Recent advances in high-capacity free-space optical and radio-frequency communications using orbital angular momentum multiplexing

1. Introduction

Free-space communication links are important in many data transfer applications, and they can use either optical or radio-frequency (RF) waves [1,2]. However, as the demand for data increases, there is a keen interest in increasing the data capacity of such communication systems [3]. In the past, the capacity of a communication system can be dramatically increased by multiplexing and simultaneously transmitting multiple independent data streams [4,5]. This can be achieved by using various properties of the electromagnetic (EM) wave, including time, wavelength and polarization, such that multiple data streams can be efficiently multiplexed and demultiplexed using appropriate device technologies [3,6,7]. Meeting future bandwidth demands may require new forms of data channel multiplexing [8–10].

One approach that has recently attracted wide interest is to use the spatial property of an EM wave, such that different spatial waves are multiplexed (i.e. space division multiplexing (SDM)) [9]. A special case of SDM is the utilization of orthogonal spatially overlapping and co-propagating spatial modes, known as mode-division multiplexing [8]. In such a system, multiple data channels each identified by a different spatial mode can be efficiently multiplexed at the transmitter and separated at the receiver. Consequently, the system transmission capacity and spectral efficiency (i.e. bits per second per hertz) could be increased by a factor equal to the number of transmitted spatial modes [11,12].

One orthogonal spatial modal basis set that could be used for SDM is orbital angular momentum (OAM) [13,14]. An EM wave carrying OAM has a helical transverse phase of the form exp(iℓØ), where Ø is the azimuthal angle and ℓ, the OAM charge, is an unbounded integer (with either negative or positive signs) that represents the number of 2π phase changes in the azimuthal direction [15]. Owing to the helical phase structure, an OAM beam has a ring-shaped intensity profile with a central null, and its wavefront twists along the propagation direction with a twisting rate depending on ℓ [16]. OAM beams with different ℓ values are mutually orthogonal [16], so that beams carrying different OAMs can act as independent channel carriers for efficiently (de-)multiplexing multiple information-bearing signals [11]. Moreover, owing to the fact that the OAM spatial domain is independent of other properties of an EM wave, OAM multiplexing is in principle compatible with other existing multiplexing techniques, such as frequency or wavelength division multiplexing (FDM or WDM), and polarization division multiplexing (PDM) [17,18]. Specifically, beams with the same wavelength and polarization can be re-used by applying different OAM chargers to each of the many beams, enabling a potentially significant increase in the system transmission capacity.

Applying OAM to enhance classical communication systems has been quite interesting, and it is especially exciting given that this is the 25th anniversary of the renowned paper by Allen, working with Han Woerdman and colleagues at Leiden University in The Netherlands [13]. Using OAM for communications was pioneered to a large extent over a decade ago by the groups of Padgett [9] and Zeilinger [14], and the community of researchers pursuing this area has grown significantly over the past few years. There has been progress in recent years in SDM communication using OAM multiplexing, pushing it towards achieving a higher transmission capacity, longer link distance, link robustness and system design guidelines. In this paper, we describe these advances in both OAM-based free-space optical (FSO) and RF communications. We also discuss the technical challenges associated with these OAM-based SDM systems and potential mitigation techniques for improving system performance.

2. Space division multiplexing communications using orbital angular momentum beams

In general, any orthogonal spatial modal set that can allow for efficient generation, (de-)multiplexing and detection can be used for SDM [19]. For an SDM system using OAM beams, each channel is identified by an OAM mode with a different ℓ value [20]. As depicted in figure 1a, multiple independent data channels, each on a different OAM beam, are spatially combined and the resulting multiplexed OAM beams are then transmitted through a single aperture towards the receiver. After coaxially propagating through the same free-space medium, the arriving beams are collected at the receiver by another aperture, and subsequently demultiplexed and detected for data recovery. It should be noted that an OAM beam diverges approximately as the square root of |ℓ| and high-order modes diverge more during propagation [21,22]. Since OAM, as a fundamental property, can be carried by any helical-phased EM waves, including light and radio waves, OAM multiplexing can be thus used in all frequency ranges [23]. As shown in figure 1b, the use of OAM multiplexing might have potential applications in scenarios such as data centres and back-haul connections.

