5112 Vol. 46, No. 20 / 15 October 2021 /Optics Letters Letter

Non-line-of-sight optical communication based onorbital angular momentumZhanwei Liu,1,† Yiwen Huang,1,† Haigang Liu,1,5 AND Xianfeng Chen1,2,3,4,*1State Key Laboratory of AdvancedOptical Communication Systems andNetworks, School of Physics and Astronomy, Shanghai Jiao TongUniversity, Shanghai 200240, China2Shanghai Research Center for QuantumSciences, Shanghai 201315, China3Jinan Institute of Quantum Technology, Jinan 250101, China4Collaborative Innovation Center of LightManipulation and Applications, ShandongNormal University, Jinan 250358, China5e-mail: liuhaigang@sjtu.edu.cn*Corresponding author: xfchen@sjtu.edu.cn

Received 25 August 2021; revised 14 September 2021; accepted 17 September 2021; posted 20 September 2021 (Doc. ID 441441);published 6 October 2021

Optical non-line-of-sight (NLOS) communication canexploit the indirect light path to provide free-space com-munications around obstacles that occlude the field ofview. Here we propose and demonstrate an orbital angularmomentum (OAM)-based NLOS communication schemethat can greatly improve its channel dimensionality. To ver-ify the feasibility for extending the amount of multiplexedOAM channel dimensionality, the effects of bit accuracyversus the number of channels in measuring OAM modesare quantified. Moreover, to show the ability for broadcastNLOS tasks, we report a multi-receiver experiment wherethe transmitted information from scattered light can berobustly decoded by multiple neuron-network-based OAMdecoders. Our results present a faithful verification of OAM-based NLOS communication for real-time applications indynamic NLOS environments, regardless of the limit ofwavelength, light intensity, or turbulence. © 2021 OpticalSociety of America

https://doi.org/10.1364/OL.441441

Optical wireless communication has been extensively investi-gated for its potential to expand the transmission capacity andresolve the wireless traffic problem [1,2]. Challenges occur interms of free-space optical communication when opaque obsta-cles occlude the field of view or atmosphere scatters the signal,which makes it hard to align the transmitter and receiver [3].Non-line-of-sight (NLOS) communication has consequentlyemerged as a candidate for both indoor and outdoor scenar-ios, relieving the acquisition requirement while maintainingthe transmission rate. In recent years, researchers have mainlyfocused on improving the data transmission rates of outdoorNLOS ultraviolet communication, since the background ultra-violet noise from solar radiation is absorbed by atmosphere[4–7]. In addition, wavefront shaping technology has beenutilized to enhance diffusely reflected light, maximizing theoptical power at indoor receivers [8].

To further expand the channel capacity of NLOS communi-cation, optical orbital angular momentum (OAM), described

by theoretical unlimited topological charge `, can be consid-ered to add the dimensionality of data transmission [9–11].Pioneering works on the possibility of employing OAM at bothline-of-sight (LOS) and NLOS wireless communication wereresearched [12–17]. Experimental works on OAM-based LOScommunication have also been realized [18,19]. However, acrucial limitation to further extending the channel amount ofthis scheme is the resolution of OAM modes at the receiver [20–22]. Even weak turbulence causes considerable problems forcommunication systems based on OAM, which is more severein NLOS scenarios due to strong scattering or diffuse reflec-tion process [23]. Such aberrations and diffuse losses criticallyaugment the difficulties of discriminating OAM modes.

Here, we propose and demonstrate an approach to collocateNLOS communication with infinitely dimensional OAMmodes. To take full advantage of its bandwidth resources, anintelligent neuron network (NN) algorithm is designed at thereceiver to decode information from NLOS light [24]. Thealgorithm also contributes to precisely measuring OAM modes[25–27]. Nevertheless, the literature is associated with theconventional pixel-array camera device that captures spatialintensity distributions of OAM modes, limited by the low-photon light in NLOS scenarios because of the inevitable shotnoise [28]. Even though electron-multiplying charge cou-pled device cameras can excellently detect low-photon light[29,30], cost efficiency is worth considering, especially for wideapplications in arbitrary electromagnetic spectral ranges.

