many causes of modal coupling and crosstalk, including the following for OAM-multiplexed FSO communication links, as shown in Fig. 8: (a) Turbulence: atmospheric turbulence can cause a phase distortion at different cross-sectional locations of a propagating beam. Given this phase change distribution in a changing environment, power can couple from the intended mode into others dynamically (e.g., perhaps changes of the order of milliseconds). 26-29 (b) Misalignment: misalignment between the transmitter and receiver means that the receiver aperture is not coaxial with the incoming OAM beams. In order to operate an OAMmultiplexed link, one needs to know which modes are being transmitted. A receiver aperture that captures power around the center of the beam will recover the full azimuthal phase change and know which l mode was transmitted. However, a limited-size receiver aperture that is off-axis will not recover the full phase change and inadvertently "thinks" that some power resides in other l and/or p modes. 30 (c) Divergence: FSO beams of higher OAM orders diverge faster than lower-order OAM beams, thus making it difficult to fully capture the higher-order OAM beams with a limited-sized receiver aperture. Power loss occurs if the beam power is not fully captured, but even modal coupling can occur due to the truncation of the beam's radial profile. This truncation can result in power being coupled to some other LG beams with different p values (p modes). 30 log-polar-based mode sorter that geometrically transforms the spiral spatial phase of OAM beams into a tilted spatial phase, 35,36 and (c) designing refractive index distribution of the fiber designed to achieve in-fiber mode conversion from the fundamental mode to the vector mode. 37 It should also be mentioned that (i) modal coupling "tends" to be higher to the adjacent modes and (ii) separating data channels with a larger modal differential can help in alleviating the problem. 28,38,39 Of course, larger modal separation leads to larger beam divergence, so a trade-off analysis is usually recommended.

A. Atmospheric turbulence
Atmospheric turbulence is one important challenge that needs to be considered for an OAM-multiplexed FSO communication system. Inhomogeneities in the temperature and pressure of the atmosphere can lead to variations in the refractive index along the transmission path. 27,40 As in an OAM-multiplexed link, the orthogonality among multiple co-propagating OAM beams depends on their helical phase front, turbulence-induced refractive index inhomogeneities can cause intermodal crosstalk between different data channels with different OAM orders, as they can easily distort the phase front of OAM beams [ Fig. 9(a)]. 28,41,42 The effects of atmospheric turbulence on the performance of OAM-multiplexed systems have been experimentally evaluated in the laboratory in several ways. [27][28][29] One example of the emulation of atmospheric effects in the laboratory is shown in Fig. 9(a), which presents the concept of using a rotating phase plate to emulate the turbulence effects. The phase screen plate is mounted on a rotating stage and placed in the optical path of the beams. On the rotating plate, the pseudorandom phase distribution obeys Kolmogorov spectrum statistics. 28 The strength of the emulated turbulence effect generally depends on the Fried parameter r 0 and the beam size that is incident on the plate. In order to evaluate the turbulence effects, the modal crosstalk is characterized by measuring the power of the distorted beam in each OAM mode. Figure 9(b) presents the normalized power distribution among the neighboring OAM modes under weak and strong turbulences for an OAM +3 transmitted beam. It is shown that under the weak turbulence, the majority of the power is still in the transmitted OAM mode (i.e., OAM +3), and only a small part of the power is coupled to other neighboring OAM modes.

PERSPECTIVE scitation.org/journal/app
However, as the turbulence strength increases, the power coupling into other OAM modes becomes higher, which could induce severe signal fading and crosstalk.

B. Misalignment
The efficient multiplexing and de-multiplexing of OAM beams requires coaxial propagation and reception of the transmitted modes. Unlike the case of using Gaussian beams, any misalignment between the transmitter and receiver apertures or only partial collection of the OAM beams at the receiver would result not only in power loss but also, more severely, in interchannel crosstalk (i.e., power coupled to other modes). In an ideal OAM multiplexed communication link, the transmitter and receiver would be perfectly aligned [i.e., the center of the receiver would overlap the center of the transmitted beam, and the receiver plane would be perpendicular to the line connecting their centers, as shown in Fig. 10(a)]. However, due to jitter and vibration of the transmitter/receiver platform, the transmitter and receiver may have relative lateral shift (i.e., lateral displacement) or angular shift (i.e., receiver angular error), as depicted in Figs. 10(b) and 10(c), respectively. Both types of misalignment may lead to the degradation of system performance.
Figures 10(d) and 10(e) illustrate the effect of the lateral displacement and receiver angular error when only OAM +3 is transmitted with a beam diameter of 3 cm. 30 Given a fixed link distance of 100 m, the power coupling into other modes increases with an increase in the lateral displacement or receiver angular error, whereas the power on OAM +3 (i.e., the transmitted mode) decreases. This is because a larger lateral/angular displacement causes a larger mismatch between the received OAM beams and the receiver. The power coupled to OAM +2 and OAM +4 is greater than that of OAM +1 and OAM +5 due to their smaller mode spacing from OAM +3. This indicates that a system with larger mode spacing is more tolerant to the lateral displacement.

C. Beam divergence
For a communication link, it is preferable to collect as much signal power as possible at the receiver to ensure a sufficient signalto-noise ratio (SNR). Based on diffraction theory, a light beam diverges while propagating in free space. Since optical elements usually have limited-size apertures, the diverged beam might be too large to be fully collected, resulting in signal power loss. For an OAM-multiplexed link, the transmitted beams with higher OAM orders diverge faster than lower-order OAM beams. This makes it difficult to fully capture them with a limited-size receiver aperture, which leads to signal power loss. Moreover, a limited-size receiver aperture can also degrade the orthogonality between p modes, [30][31][32]43 as shown in Fig. 11. Truncation might occur in the beam's radial profile, and this could potentially induce a modal coupling from the desired mode to some other LG beams with different p values (p modes). 31,43 For an MDM link using LG modes with different p values, this modal coupling might cause channel crosstalk. The divergence effect of an LG beam mainly depends on the frequency, transmission distance, beam waist at the transmitter, and mode indices. Therefore, in order to reduce the signal power loss and channel crosstalk, the key parameters related to the beam divergence need to be carefully considered when designing an OAM-based link.