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Given that OAM multiplexing employs the orthogonality among OAM beams to enable efficient (de)multiplexing, it requires coaxial propagation and reception of the transmitted modes [12]. This suggests that OAM-multiplexed links may require a more precise system alignment than non-OAM, single-beam communication links [24]. To date, most of the OAM-based free-space SDM systems rely on line-of-sight (LOS) connection between the transmitter and receiver [25,26]. We describe below OAM-multiplexed LOS systems at two different frequency ranges: optics and radio waves.

(a) Orbital angular momentum-multiplexed free-space optical communications

In general, one major concern for an FSO system is its link reliability and robustness stemming from harsh time-varying channel conditions, such as fog, rain and atmospheric turbulence [27,28]. In addition to power loss, these channel conditions may distort the transmitted beam, resulting in significant system performance degradations and even link outage. Moreover, these effects may fluctuate over time with wide dynamic ranges in magnitude [29].

Among these conditions, atmospheric turbulence is generally considered a major factor that limits the system performance [29,30]. It is known that inhomogeneity in the temperature and pressure of the atmosphere lead to random variations in the refractive index along the transmission path, and can easily distort the phase front of a light beam [28]. For FSO links using phase-front-sensitive OAM beams, the effects of atmospheric turbulence become more challenging due to the fact that the proper demultiplexing of the received OAM beams depends on their helical phase-front structures [31,32]. Atmospheric turbulence may lead to fluctuations in the power of received OAM channels and inter-modal crosstalk between channels with different OAM values [33]. Under a dynamic turbulent atmosphere, these degradations are slowly time-varying processes with a time scale of the order of milliseconds (generally much longer than the signalling period) [28,34].

(b) Orbital angular momentum-multiplexed radio-frequency communications

LOS RF communications with fixed transmitter and receiver locations is of increasing importance due to its potential in many applications [35,36]. Conventional LOS RF links can use the well-established multiple-input multiple-output technique with multiple spatially separated aperture elements at the transmitter and receiver for parallel data channel transmission [37]. This technique, called multi-antenna SDM (MA-SDM) systems thereafter, could provide capacity gains relative to the traditional single-aperture systems. In such a system, each data-carrying beam is received by multiple receivers, and signal processing is critical for reducing the crosstalk among channels and thus allow data recovery [38].

LOS RF links can also employ OAM multiplexing for the simultaneous transmission of multiple data channels. An OAM-multiplexed link in the RF regime has a similar concept to that at optical frequencies by multiplexing and transmitting multiple radio OAM waves through a single aperture [11,39]. This approach is different from conventional MA-SDM systems, because it employs OAM beam orthogonality to minimize inter-channel crosstalk and achieve efficient demultiplexing, thus reducing the need for multi-channel signal processing to mitigate channel interferences. Compared with an optical beam, the much longer wavelength of a radio carrier wave suggests less sensitivity to various channel conditions and more divergence upon propagation [21]. Consequently, atmospheric turbulence is not likely to pose severe limitations for this frequency range. On the other hand, the significantly increased divergence of radio OAM waves might impose constraints on the achievable link distance for OAM-multiplexed RF communications.

3. Orbital angular momentum-multiplexed free-space optical communications

The idea of using OAM modes for FSO communications was first proposed and demonstrated by Gibson et al. in 2004 [9]. It was shown that OAM modes can be used for data encoding by sequentially transmitting a different OAM beam, each representing a data symbol, within each time slot. Researchers later realized that each beam can also act as a channel carrier and a group of orthogonal OAM beams can be used to spatially multiplex multiple data streams [18,19]. Recently, high-capacity system transmission results using OAM beams performed under laboratory and field environments or in the field have been reported [10,17,18,40]. Meanwhile, significant efforts have also been made to meet the challenges that hinder its future implementations, pushing towards a high-capacity, long-distance OAM-based FSO link affected by practical atmospheric turbulence conditions [41,42].