In this Letter, we use a single-photon avalanche diode (SPAD)assisted by a spatial light modulator (SLM) to serve as a single-pixel detector [31,32] to translate the encoded informationin OAM-based NLOS communication. We experimentallyestablish a free-space diffuse reflection NLOS platform, andthe characteristics of a multi-receiver broadcast and the effectsof bit accuracy versus the number of channels in measuringOAM modes are investigated. In the experiment, an approxi-mately 1% bit error rate (BER) is obtained when we transmit anout-of-view image by extending six OAM channels.

A diagram of the common OAM-based NLOS communi-cation scenario is depicted in Fig. 1. OAM can be carried on

0146-9592/21/205112-04 Journal © 2021Optica PublishingGroup

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Fig. 1. (a) Scenario of OAM-based NLOS communication. Helixlight from the transmitter will be scattered by atmosphere, leadingto phase distortion at the receiver for some extent. (b) Schematic ofindoor OAM-based NLOS communication case. The vortex light canbe diffusely reflected by opaque obstacles to cover the whole room.

light by uploading phase holograms on SLM. Due to the diffusereflection from the NLOS link, the initial complex field Ui withhelix phase factor exp(i`φ) will evolve into Uo at the receiver.The optimization target f for the phase recognition task toinversely derive the prediction of topological charge p` can bedescribed by

f =minθ

J (`, p`)+ α H(θ), (1)

where J denotes the cross-entropy objective function to be opti-mized [25], α is the regularization parameter, θ is the collectionof trainable parameters in the NN model, and H represents thecalculation process. The prediction p` estimates the topologicalcharge value according to the scattered light intensity distribu-tion at the receiver Io = |Uo |

2. Although the helix wavefrontof Ui may suffer turbulence when being transmitted in NLOScommunication, the blurry phase is still recognizable. Becausethe phase of propagated light will merge with the projectionvectors, the initial scattered OAM modes are projected into newspatial distribution, Uo , which causes the variation in photoncounts Tcount at SPAD. Consequently, SPAD can record thequantitative projection of Io as the vector varies, so the predic-tion of transmitted OAM modes after NLOS scattering can beexpressed as

p` = HTcount. (2)

The NLOS communication experimental setup is arrangedas shown in Fig. 2. A 1551 nm laser is attenuated by two vari-able optical attenuators to control the light intensity. Thepolarization of emitted light is aligned to be horizontal bya fiber polarization controller and a polarizing beam split-ter. Then light is coupled into space by a fiber collimatorand illuminates a reflective SLM (SLM1). The SLM in ourexperiment can achieve precise phase modulation with a highefficiency of 95% for horizontally polarized light whose wave-length is within the scope of 1505–1650 nm. By successivelyuploading designed phase holograms on SLM1, the signalphotons with Gaussian mode are transferred into OAM statesUi with different helical phase structures. Here, we chooseOAM base |`i 〉 = | ± 1〉, | ± 2〉, | ± 3〉, totally six channelsto encode the OAM superposition states as Ui according to|`mul〉 =

∑num_channelsi (|`i 〉/N), where |`〉 represents the OAM

state with topological charge `, and each individual mode occu-pies one bit designated as “1” or “0,” and N denotes the numberof “1” in |`mul〉. A glass diffuser is selected to provide NLOSscattering, so the phase distribution of Ui will be distorted. Atthe receiver part, another SLM (SLM2) is utilized to upload

Fig. 2. Schematic of the NLOS platform. VOAs, variable opticalattenuators; PC, polarization controller; FC, fiber collimator; PBS,polarizing beam splitter; GD, glass diffuser; SLM1−2, spatial lightmodulator; L1−2, lens; SPAD, single-photon avalanche diode; NN,neuron network. The single-photon detector we used is InGaAs.

projection vectors; therefore, the phase distribution of lightevolves into Uo . Considering the known spatial properties ofmeasured OAM, we utilize the subsets of Laguerre–Gaussianmodes to be the projection vectors |`p〉 based on quantumtomography theory [33]. Then a SPAD records the projectedphoton counts Tcount and sends it to NN to demodulate theinformation of the wavefronts. The maximum photon countrecorded at the receiver in experiment is approximately 105 persecond. It is noticeable that the 1551 nm light is used only todemonstrate the scheme, and all of the experimental devicescan be flexibly substituted at any wavelength, especially for thedetector. The details for calibration of single-pixel detectorsand the configuration of projection vectors |`p〉 are shown inSupplement 1.