IV. ADVANCES IN CROSSTALK MITIGATION FOR OAM-MULTIPLEXED COMMUNICATION LINKS
Crosstalk mitigation is one of the key challenges for OAM multiplexed communications. Various optical and digital techniques The concept of circular aperture truncation effects to OAM-carrying beams due to OAM beam divergence and limited-size receiver aperture. OAM l = 3 mode (i.e., LG l = 3, p = 0 mode) is shown as an example: the beam diverges during propagation, and the radial beam profile is distorted at the receiver side due to the circular truncation, which induces a modal coupling from the transmitted mode to some other LG modes with different higher order p values.
have been proposed for crosstalk mitigation in OAM-multiplexed links, as shown in Fig. 12. Conventional approaches for crosstalk mitigation include the following: (i) Adaptive optics (AO): AO, such as by using digital micromirrors, spatial light modulators (SLMs), or multi-plane-light converters (MPLCs), can mitigate modal crosstalk. 34,[44][45][46] For example, if atmospheric turbulence causes a certain phase distortion on an optical beam, an SLM at the receiver can induce an inverse phase function to partially undo the effects of turbulence. 45 Typically, there could be a feedback loop such that a data or probe beam is being monitored for dynamic changes and the new phase function is fed to an SLM, as shown in Fig. 13(a1). With the usage of the AO system, the distorted OAM beams can be efficiently compensated, as shown in Figs. 13(a2) and 13(a3). (ii) Electrical digital signal processing (DSP): crosstalk due to modal coupling has many similarities to crosstalk that occurs in multiple-transmitter-multiple-receiver (i.e., multiple-input multiple-output, MIMO) radio systems, 47,48 as shown in Fig. 13(b1). Multiple optical modes are similar to parallel radio frequency (RF) beams that experience crosstalk. Similar to electronic DSP that can undo much of the crosstalk in MIMO RF systems, these DSP approaches could also be used for mitigating OAM modal crosstalk. 49 With MIMO equalization, the error vector magnitude (EVM) of the four channels can be improved, as shown in Figs. 13(b2) and 13(b3). The EVM is a parameter that could quantify the performance of a communication system, and a lower EVM value indicates a better signal quality.
In the conventional receiving system for an OAM multiplexed link, mitigating OAM crosstalk and channel demultiplexing are typically achieved separately. 33,45 As mentioned above, AO and DSP can be applied to mitigate crosstalk. Additionally, MPLC has been demonstrated as a scalable and reconfigurable mode demultiplexer. 33,34 It might be desirable to mitigate crosstalk and demultiplex channels simultaneously. Recently, it was shown that the wavefront-shaping-and-diffusing method could simultaneously mitigate turbulence and demultiplex channels, but this approach involves some power loss. [50][51][52] Another approach is to use an MPLC to mitigate crosstalk and demultiplex channels, and this method theoretically has no inherent power loss. 53,54 Such an approach was demonstrated experimentally using a single MPLC to simultaneously mitigate the turbulence-induced crosstalk and demultiplex two channels carried by OAM modes. 54 As shown in Fig. 14(a), input coaxial OAM beams having different mode orders are converted to Gaussian beams at different output positions using the cascaded phase patterns calculated by the wavefront-matching method. 33,34 To mitigate turbulence-induced crosstalk, the patterns are updated by combining the genetic algorithm with the wavefront matching method. Figure 14(b) shows the measured crosstalk matrix without FIG. 12. Different crosstalk mitigation approaches for an OAM-multiplexed FSO link. An extra beacon beam or the transmitted data-carrying modes can be used as a probing channel to characterize the distortion from the turbulent media. Reports have shown various approaches for crosstalk mitigation: Optical approaches (e.g., AO, combinations of modes, and MPLC-based method) have been utilized to mitigate crosstalk at the transmitter and/or receiver, while MIMO method has been utilized to mitigate crosstalk at the receiver in the electrical domain. Besides an increasing array of potential methods for crosstalk mitigation in OAM-based links, advanced technologies including the artificial neural network-based pattern recognition algorithm 15 are also considered. As with most issues, cost and complexity will play a key role in determining which, if any, mitigating approach should be used. In this section, we will discuss the recent advances in crosstalk mitigation approaches for OAM-multiplexed FSO communications, as shown in Fig. 15. Specifically, we will mainly discuss approaches based on transmitting the coherent combination of multiple OAM modes at the transmitter for turbulence mitigation.