(a) High-capacity orbital angular momentum-multiplexed transmission

Initial demonstrations were carried out in the laboratory, including the transmission of two multiplexed beams with each carrying an on–off keying signal [19,20]. Later experiments further showed the possibility of multiplexing and transmitting more OAM modes. In 2011, Wang et al. [43] first reported a terabit per second free-space link by combining OAM multiplexing with polarization multiplexing. Four OAM beams on each of two orthogonal polarizations were spatially combined and the resulting multiplexed eight OAM modes then co-axially propagated over approximately 1 m in free space. The received OAM beams were de-multiplexed at the receiver and sequentially detected to recover the data streams. Each of the beams was encoded with a 42.8 GBd 16-quadrature amplitude modulation (16-QAM) signal, allowing a total capacity of approximately 1.4 (42.8 × 4 × 4 × 2) Tbit s⁻¹. All eight OAM data channels were located on the same wavelength, providing a spectral efficiency of 25.6 bit s⁻¹ Hz⁻¹ [10]. Figure 2 presents some of the experimental results.

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The above experiment was expanded by adding the wavelength dimension, simultaneously using OAM, polarization and wavelength for multiplexing. A total of 1008 data channels were carried by 12 OAM values, two polarizations and 42 wavelengths [17]. Each channel was encoded with 50 GBd quadrature phase-shift keying, providing an aggregate capacity of 100.8 Tbit s⁻¹ (12 × 2 × 42 × 50 × 2 Gbit s⁻¹). Another study [18] further pushed the link capacity beyond petabits per second by multiplexing more OAM channels and using higher order modulation formats.

These free-space OAM system demonstrations attempted to approximate an OAM-carrying Laguerre–Gaussian (LG) beam and used OAM beams with different ℓ. As an LG beam has two indices (i.e. an azimuthal index ℓ related to OAM and a radial index p related to the radial nodes), LG modes can form an orthogonal and complete modal set. OAM does exist for LG modes with higher values of p and OAM beams with higher p indices can also be included for multiplexing, as has been shown in various reports [44,45].

(b) Atmospheric turbulence effects and turbulence mitigations for orbital angular momentum beams

(i) Atmospheric turbulence effects

As described in §2a, atmospheric turbulence presents a critical challenge to OAM-based FSO links by giving rise to fluctuations in power and inter-model crosstalk among the received OAM channels [46]. Theoretical works performed by Paterson [31] and Tyler & Boyd [32] provided the quantitative analysis on the effects of atmospheric turbulence on OAM beams, considering the typical Kolmogorov spectrum statistics model. It was revealed that the amount of power of the transmitted OAM modes that leaked into neighbouring modes is proportional to the strength of turbulence D/r₀, where D is the beam width and r₀ is the atmospheric coherence length [28]. Specifically, the ensemble average of the normalized power on the OAM mode ℓ = ℓ_j, 〈P_j〉, when transmitting the OAM mode ℓ_i can be approximated by [32]:

where Δ = |i − j| and Γ(·) is the gamma function. This expression predicts that, as the turbulence strength increases, the power of the transmitted OAM mode starts to leak to neighbouring modes and tends to be equally distributed among modes for strong turbulence. This power leakage behaviour was also experimentally verified in [47] by emulating turbulence with controllable strength in the laboratory. As an example, figure 3 shows the measured OAM power spectrum of the received beam when transmitting the OAM ℓ = +3 beam under different turbulence strengths [34]. One can see that the received power is better confined to the transmitted OAM mode under weak turbulence, but it spreads to neighbouring modes as the turbulence strength increases.

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Furthermore, the influence of atmospheric turbulence on OAM beams was experimentally investigated from a system perspective by evaluating the system power penalty [34]. In this study, atmospheric turbulence was created by a thin-phase screen plate placed in the middle of the link path. The thin plate had a phase distribution obeying Kolmogorov spectrum statistics with a specific r₀, and was mounted on a rotation stage to simulate the turbulence dynamic nature. The strength of the emulated turbulence could be varied by using a plate with a different r₀ or by adjusting the size of the beam that was incident on the plate. It was found that the power penalty may exceed 10 dB under a weak-to-medium turbulence condition and link outage may occur under strong turbulence.