To exhibit the potential of our scheme in terms of NLOScommunication, a multi-receiver broadcast experiment isperformed to demonstrate its robustness for being applied inatmosphere and underwater communication. For the purposeof visualization, pixels of a rainbow image are decoded to binarycode in Fig. 3(a), and then encoded by the six-channel OAMsuperposition state. Here, we randomly select three positions1 m away from the diffuser to locate receivers that emulate thebroadcast scenario, and the schematic is shown in Fig. 3(b).First, each position performs one acquisition of all scatteredOAM superposition states with 20 different initial phases toconstruct the dataset before communication. After OAM-based NLOS transmission, the desired information can bedecoded according to the prediction of photon counts [Eq. (2)]by the pre-trained NN model. The obtained bit accuracy (1 -BER) of the train set, test set, and rainbow image is depicted inFig. 3(c). Due to the robustness of the intelligent NN algorithm,the bit accuracy of the rainbow image at all three receivers iscomparable to the corresponding test set, and the highest onecan reach 98.91%. The fluctuation at P2 is caused by its lowervalid photon counts because P2 is located at a relatively largereflection angle from the diffuser where the optical power is only−74.42 dBm. The rough phase distortion of the glass diffuseris against the impact of projection measurement, which canbe improved is atmosphere and underwater scattering. Theaccuracy gap at three receivers between the train set and rainbowimage is called “overfitting” in a machine learning method. Todecrease this difference, enlarging the scale of the dataset andadjusting the NN architecture will be effective.

To further explore the extent of increasing the channeldimensionality of OAM-based NLOS communication, we

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Fig. 3. (a) Principle of transforming the colorized rainbow imageto 6-bit OAM codes. The RGB channels are individually decoded tobinary code and then encoded to OAM superposition states. AfterNLOS communication, the NN will extract each state and recombineto an image. (b) Schematic of the multi-receiver broadcast experiment.We first set the position of P1 at the regular reflection angle of the dif-fuser, then P2 and P3 are located at both sides of P1. (c) Bit accuracy andreceived image information of three positions. Optical powers detectedat three receivers are−70.47 dBm,−74.42 dBm, and−72.70 dBm.

next verify the feasibility of transmission with a fractional OAMbase [34,35] that can add the channel number with small `.The details and results are shown in Supplement 1, Note 3. Forthe 1`= 0.1 case, all three receivers obtain lower bit accuracycompared to the large channel interval 1`= 1 listed above,indicating that a subtler distinction of phase distribution willmake measuring more difficult. The influence of lower opticalpower is amplified for the 1`= 0.1 case at P2, which has a3.1% drop in bit accuracy compared to P1, indicating that thesmall OAM interval case is more susceptible to noise. Notably,broadcast communication for arbitrary positions of receiversis realized in our approach under low light intensity withoutfeedback adjustment.

Then, we investigate the relation between channel dimen-sionality and the measurement approach. The histograms inFig. 4 display the impact on NLOS communication bit accuracyversus the number of OAM channels and the number of projec-tion vectors. Obviously, when the amount of multiplexed OAMchannels in |`mul〉 decreases, the NN can more precisely measurethe topological charge value for transmitted light as a resultof the simpler phase distribution on Ui . In addition, since theincreased number of projected measurement can acquire moreinformation from the light intensity at the receiver, increasingthe number of projection vectors can efficiently decrease theBER. Due to the perceptible differences, four OAM channelsto transmit data in NLOS communication can achieve almost100% test accuracy under at most eight projected measure-ments, and five OAM channels of communication can alsoobtain >98% bit accuracy even though the OAM intervalis 1`= 0.1, as shown in Fig. 4(b). Accordingly, more denseintervals of OAM channels can be exploited in NLOS com-munication. Nevertheless, six OAM channels will result in anobvious decrease in bit accuracy, where1`= 1 with 12 vectorsachieves 97.97%,1`= 0.1 achieves 92.50%, and the effect ofprojection vectors is magnified. This is because every additionalchannel will double boost the scale of data, leading to a more