A. Mode-combination-based mitigation
Aside from the conventional crosstalk mitigation approaches, it would be beneficial to develop an alternative approach that (a) only needs in-fiber power measurement instead of using wavefront sensors to measure the spatial amplitude and phase profile of the optical beams and (b) can mitigate the crosstalk from other data channels without recovering all the data channels at the receiver. Recently, multiple optical approaches have been developed to address these issues. 43,[55][56][57][58] These approaches are based on the transmission or detection of a combination of multiple spatial modes. The steps to achieve this include (i) measuring the complex transmission matrix of the imperfect MDM links using the modal power distribution, (ii) calculating the phase patterns to generate/detect different combinations of multiple modes based on the measured transmission matrix, and (iii) applying the phase patterns to mitigate the crosstalk. 43,55 This method is feasible because a structured beam can be decomposed into a set of LG modes that carry OAM, as shown in Fig. 16. The coefficient of each LG mode in the decomposition can be complex, containing both amplitude and phase information. Therefore, one can control the amplitude and phase shift for each LG mode and coherently combine all modes to generate a structured beam that performs the desired function.
An optical turbulence mitigation approach based on mode combination has been recently demonstrated. 55 The experimental results for 200-Gbit/s two-OAM-multiplexed links showed that the inter-channel crosstalk could be reduced by >10 dB. The concept of turbulence compensation using mode combination is illustrated in Fig. 17(a). At the transmitter side, the inverse transmission matrix is applied using a compensation phase pattern at the transmitter for each channel, which results in the signal from each transmitted channel being carried by the combination of multiple (e.g., 2) OAM modes with designed complex weights. The weights are calculated based on the inverse of the complex transmission matrix under the corresponding turbulence realization, and such combinations of OAM modes could perform the inverse function of turbulence-induced crosstalk. When the beams from the two channels are transmitted through the turbulence, the signals on the two transmitted modes will couple to their neighboring modes and experience coherent interference on those modes. Therefore, the channels could have little power on the designated modes due to their destructive interference and relatively high power on the others. By receiving the mode on which the undesired channel has little power, the desired channel can be recovered with little inter-channel crosstalk. The same concept can be applied to recover the second channel when receiving another mode. As an example, the compensation phase patterns used for beam generation in channel A and the intensity profiles of the generated beams are shown in Fig. 17(b). FIG. 16. The concept of the LG mode decomposition and the complex LG spectrum. A structured beam can be decomposed into a set of LG modes that carry OAM. The complex coefficient, i.e., each element of the complex LG spectrum, can be calculated using the overlapped integral between the electric fields of the structured beam and each LG mode. We can control the amplitude (A) and phase shift (θ) for each LG mode and coherently combine all modes to generate a structured beam. This approach was demonstrated for two-OAM (l = +1 and l = +2) multiplexed channels each carrying a 100-Gbit/s QPSK signal. 55 When the compensation approach was applied, the transmitted channels A and B carried beams α and β, respectively, which were combinations of OAM l = +1 and l = +2. The receivers for channels A and B recovered the signals on OAM modes l = +1 and l = +2, respectively. The results of this demonstration are shown in Fig. 18. The back-to-back case is illustrated in Fig. 18(a1). As shown in Fig. 18(a2), with the turbulence effect, the inter-channel crosstalk increases to −8.7 dB and −5.5 dB for channels A and B, respectively, in the absence of the compensation, and this crosstalk decreases to −22.1 dB and −17.8 dB for the two channels with the compensation. The bit error rate (BER) performance for the channels is shown in Fig. 18(b). By applying pre-compensation phase patterns in the link, the BER performance can be improved. These results indicate that transmitting a combination of multiple OAM modes with designed mode weights instead of a single OAM mode could improve the performance of an OAM-multiplexed link by reducing the crosstalk.
In addition, the mode-combination-based approach was also utilized to mitigate the effect of the limited-size aperture or a misalignment in an MDM link. 43 This can be achieved by transmitting each data channel on a combination of multiple LG modes, as shown in Fig. 19(a). The complex transmission matrix H of the link can  Fig. 19(b)]. Besides the orthogonalization, intensity profiles of the transmitted beams would also be spatially shaped, which might simultaneously reduce the power loss caused by the limited-size aperture or the misalignment.
The above approach was experimentally demonstrated in a four-channel multiplexed link with each channel carrying a 100-Gbit/s QPSK signal. 43 The results for crosstalk mitigation under horizontal displacements are shown in Fig. 20 as examples. Figure 20(a) presents that when transmitting data channels on pure LG modes with different p values (LG 10 , LG 11 ), the crosstalk becomes larger with an increase in the horizontal displacement. However, when using the orthogonal beams (beams 1 and 2) that are generated by using designed complex combinations of LG 10 and LG 11 modes, the crosstalk for both channels could be <−27 dB with the displacement. Figure 20(b) shows the case of LG modes with different l values (LG 10 , LG −10 ) under various displacements. The crosstalk of (LG 10 , or LG −10 ) increases with the displacement, but for the designed orthogonal beams (composed of LG 10 and LG −10 ), it could stay at a relatively low level (<−17 dB) in association with the displacement for both channels. These results indicate that by simultaneously

PERSPECTIVE
scitation.org/journal/app transmitting and receiving orthogonal beams that are composed of multiple LG modes, the performance of an LG-multiplexed link can be potentially improved.

V. OAM MULTIPLEXING FOR FSO AIRBORNE COMMUNICATIONS
The communication capacity needs of manned and unmanned aerial platforms have been increasing dramatically over the past several years, thereby driving the need for higher-capacity links between these platforms and their ground stations. [59][60][61][62] OAM multiplexing techniques may be utilized to increase the data capacity and spectral efficiency and to reduce the probability of interception in FSO airborne communications.

A. Challenges for OAM multiplexing for FSO airborne communications
As shown in Fig. 21, there are several scenarios in airborne and satellite FSO communications that require distinct applications and pose specific challenges including (i) Satellite-to-satellite links usually require ultra-long-distance beam propagation (>1000 km) and careful control over the laser beam divergence. In such a scenario, high sensitivity of the receiver detector is desirable since only a limited proportion of the transmitted beam can reach the receiver. 63 Ultralong links might also necessitate extremely large apertures due to the increased beam divergence of higher order modes. 63 (ii) Satellite-to-ground-station links generally utilize a laser beam to propagate through the Earth's atmosphere and the accumulated atmospheric turbulence effects would induce severe distortion on the wavefront of the optical beam. 63 (iii) Airplane-to-ground links involve a fast-moving airplane at a distance range of ∼1 km-100 km. Both the optical beam pointing/tracking and atmospheric turbulence effects are challenges in this scenario. 64 (iv) UAV-to-ground-station communications: a relatively slowmoving unmanned-aerial-vehicle (UAV) is hovering at a distance of <kilometer away from the ground station. UAVs have drawn a lot of attention over the recent years due to their potential for proliferating numerous applications. 59,[65][66][67] In UAV-to-ground-station communications, distances may be relatively short range and a key challenge is to miniaturize the optical hardware.
In addition, these free-space applications share some common desirable characteristics, including (1) low size, weight, and power (SWaP), which can be alleviated by advances in integrated OAM devices, 68 and (2) accurate pointing, acquisition, and tracking (PAT) systems, which help limit modal coupling and crosstalk. 30