(ii) Mitigating turbulence effects

Given the performance degradations described above, it would be desirable to have techniques to mitigate the turbulence effects [48]. Currently, the reported turbulence mitigation approaches can be generally divided into two categories: (i) adaptive optics (AO) system compensation that can help optically correct the distorted wavefronts of received OAM beams [49–51] and (ii) signal processing-based mitigation that employs algorithms in the electrical domain at the receiver to reduce the signal degradation effects [52–54].

AO compensation. In general, an AO compensation system operates in a closed-loop configuration and its one typical working iteration includes: (i) measuring the wavefront of the distorted beams, (ii) calculating the correction patterns based on the wavefront measurement results, and (iii) applying the correction patterns onto the beams to undo the distortions. As for an FSO system using helical phased OAM beams, it is challenging to directly measure an OAM beam's wavefront using conventional wavefront sensors due to its inherent phase singularity [55]. Moreover, it is required that the receiver's AO system should be able to simultaneously compensate multiple coaxially propagating OAM beams.

An AO system that uses a separate Gaussian beam to probe turbulence-induced wavefront distortions was recently proposed to overcome these problems [49]. As depicted in figure 4a, a Gaussian beam coaxially propagates with the OAM beams through the turbulent atmosphere. At the receiver, this Gaussian beam is separated from the distorted OAM beams for wavefront measurements, based on which the required phase correction patterns can be derived to undo the distortions of all the received OAM beams. The detailed implementation of the AO system is shown in figure 4b. Figure 5 shows the measured intensity profiles of OAM beams and bit error rate (BER) curves before and after compensation. For the convenience of beam separation, the Gaussian beam was orthogonally polarized with respect to the other OAM beams. One can clearly observe that the distorted OAM beams up to ℓ = +9 were partially corrected, and the power penalty decreased due to the crosstalk reduction by compensation.

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Although this Gaussian probe can also carry an independent data channel, its occupation of one polarization sacrifices the polarization degree of freedom for multiplexing. This issue could be avoided by putting the Gaussian probe on a separate wavelength for turbulence sensing, as described in [50]. It was found that the compensation performance degraded slowly with the increase in the beacon's wavelength offset, in the 1520–1590 nm band, from the OAM beams.

Signal processing-based mitigation. Signal processing algorithms in the receiver can also be used to help combat turbulence effects on OAM-based FSO systems. This type of mitigation approach can shift the complexity of the optical subsystem to the electrical domain, providing a complementary approach to AO-based compensation. In [52], a multi-channel equalization algorithm was implemented in the receiver digital signal processing (DSP) to reduce the crosstalk effects caused by weak turbulence and recover all the data channels in a four-OAM-mode multiplexed link. This approach has been previously used in few-mode and multi-mode fibre-based mode division multiplexed systems to mitigate the mode coupling effects [8]. Experimental results showed that this DSP-based multi-channel equalization can improve the BERs of the received channels and reduce system power penalties.

However, multi-channel equalization is not universally useful for all channel conditions [52,56]. Particularly, outage may occur under strong turbulence distortions when the crosstalk among OAM channels exceeds a certain threshold or one of the channels is barely detectable due to severe power fading [56]. A modified scheme was reported to relieve this concern, through the incorporation of additional OAM transmitters/receivers to create redundancy [53]. By exploiting the spatial diversity provided by the multiple-aperture architecture, both weak and strong turbulence can be potentially mitigated using multi-channel equalization combined with a diversity reception strategy.

Other signal processing approaches that have been shown to help mitigate turbulence effects in OAM-based FSO links, include the Gerchberg–Saxton algorithm [57], artificial neural network-based recognition [54] and the stochastic parallel gradient descent algorithm [58].