Fig. 4. Relation between the bit accuracy of OAM-based NLOScommunication and the number of projection vectors and multi-plexed OAM channels. (a) Interval between adjacent OAM channelsis 1`= 1. (b) Interval between adjacent fractional OAM channels is1`= 0.1.

complicated phase combination. Similarly, the drop in bit accu-racy for finer1` is relatively larger owing to the tiny differencebetween recorded photon counts. A valid way to employ morechannels is to enlarge the scale of the train dataset and projectionvectors.

The single-pixel detector in our scheme can provide flexiblenovelty for combining the unlimited dimensionality of OAMmodes and NLOS communication in a theoretically arbitrarywavelength range. In this method, the end-to-end algorithm canignore the turbulence and scattering process in NLOS scenarios,efficiently distinguish the multiplexed OAM channel, and avoidthe requirement of perfect alignment between the transmitterand receiver in OAM-based communication. The precise mea-surement of multiplexed OAM superposition states can add atleast six channels for NLOS communication in our demonstra-tion. Furthermore, the sharply decreased number of featurescan significantly accelerate calculation time, which improvesthe flexibility of real-time communication in a dynamic NLOSenvironment. Indeed, the main limitation of bit rate exhib-ited in experiment is the low frame rate of SLM (60 Hz) thatdramatically increases the acquisition time. Fabricating the spe-cially designed optical elements to parallelly detect OAM can bea good candidate [36,37], and an optical artificial NN [38] canbe applied to perform all-optical operation, which can hugelyincrease the NLOS bit rate. Moreover, the performed com-munication capacity can be further expanded by wavelengthdivision multiplexing and polarization division multiplexingtechnology. It is certain that this approach can perform better atshort distances, such as indoor wireless communication [8]. Asfor long distance cases, the probable limitation of the method isthe detection of scattered light, which is imitated by attenuatingthe emitting laser and utilizing a strongly reflected diffuser in theabove experiment. Increasing the power of the emitting laser willbe useful to some extent. Even if the implementation of actuallong distance NLOS communication is much more complex,we think the relatively small topological charge of OAM in ourapproach can facilitate the detection.

Overall, we propose an approach to extend NLOS commu-nication channel dimensionality based on unbounded OAMmodes. A diffuse reflection NLOS communication system isexperimentally realized with a single-pixel detector, and thetheoretically minimum channel interval can achieve less than1`= 0.1 under projection measurement. A multi-receiverexperiment is exhibited to demonstrate its robustness for broad-cast NLOS communication where ≈1% BER is obtained.

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According to the affect on BER with the amount of multiplexedOAM modes and the amount of projection vectors, the behaviorof the method can be further improved by increasing projectionvectors and enlarging the dataset, which offers new oppor-tunities for real-time and high-capacity OAM-based NLOScommunication.

Funding. National Key Research and Development Program ofChina (2017YFA0303701, 2018YFA0306301); National Natural ScienceFoundation of China (11734011, 12004245); Shanghai Municipal Scienceand Technology Major Project (2019SHZDZX01-ZX06); ShandongQuancheng Scholarship (00242019024).

Acknowledgment. We thank Professor FeiHu Xu from the University ofScience and Technology of China for his productive suggestions.

Disclosures. The authors declare no conflicts of interest.

Data Availability. Data underlying the results presented in this Letter arenot publicly available at this time but may be obtained from the authors uponreasonable request.

Supplemental document. See Supplement 1 for supporting content.

†These authors contributed equally to this Letter.

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