B. OAM-multiplexed communication links to and from UAV platforms
One example of the aerial platforms is the UAV, such as flying drones that are proliferating for numerous applications. 59,[65][66][67][69][70][71] As the first example of OAM-multiplexed FSO airborne communications, an 80-Gbit/s OAM-multiplexed FSO link between a flying drone and a ground station was demonstrated. 59 As shown in Fig. 22, the ground station contained an OAM transmitter, an OAM receiver, and a beam tracking system. A retroreflector carried by the UAV was flown up to ∼50 m away (i.e., ∼100 m round trip) from the ground station to efficiently reflect the OAM beams that were emitted from the transmitter back to the receiver with little distortion.
As one example of misalignment issues, the effects of beam jitter on the system performance for OAM-multiplexed UAV platforms were evaluated. 59 In order to evaluate the effects of beam jitter, the statistics of the received beam centroid were measured. Figure 24 shows the relative positions of the beam when the UAV hovers in the air ∼50 m relative to the ground station and ∼10 m above the ground with the tracking system on Fig. 23(a) and moves horizontally in the air at a speed of ∼0.1 m/s with the tracking system on Fig. 23(b), respectively. The OAM ℓ = +3 beam was transmitted. The statistics of each scenario were obtained by continuously capturing 1000 intensity profiles of the beam over a 120-s period using an infrared camera. The beam jitter variance was ∼0.09 mm 2 when the UAV was hovering and increased to ∼0.46 mm 2 when moving, respectively.

C. MIMO for OAM-multiplexed UAV platforms under atmospheric turbulence effects
The atmospheric turbulence might not degrade much the performance of OAM-multiplexed UAV platforms under a clean weather condition and over a short distance. However, the effects of atmospheric turbulence would be more significant as transmission distances increase and weather conditions become worse. Due to the stronger distortion induced by the atmospheric turbulence, the received signal carried on a particular OAM mode may include larger power of signals leaked from other channels.
To mitigate atmospheric turbulence in UAV platforms, the MIMO equalization algorithm has been demonstrated to compensate for the inter-channel crosstalk. 71 A rotatable phase plate with a pseudo-random phase distribution was added to the 100-m UAV-to-ground link (the link presented in Fig. 22) to emulate the atmospheric turbulence. A 4 × 4 adaptive MIMO equalizer was implemented in a four-channel OAM multiplexed link and each channel carried 20-Gbit/s QPSK data. Figure 24(a) illustrates the measured 20-Gbit/s QPSK constellation diagrams and corresponding EVMs for the OAM l = +3 and l = −1 beams without and with the MIMO equalization. The MIMO equalization reduced the EVM from 32% to 54%-26% and 27% for the OAM l = +3 and l = −1 beams, respectively. Figure 24(b) shows BERs for both channels as functions of the transmitted power when the UAV was hovering with the phase plate fixed at a random angle. The experimental results indicate that MIMO equalization can help mitigate the crosstalk caused by turbulence and improve both the EVM and the BER of the signal in an OAM-multiplexed link for flying platforms.

D. OAM beams for optical beam tracking
Beam tracking is considered important for a single-beam non-OAM FSO link, where misalignment between the transmitter and the receiver leads to an increase in power loss and BER. 69,72 For OAM-multiplexed UAV platforms, beam tracking might be even more important. 59 This is because the misalignment issue not only causes power loss but also power coupling among different OAM modes, thereby increasing the inter-channel crosstalk and BER.
To maintain the precise alignment between the transmitter and the receiver, a pointing, acquisition, and tracking (PAT) system is typically used in UAV platforms. 59 Beam tracking was demonstrated in single-beam non-OAM FSO links with or without using a probe beam at a separate wavelength. 69,72 Later on, beam tracking was also demonstrated in OAMmultiplexed FSO links using a Gaussian beacon. Such beam tracking systems typically utilize the displacement of the fundamental Gaussian beam as an error signal and utilize a fast-steering mirror (FSM) to correct the misalignment. As illustrated in Figs. 25(a) and 25(b), it has been proposed to use spatial gradient of an OAM beam as the error signal for beam tracking. 73 As presented in Fig. 25(c), when there is a displacement between the transmitter and receiver, the spatial gradient of an OAM beam can indicate the amount of displacement. Moreover, due to the unique phase and amplitude structure of an OAM beam, the spatial gradient of the OAM beams could potentially provide a low tracking error.

VI. OAM MULTIPLEXING IN UNDERWATER ENVIRONMENT
There is a growing interest in high-capacity underwater wireless communication systems for supporting the significant increase in the demand for data, such as from sensor networks, unmanned underwater vehicles, and submarines. 74 Traditionally, acoustic waves have been used for underwater communications, but this technique has quite limited bandwidth capacity. 75 Alternatively, communication using optical frequencies in the low-attenuation blue-green region can enable higher-capacity underwater transmission links due to the much higher carrier-wave frequency. 76