(c) Orbital angular momentum-based free-space optical links beyond laboratory distances

The laboratory demonstrations of OAM-multiplexed FSO links were generally limited to a metre-scale short distance. The expansion of an OAM link over a much longer distance might give rise to several issues, including divergences of OAM beams with different orders, system pointing and misalignment, and atmospheric turbulence effects [40,59]. The transmission of OAM beams over a 3 km link across the city of Vienna was reported by Zeilinger's group in Austria [54]. In this experiment, the data bits were sequentially transmitted at a rate of a few bits per second on one of 16 different OAM superposition states (ℓ = ±0, ± 1, … ±15). An artificial neural network algorithm was used to distinguish the received mode-intensity patterns, thus recovering the encoded bit information. This experimental scheme was recently extended to a link distance of 143 km between the two Canary Islands of La Palma and Tenerife [60]. Figure 6 shows the link layout and set-up. The received mode superpositions can be identified with an accuracy of more than 80% up to the third mode order and the decoded message had an error rate of 8.33%. These two long-range experiments indicate the feasibility of kilometre-scale long-distance OAM mode transmission through the atmosphere.

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Additionally, the transmission of multiplexed high-speed data-carrying OAM beams was experimentally demonstrated outside the laboratory [40,61]. Ren et al. [40] reported a 400 Gbit s⁻¹ data link over 120 m by multiplexing four OAM beams with ℓ = −3, −1, +1 and +3. As shown in figure 7, the transmitter and receiver were located at the same site on the roof of a building. The transmitted OAM beams were reflected twice by two flat mirrors placed 30 m away, achieving a 120 m propagation path. The influence of beam wander (i.e. tip/tilt abreactions) of the link was measured and characterized. Experimental results showed that beam wander significantly degrades the link performance and power penalties increase rapidly when the lateral displacement increases.

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(d) Link parameter design for orbital angular momentum-based free-space optical systems

In general, a long-distance FSO system requires a careful design of link parameters. When involving OAM beams, the parameter design of a long-distance link becomes complicated due to their unique intensity and phase profiles [24]. As described in §2, the divergence of OAM beam scales approximately with the square root of |ℓ|, indicating that high-order modes have a much larger beam size at the receiver. In addition, OAM multiplexing requires coaxial propagation and reception of the transmitted modes. Unlike the case of using a single Gaussian beam, any misalignment between transmitter and receiver apertures or only partially collecting the OAM beams at the receiver would result not only in power loss but, more severely, in inter-channel crosstalk, as presented in figure 8a. Figure 8b illustrates two types of misalignment: namely lateral misalignment and receiver angular error. These factors need to be carefully considered in the choice of the link parameters of an FSO system using OAM multiplexing.

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A simulation model was established in [24] to investigate signal power and crosstalk effects for received OAM channels over pure free-space propagation. The trade-offs between the OAM modes chosen for transmission, system misalignment tolerance, transmitted beam sizes, aperture sizes and link distance were explored. Based on these trade-offs, design considerations and general guidelines were provided. As an example, figure 9a shows misalignment effects on the crosstalk of the adjacent channel ℓ = +4 under different link distances and transmitted beam sizes when only OAM beam ℓ = +3 is transmitted. As can be seen from the figure, a larger beam size at the receiver will result in two opposing effects in the cases of lateral misalignment and receiver angular error: (i) a smaller lateral-displacement-induced crosstalk (because the differential phase change per unit area is smaller) and (ii) a larger tilt-phase-error-induced crosstalk (because the phase error scales with a larger optical path delay). Figure 9b shows the power penalty analysis for a four-OAM-mode multiplexed link under various lateral displacements and receiver angular errors. It can be found that a system with smaller mode spacing shows a lower system power penalty under a small lateral displacement or receiver angular error, whereas larger mode spacing shows a lower power penalty when the lateral displacement or receiver angular error is large.

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4. Line-of-sight radio-frequency communications using orbital angular momentum beams

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 system capacity and spectral efficiency of LOS RF communications is being actively investigated [62,63]. Progress in high-capacity system demonstrations, and in device and component technologies for radio OAM beams, has been also reported [64–67].

(a) High-capacity radio-frequency transmission using orbital angular momentum beams

Although radio OAM waves were first discussed in the late 1990s [68], the use of OAM beams for RF communications has remained relatively unexplored until a few years ago when Tamburini et al. [63] reported a data transmission link using OAM beams as data carriers. In this experiment, a Gaussian beam and an OAM beam with ℓ = +1 at approximately 2.4 GHz were each transmitted by a Yagi–Uda antenna and a spiral parabolic antenna, respectively, which were placed in parallel. These two beams were distinguished by the differential output of a pair of antennas at the receiver side. In a later experiment, the number of channels was increased to three (carried on OAM beams with ℓ = −1, 0 and +1) using a similar apparatus to send an approximately 11 Mbit s⁻¹ signal on an approximately 17 GHz carrier [63]. However, different OAM beams in these demonstrations propagate along different spatial axes and were not transmitted through the same aperture. Intensive investigations on OAM-multiplexed RF LOS communications to fully exploit the advantages of OAM modes were performed later, particularly at millimetre-wave (mm-wave) frequencies [64,65].

The proof-of-concept experiment of OAM multiplexing in the RF regime was first demonstrated by Yan et al. [11] in a laboratory environment, showing a 32 Gbit s⁻¹ mm-wave link at a carrier frequency of 28 GHz. Four different OAM beams with ℓ = −3, −1, +1 and +3 on each of two polarizations were generated using spiral phase plates (SPPs) made out of high-density polyethylene. Figure 10a presents the observed intensity profile for each of the beams and their interferograms with a Gaussian beam. After spatial combining using specially designed beamsplitters, the resulting eight multiplexed OAM beams propagated over 2.5 m and were then separated at the receiver. All eight OAM channels, each carrying a 1 GBd 16-QAM signal, were sequentially recovered, achieving a capacity of 32 Gbit s⁻¹ and a spectral efficiency of approximately 16 bit s⁻¹ Hz⁻¹ at 28 GHz. As an example, figure 10b,c shows the recovered 16-QAM constellations and measured BER curves for the two polarized ℓ = +3 channels.

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Later works explored OAM-multiplexed RF communications at other carrier frequencies or using specially designed radio OAM devices [64,65,69]. For example, Li et al. [65] reported a 1 Gbit s⁻¹ data link at 8.3 GHz by multiplexing two OAM beams with ℓ = +1 and +2, in which two stacked patch antenna arrays were designed and fabricated, and functioned as the OAM transmitter and receiver, respectively. The effects of other channel conditions beyond pure LOS free-space propagation were also investigated recently. Initial studies on the effects of multi-path and object obstructions have been performed [70,71]. As shown in [71], a specular reflection-induced multi-path distorts received OAM beams and causes intra-channel and inter-channel crosstalk, resulting in significant system performance degradations.

Additionally, a similar link design model, as described in §3c, has been applied for mm-wave OAM links to design link parameters and explore potential system limitations [24]. Owing to its much longer wavelength compared with an optical beam, a mm-wave OAM beam diverges more, which would limit the achievable link distance given a fixed-size aperture. Moreover, for the same reason, OAM devices at RF generally have larger physical dimensions than those at optical frequencies. These issues together with other features that are specifically related to RF systems, such as the gain and shape of an antenna, should be particularly considered.

(b) Generation and detection of radio orbital angular momentum beams

Various approaches have been put forward to generate, (de-)multiplex and detect radio OAM beams. Turnbull et al. [68] first showed the generation of OAM beams at 90 GHz using SPPs made of Teflon. By making use of existing RF components and technologies, other techniques based on different antenna structures have been reported. For example, a helicoidal parabolic antenna was proposed to generate OAM beams with antenna gain [62,63]. Additionally, conventional phase array antennas that have been widely used in RF MA-SDM systems were used for OAM generation by configuring each antenna element with an appropriate phase delay [67]. It was further shown that this approach could also be used for the simultaneous generation and steering of an OAM beam [72,73]. Figure 11a presents the concept. By including additional phase delays in the desired steering direction on the eight antenna elements, the generated OAM beam can be steered by up to 30°. As an example, figure 11b shows that the measured intensity profiles of steered OAM beam ℓ = +1 with steering angles of 0°, 5° and 10°.