A. Propagation effects in underwater environment
Blue-green light exhibits relatively low absorption in water, thereby potentially enabling high-capacity links with a distance of ∼100 m. 76 Note that radio waves simply do not propagate well underwater, and common underwater acoustic links have a very low bit rate. As shown in Fig. 26, maritime and underwater environments pose various challenges, including loss, turbidity, scattering, currents, and turbulence. An interesting challenge is transmitting from above the water to below the water such that the structured optical beam would pass through inhomogeneous media surrounding the interface, including nonuniform aerosols above water, the dynamically changing geometry of the air-water interface, and bubbles/surf below the surface. [77][78][79][80][81][82] There were several reports of propagation of OAM beams through turbid media that include water current and particle scattering effects. 77,78 For example, Fig. 27(a) shows the distorted intensity profiles of OAM beams affected by different environmental effects. 78 The effects of water current, scattering, and turbulence were FIG. 26. Challenges in different scenarios for underwater FSO links. Environmental effects including turbulence (e.g., from water currents), scattering (e.g., from a turbid medium), and power loss due to water absorption are stronger than those in atmospheric environment. In addition, transmitting data from above the water to below the water could be an interesting challenge: the structured optical beam may pass through the inhomogeneous media surrounding the interface, including nonuniform aerosols above water, the dynamically changing geometry of the air-water interface, and bubbles/surf below the surface. emulated by using circulation pumps, adding Maalox solution to water, and creating a thermal gradient by mixing cold/hot water. When OAM beams of l = +1 and +3 and a Gaussian beam were transmitted one at a time, the following were observed: (i) In tap water: the ring-shaped intensity profiles of the OAM beams tend to be maintained after ∼1-m propagation and are slightly distorted by the water current. 78 (ii) With scattering: there was a small time-varying change in the intensity profiles, which might be a result of the natural dynamic diffusive movement of the small particles contained in the water. 78 (iii) With water current or turbulence: phase distortion became stronger such that the phase front of the OAM beam was distorted. 78 Besides the transmission of a single vortex beam, another work explored the utilization of spatial profiles generated by the coherent combination of multiple concentric optical vortices in the underwater environment. 74 This approach provides an alternative way for utilizing OAM modes in the underwater environment. The intensity profiles of the combinations of concentric optical vortices are presented in Fig. 27(b). Due to the interference between concentric vortices, the resulting beam has a periodic constructive and destructive interference around the center of the beam, i.e., a "petal" pattern. The results show that the "petal" pattern experiences little distortion when the beams propagate through clear water. However, after propagating through turbid water, the intensity profiles of the beams are distorted due to the scattering effects.

B. OAM-multiplexed links in underwater environment
In the previous session, we describe propagation effects of OAM-carrying beams in underwater environment. We will present examples of OAM-multiplexed communication links in the underwater environment considering the above-discussed effects in this session. For underwater environments, there have been several reports on blue-green light non-OAM links with a single-beam and a distance of ∼100 m. 76 To further increase the data capacity in underwater environment, blue-green light OAM-multiplexed links were demonstrated over a few meters in an emulated underwater environment. 77,78,82 A direct way to modulate a blue-green light is to use an internal modulation. For example, by directly modulating the driving current of a 520 nm laser diode, a 1-Gbit/s signal was produced. 78 However, due to the limited bandwidth of the internal modulation of the commercially available laser diodes, the maximal data rate of the green beam was ∼1 Gbit/s. To achieve larger data rates in underwater environment, a high-speed modulated light at a lower frequency can be wavelength converted to blue-green light by second harmonic generation. For example, by using a 10-Gbit/s 1064-nm lithium niobite modulator and a frequency-doubling module, a 10-Gbit/s signal was generated, and the carrier wavelength was converted from 1064 nm to 532 nm. 78 Figure 28 presents the average BER of the channels on the OAM +1 and +3 beams with and without equalization, with each OAM beams carrying a 10-Gbit/s on-off keying signal. 78 To mitigate the thermal-gradient-induced crosstalk in water, the constant modulus algorithm (CMA) equalization is implemented in the DSP.

PERSPECTIVE scitation.org/journal/app
The measured BERs were averaged over 1 min of data for two OAM channels (ℓ = + 1 and +3) before and after applying the CMA equalization. Due to inter-channel crosstalk, the measured BER curves without 2 × 2 equalization reached a BER error floor. With the CMA equalization, the BER performance is improved and could reach below the forward error correction (FEC) limit. 78 We note that the FEC limit is a BER upper limit under which the FEC method can be performed when coding the channel that can control the errors over unreliable or noisy communication channels.

VII. NOVEL BEAMS
This section is for the completeness of this review paper besides the discussions for free-space communications. The excitement in the field of novel beams originated by the ability to utilize orthogonal structured optical beams. However, there is much work in the fields of optics and photonics on several types of novel variations of optical beams (e.g., Airy and Bessel types), with more being explored at an exciting pace.
Over the next several years, it would not be surprising if novel beams are used to minimize certain system degrading effects. There have been initial results for some of these concepts, but a partial "wish list" for novel beams could be beams (i) that are more resilient to the modal coupling caused by turbulence and turbidity, (ii) that have limited divergence in free space, (iii) that are resilient to partial obstruction such that their phase structure can "self-heal" (e.g., Bessel-type beams), and (iv) whose phase structure can readily be recovered even if the transmitter and receiver are misaligned.
Generally, FSO communication links rely on the line-of-sight (LOS) operation, and thus, the obstructions in the beam path are one of the potential challenges. In particular, for OAM communication links that are partially blocked, an OAM beam will produce distortions in its beam profile. This will reduce the orthogonality between the different OAM beams and cause power coupling from the desired OAM mode to neighboring OAM modes, thereby leading to signal fading and channel crosstalk. As one example, Bessel-Gaussian (BG) beams have displayed the unique property to reconstruct or "self-heal" the transverse intensity and phase profiles after experiencing an obstruction. The self-healing property of BG beams is due to the delocalized transport of the beam energy and momentum, which can replace the scattered light by the obstructions. 83 As another example of novel beams, the Airy beam has unique properties, including being non-diffracting, self-bending, and self-healing. 84 Due to its curved parabolic trajectory, the Airy beam has been demonstrated to be able to circumvent obstacles in an FSO interconnection link. [85][86][87] As one example of approximations to true Bessel beams, BG beams are non-diffractive and self-healing over a limited Besselrange. The self-healing property of the BG beams was utilized to mitigate the degrading effect due to obstruction in short-range FSO OAM communication links. 88 As shown in Fig. 29(a), N OAM beams, each carrying a distinct data channel, are spatially multiplexed and transmitted through an axicon to be transformed into BG beams. Within the Bessel region, the beams are propagation invariant and, therefore, can sustain partial obstructions. At the end of the Bessel region, an exit axicon that has opposite cone angles is placed to remove the conical phases. Finally, an OAM mode demultiplexer separates each OAM beam. In the experiment, two OAM-multiplexed channels (OAM l = +1 and l = +3) each carrying 100-Gbit/s QPSK signals were transmitted through a path with obstructions. 88 As an example, the transverse intensity profiles of the obstructed and unobstructed BG beam with l = +3 are presented in Fig. 29(b). An obstruction was placed at the beam center, and images of the transverse intensity profiles were taken at various locations along the propagation direction. A comparison between the obstructed and unobstructed beams in the plane of the demultiplexer revealed the self-healing property of the BG beam. Figure 29(c) illustrates the BER measurement for the unobstructed and obstructed BG beams. Both channels achieve BERs below the FEC limit.