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The generation and multiplexing of multiple OAM beams by a single component has also been investigated [65,69]. By extending the circular patch antenna array approach into a stacked fashion, two multiplexed OAM beams with ℓ = +1 and +2 were generated in a single device fabricated using printed circuit board technology [65]. Moreover, a travelling-wave slot antenna based on a ring cavity resonator and a feeding network was fabricated to produce two co-axially propagating OAM beams with ℓ = −3 and +3 at approximately 94 GHz [64].

(c) Orbital angular momentum multiplexing and multi-antenna space division multiplexing systems

Although OAM multiplexing and the well-established MA-SDM systems represent different implementations, they exploit the spatial degree of freedom for the simultaneous transmission of multiple data channels. There have been intensive discussions as to the fundamental relationship between these two types of spatial multiplexing [74,75]. It was later shown that multi-antenna techniques can be used to generate OAM through suitably structured antenna arrays [67,76]. However, it is also possible to use several spatially separated apertures, each of which contains multiple OAM beams to distribute the spatial degree of freedom, in an arrangement that could be interpreted as combining MA-SDM with OAM multiplexing [77]. It should be noted that a fixed volume that is available for placing transmitter or receiver apertures provides certain spatial degrees of freedom for both multiplexing techniques [78]. An initial experimental demonstration of this concept was reported, in which a 2 × 2 mm-wave MA-SDM link at 28 GHz with each transmitter containing two OAM beams was implemented [79]. Each of the four OAM channels was encoded with a 1 GBd 16-QAM signal, achieving a total capacity of 16 Gbit s⁻¹. A 4 × 4 multi-channel signal processing at the receiver was used to mitigate interferences and recover all four data channels [80].

5. Discussion and perspective

Recent years have seen progress in the use of OAM multiplexing for LOS free-space communications in both the optical and RF regimes. There is no doubt that OAM multiplexing, as one SDM approach, can multiply system capacity and spectral efficiency, potentially helping address the capacity demands in many applications. However, there still exists a rich set of issues to further explore for its potential implementation in the future. The following points are worth mentioning:

• 1. This paper describes using OAM for potentially enhancing capacity in SDM communication systems. There are several issues relating to the OAM modes as well as to other modal groups:

  • (a) As long as orthogonality can be maintained among different modes, there exist other modal groups that can also be used for mode multiplexing, e.g. Hermite–Gaussian modes and vector modes [81,82].

  • (b) As opposed to several other types of modal groups, OAM has circular symmetry. This characteristic makes the beams conveniently matched to many optical components and subsystems for ease of implementation.

  • (c) OAM beams in this paper can be considered LG modes. In general, LG modes represent a complete two-dimensional modal basis set and can be described by two indices (i.e. an azimuthal index ℓ and a radial index p), and OAM can exist for LG modes with different values of p. If only p = 0 is used for multiple beams of different ℓ values, then this can be considered a subset of the fuller two-dimensional set of LG modes [83]. However, as OAM can exist for p ≠ 0 as well, then the use of different values of p and different ℓ values can produce a fuller set of modes and theoretically a higher system capacity over a given spatial area [44,45].

• 2. The use of OAM multiplexing under more complicated and harsher channel conditions than described in this paper (e.g. rain, fog and obstructions) remains challenging. It would be important to investigate the system performance under these conditions and develop potential techniques to combat the degradation effects [70].

• 3. The future of OAM deployment relies heavily on the development of an ecosystem for OAM generation and multiplexing. Currently, most of the reported systems with OAM multiplexing use bulky and expensive components that are not necessarily optimized for OAM operation. The advances in enabling devices, components and subsystems have become critically important [84]. Following the historic trends for many previous advances in communications, it would be essential for the OAM ecosystem to provide reductions in cost and size, and offer compatibility with existing technologies.

Authors' contributions

All the authors contributed to the writing of the manuscript.

Competing interests

The authors declare no competing interests.

Funding

Our work was supported by the Air Force Office of Scientific Research, the DARPA InPho (Information in a Photon) Program, the Intel Labs Research Office, NxGen Partners, the NSF EECS program and the NSF MRI program.

Footnotes

One contribution of 14 to a theme issue ‘Optical orbital angular momentum’.