VIII. UTILIZING OAM IN QUANTUM SYSTEMS
In the case of a quantum communication system, an individual photon can carry one of many different OAM values; this is similar to digital data taking on one of many different amplitude values and enables OAM-based encoding in quantum systems. If each photon can be encoded with a specific OAM value from M possibilities, the photon efficiency in bits/photon can be increased. This has the potential to be quite useful for quantum communication systems, which are typically photon "starved" and for which qubits can commonly be encoded on one of the only two orthogonal polarization states. [89][90][91][92][93] Figure 30 presents the concept of the OAM-based quantum encoding. Using an OAM mode converter, within each symbol period, the coming single Gaussian photon is converted to the respective OAM photon and occupies one of the M OAM states. Each photon has a helical phase front after being processed by the OAM converter. The accumulated intensity structure indicates that it has a ring-like intensity probability distribution. 89 A larger alphabet for each qubit is, in general, highly desirable for enhancing the system performance. However, there is much research needed to overcome the challenges in fielding an OAMencoded quantum communication system, such as (i) mitigating coupling among orthogonal states and (ii) developing transmitters that can be tuned rapidly to encode each photon on one of many modes.

A. AO for quantum OAM encoding systems
Similar to OAM based classical FSO communication links, the system performance degradation due to the atmospheric turbulence is a key challenge also for OAM-based quantum FSO links. Turbulence affects the phase front of the photon and thereby increases the intermodal crosstalk in the quantum communication system.
In order to mitigate the turbulence effect, the AO approach can be applied to OAM-encoded quantum communication links by using a classical Gaussian probe beam (i.e., OAM ℓ = 0) for the phase detection on a wavefront sensor. As shown in Fig. 31, the AO approach was demonstrated for the compensation of emulated turbulence in an OAM-encoded FSO quantum communication link at a transmitted rate of 10 Mbit/s. 92 The quantum channel and the classical Gaussian probe beam propagate coaxially through the emulated atmospheric turbulence. Using the distortion information gathered from the classical Gaussian probe beam, the AO system compensates the turbulence effects on the received channel and mitigates the distortion on the OAM-carrying photons. Due to the large power difference between the quantum channel and the classical probe beam (the power of the quantum channel is ∼100 dB lower than that of the classical probe beam), one may need to transmit the probe beam with different polarization, wavelengths, and OAM orders compared to the quantum channel in order to efficiently separate the classical probe beam from the quantum channel at the receiver side. Figure 32 shows the channel transfer matrices (top panels) when sending OAM modes {ℓ = −3, . . ., +3} one by one, as well as the photon count ratio (bottom figures) on the received OAM modes (i.e., the ratio of the received photons on the desired OAM modes to the total received photons) when sending only OAM ℓ = 1 photons in different cases: (from left to right) the back-to-back link (i) without probe and (ii) with the probe under atmospheric turbulence distortion, (iii) without probe, and (iv) with the probe and without AO mitigation, and (v) with the probe and with AO mitigation. Turbulence-induced distortion to the wavefront of OAM-carrying photons increases the probability of OAM photons existing in the undesired orders. Photons are better confined to their desired OAM orders with AO mitigation. 92

B. OAM-based quantum key distribution
Quantum cryptography, such as the quantum key distribution (QKD), can be utilized to build secure communication links between many parties. There have been reports of the demonstration of such systems in polarization-based optical systems. 94 As another degree of freedom, the OAM state of the light has the potential to enable QKD schemes using a higher-dimensional encoding scheme. [98][99][100][101] Figure 33(a) presents the concept of utilizing high-dimensional OAM-based QKD in a ∼300-m FSO quantum communication link. 102 Two sets of mutually unbiased bases (MUBs) including two vector modes and two OAM modes were combined to form four-dimensional quantum states. The transmitter part consists of a single-photon source and the setup of Alice (i.e., transmitter) to prepare states. The receiver part consists of the single-photon detection system and Bob's (i.e., receiver) setup to measure the states. A two-or four-dimensional BB84 protocol was performed under different atmospheric conditions exhibiting moderate turbulence effects. Specifically, Alice prepares the signal photon in one of the MUB states using an appropriate sequence of wave plates and q-plates and combines these with idles photons using a polarization beam splitter (PBS) and spatially magnifies the beams. Bob used a mirrored sequence of wave plates, PBSs, lenses, and q-plates and measured the signal photon by projecting the photon onto one of the states from one of the MUBs. 102 To optimally detect the signal photon, Bob should project onto the same state that Alice sent. Probability-of-detection matrices for the quantum states [ Fig. 33(b)] give quantum-bit-error rates (QBERs) of 5% and 11% in the two-and four-dimensional protocols, respectively, which are below the respective security thresholds. In typical QKD schemes, a classical key is shared between the two parties. 94 In the past decade, schemes for generating correlated classical keys shared among multiple parties were developed, namely, the quantum secret sharing (QSS) protocols. 103 The most common candidate for the experimental implementation of single photon QSS schemes is based on the polarization of light (two dimensions). 104,105 A recent work demonstrated a proof-of-concept implementation of a QSS scheme using OAM states with a dimension of 11. 106 As shown in Fig. 34(a), a distributor generates a photon that is a combination of 11 OAM states. Every participant applies their unitary transformation. The final participant sends the qudit state back to the distributor who measures the state. The distributor's secret can be determined through the collaboration of the remaining participants. The detected 11-dimensional probability matrix results in Figs. 34(b) and 34(c) indicate that OAM states offer a higher dimensionality and can be utilized for high-dimensional quantum information processes. 106

IX. OAM MULTIPLEXING IN RF, mm-WAVE, AND THz REGIMES
Besides using optical beams, free-space communication links can take advantage of mode multiplexing in many other carrierwave-frequency ranges to increase the system capacity. For example, OAM can manifest in various types of electromagnetic and mechanical waves, and interesting studies have explored the use of OAM in radio frequency, millimeter, acoustic, and THz waves, 8,[107][108][109][110][111][112][113][114][115][116][117][118] as shown in Fig. 35. From a system designer's perspective, there tends to be a trade-off in different frequency ranges: (i) Divergence: lower frequencies have much higher beam divergence, which makes it more challenging to collect enough power of the beam to recover the data channels. (ii) Interaction with matter: lower frequencies tend to have much lower interaction with matter such that radio waves are less affected by atmospheric turbulence induced modal coupling than optical waves.
A. OAM-multiplexed links in RF and mm-wave regimes OAM can be carried by any EM wave with a helical wavefront, and this does not depend on the carrier-wave frequency. Therefore, OAM multiplexing for communications can be applied to the RF regime. The feasibility of using OAM beams to increase the system capacity and the spectral efficiency of LOS RF communications is being actively investigated. 8,[108][109][110][111][112][113] There are exciting developments in the RF and mm-wave OAM application space, and industrial labs are increasingly engaging in R&D to significantly increase the potential capacity of fronthaul and backhaul links. 8,[108][109][110][111][112][113] One proof-of-concept demonstration presented a 32-Gbit/s OAM-multiplexed link containing four OAM modes and two polarizations at a carrier-wave frequency of 28 GHz. 8 As shown in Fig. 36, four different OAM beams with l = −3, −1, +1, and +3 on each of the two polarizations were generated using spiral phase plates (SPPs) made from highdensity polyethylene. Figure 36(a) shows the horn antenna, SPP for OAM +1, and SPP for OAM +3 at the frequency of 28 GHz. Figure 36(b) presents the observed intensity profiles for each of the beams and their interferograms with a Gaussian beam. After spatial combining using specially designed beam splitters, the resulting eight multiplexed OAM beams propagated for a distance of ∼2.5 m and were separated at the receiver. All eight OAM channels, each carrying a 4-Gbit/s 16-QAM signal, were sequentially recovered, achieving a capacity of 32 Gbit/s and a spectral efficiency of ∼16 bit/s/Hz.
The demand for larger bandwidth has gained much interest in OAM-multiplexed links at higher carrier frequencies using different types of OAM generators/receivers. 113,[116][117][118][119][120][121][122][123][124] For example, a 32-Gbit/s wireless link using OAM and polarization multiplexing was demonstrated at a carrier frequency of 60 GHz. 120 Advances in OAM generators/receivers for higher carrier frequencies include the use of RF antenna arrays that are fabricated on printed-circuit boards (PCBs). 112 For example, a multiantenna element ring can emit a mm-wave OAM beam by selectively exciting different antenna elements with a differential phase delay. 113 This is shown in Fig. 37(a), where the antenna arrays use delay lines of different lengths to set the phase of each patch antenna element in order to generate OAM beams of different orders. Moreover, the concept could be extended to multiplex N OAM beams. Multiple concentric rings can be fabricated, resulting in a larger number of

PERSPECTIVE
scitation.org/journal/app multiplexed OAM beams. 110,111 As presented in Fig. 37(b), multiple antenna array layers can be stacked at the same center for multiplexing when each layer is fed by an independent data stream and emits different OAM beams.

B. OAM-multiplexed links in the THz regime
The demand for larger channel bandwidths has also created interest in communication systems using THz carrier waves. There is a transmission window with a low atmospheric absorption loss between 200 GHz and 300 GHz, and research has focused on non-OAM communication links in this region. Since OAM multiplexing could further increase the capacity of communication links, it might be valuable to explore THz OAM-multiplexed links.
Since the wavelength of a THz wave is shorter than that of a mm-wave but longer than that of an optical wave, both divergence and turbulence effects might degrade THz OAM links. The fundamental system degrading effects for THz wireless communication links using multiple OAM beams were investigated in the simulation. 124 Simulation results in Fig. 38 show that the 0.1-THz OAM beam is distorted only a little bit under strong turbulence (Fig. 38, left panel), while the 1-THz OAM beam experiences a large distortion effect (Fig. 38, middle panel). The 10-THz OAM beam is strongly distorted even under weak turbulence (Fig. 38, right panel). A higher frequency leads to higher power leakage to neighboring modes. 28,124 The effects of limited-size aperture and misalignment are also investigated by the simulation in the THz range. 125 2D LG modal decomposition is used to analyze the modal coupling induced by both effects. As shown in Fig. 39(b), the limited aperture causes modal coupling to high-order p modes, possibly because the limited-size aperture truncates the beam in the radial direction, but has little influence in the azimuthal direction so that there is little power coupled to neighboring ℓ modes. However, with the misalignment effect, the beam profile is distorted in both the radial and azimuthal directions, and the simulation results show a modal coupling to both neighboring ℓ and p modes [ Fig. 39(c)].
C. OAM multiplexing combined with conventional spatial multiplexing In general, conventional spatial multiplexing includes multiple spatially separated transmitter/receiver antennas, and the interchannel crosstalk can be reduced by using MIMO signal processing. 126,127 In comparison, OAM multiplexing employs a pair of transmitter and receiver, and the modal orthogonality among the OAM beams enables little inter-channel crosstalk and efficient (de)multiplexing without signal processing. 108,109,128 A recent work demonstrated the combining of both these two spatial multiplexing techniques to further enhance the system capacity. 128 A 16-Gbit/s mm-wave communication link at 28 GHz using OAM multiplexing combined with conventional spatial multiplexing was demonstrated over a distance of 1.8 m in the laboratory. Figure 40 illustrates the combined system configuration containing 2 × 2 antenna apertures. Specifically, each transmitter aperture transmits two coaxial OAM beams l = +1 and l = +3, with each carrying a 4-Gbit/s data stream. A 2 × 2 MIMO-based signal processing was used at the receiver to reduce the inter-channel crosstalk. Figures 41(a) and 41(b) show the comparison of the BER performance without and with the MIMO equalization processing. The measured BER curves dropped down and reached below the FEC limit after the MIMO processing.
A more recent work demonstrated the combination of OAM multiplexing and conventional spatial multiplexing using multiple concentric uniform circular antenna arrays (UCAs) at 28 GHz. 110 As shown in Fig. 42(a), the UCAs consist of four concentric antenna   Fig. 42(b). Moreover,

FIG. 40.
Concept of a LOS mm-wave communications link that employs OAM multiplexing over conventional spatial multiplexing. The system consists of two transmitter/receiver apertures, with each transmitter aperture containing two OAM modes. At the receiver, Rx-1(or Rx-2) could receive power from all four OAM modes from the two transmitters, where the power from the two OAM modes transmitted from Tx-2 (or Tx-1) induces crosstalk.

X. OAM IN FIBER
This section is for the completeness of this review paper besides the discussions for free-space communications. MDM can be implemented in both free-space and fiber, with much of the transmitter and receiver technology being similar. However, the channel medium is different, which gives rise to the following distinctions: (i) There is no beam divergence in a light-guiding fiber.
(ii) Fiber has inhomogeneities, and coupling can occur among modes, either within a single mode group or between different mode groups, thereby creating deleterious interchannel crosstalk. 5,131,132 The excitement around using MDM for capacity increase originally occurred primarily in the fiber transmission world, especially in research laboratories. 16,19,[133][134][135][136][137][138] There were several reports of using linearly polarized (LP) modes as the modal set in fiber. However, since there was significant modal crosstalk when propagating through conventional-central-core few-mode fiber (FMF), MIMOlike DSP was used with impressive results to mitigate crosstalk. 133,134 It should be noted that modal basis sets can typically be represented by a modal combination of other sets. Therefore, it is no surprise that OAM and HG modes have also been used in conventional-type fibers, but significant crosstalk still occurs.
OAM has also been used as the modal basis set for fiber transmission for both central-core and ring-core FMFs. 5,16,20,135 Importantly, the modal coupling itself can be reduced in the optical domain by utilizing specialty fiber that makes the propagation constants of different modes quite different, thus reducing intermodal coupling. Such fibers include ring-core and ellipticalcore fiber, 20,135,139 and tens of modes with low crosstalk have been demonstrated. These specialty fibers have produced exciting results, but they are structurally different than conventional fiber and thus require a little more resolve in order for them to be widely adopted. One design of the vortex fiber is shown in Fig. 43 as an example. 68 This vortex fiber has an annular refractive index profile to provide a large effective refractive index difference among different OAM modes as compared to a normal fiber. Thus, this vortex fiber design could potentially enable the efficient co-propagation and (de)multiplexing of OAM modes with lower inter-modal crosstalk. 16,135 Another challenge for achieving MDM in fiber is the power loss due to fiber attenuation, which limits the transmission distance. In general, fiber-based amplifiers can be utilized to increase the transmission distance. For an MDM system, two main features are desired for the amplifiers: large mode gain and small difference between gains over different modes. Figure 44 presents two examples of OAM fiber amplifiers to address the above features. By using the ring-core fiber structure, OAM erbium-doped fiber amplifiers (EDFA) 140,141 and Raman amplifiers 142 have been demonstrated in these two papers, respectively. As for the performance, the example of OAM EDFA provides a high gain of >10 dB over a bandwidth of 20 nm, while the gain curve is not flat. As a comparison, the example of the OAM Raman amplifier has a low gain of ∼3 dB with a flat gain curve over a bandwidth of 30 nm.

XI. SUMMARY PERSPECTIVE
Will OAM be widely deployed in communication systems? Not clear. However, our opinion is that the R&D community is producing excellent advances that, in all likelihood, will be valuable for some important aspects that use structured light. This paper reviews the use of OAM to potentially enhance the capacity of MDM communication systems. The following points are noteworthy: (i) The use of OAM multiplexing under more complicated and harsher channel conditions than those described in this paper remains challenging. It would be important to investigate the system performance under these conditions and to develop potential techniques to combat the degradation effects. It would also be valuable to explore the limits of these conditions below which the degradation effects can be efficiently mitigated. (ii) The future of OAM deployment will rely heavily on the development of a technology ecosystem for OAM generation and multiplexing. Efficient OAM (de)multiplexing using compact and cost-efficient integrated devices would be one important issue. 143 Key desirable features of these integrated devices include 68 low insertion loss, high amplifier gain, uniform performance for different modes, high modal purity, low modal coupling and intermodal crosstalk, high efficiency for mode conversion, high dynamic range, small size, large wavelength range, and accommodation of high numbers of modes. Other functions that could be advantageous include (a) fast tunability and reconfigurability covering a range of OAM modes and (b) integration of an OAM communication system-on-a-chip that incorporates a full transceiver. (iii) OAM multiplexing could be utilized in different frequency domains. Future OAM systems might use hybrid technologies, and thus, systems that can be compatible with different OAM multiplexing technologies over different frequency domains may be valuable, including but not limited to the RF, mm-wave, THz, and optical domains. [144][145][146] Components, including broadband signal emitters/detectors and frequency converters in different frequency domains, may need to be considered to enable heterogeneous OAMmultiplexed communications. Another consideration could be the frequency channel selections, the key challenges of which include link loss and channel distortion caused by OAM beam divergence and beam interaction with matter (e.g., atmospheric turbulence) in heterogeneous OAMmultiplexed links. In such cases, potential solutions, such as AO and MIMO, could be helpful.