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Abstract
Twisted light carrying orbital angular momentum (OAM), which features a helical phase front, has shown its potential applications in diverse areas, especially in free-space optical (FSO) communications. Multiple orthogonal OAM beams can be utilized to enable high-capacity FSO communication systems. However, for practical OAM-based FSO communication links, atmospheric turbulence will cause serious power fluctuations and inter-model crosstalk between the multiplexed OAM channels, impairing link performance. In this paper, we propose and experimentally demonstrate a novel OAM mode-group multiplexing (OAM-MGM) scheme with transmitter mode diversity to increase system reliability under turbulence. Without adding extra system complexity, an FSO system transmitting two OAM groups with a total of 144 Gbit/s discrete multi-tone (DMT) signal is demonstrated under turbulence strength D/r0 of 1, 2, and 4. In our experiments, the proposed OAM-MGM scheme helps to achieve bit-error-rate (BER) mostly less than 3.8 × 10−3 under turbulence strength D/r0 of 1 and 2 with a total transmitted power of 10 dBm. Compared with the conventional OAM mode multiplexed system, the system interruption probability decreases from 28% to 4% under moderate turbulence strength D/r0 of 2.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Free-space optical (FSO) communications have gained increasing interest for their higher capacity and improved security, as compared to conventional radio-frequency (RF) techniques [1–4]. Moreover, when technologies such as mode-division multiplexing (MDM) are combined with the current FSO links, it is possible to provide even higher capacities [5–7]. In a typical MDM FSO link, several orthogonal spatial modes are transmitted simultaneously, each carrying an independent data stream to multiply the system data rate. Among the reported spatial modes, twisted light carrying orbital angular momentum (OAM), which features a helical phase front, has shown its potential applications in FSO communications [8–13]. Owing to the inherent orthogonality of OAM beams and unbounded states of OAM modes, one can realize high-capacity and spectrally-efficient twisted optical communications through efficient OAM multiplexing [14–18].
However, for practical OAM-based FSO communication links, a critical challenge is atmospheric turbulence which can easily distort the wavefront of OAM beams and cause random mode spreading [19,20]. The turbulence effects could be particularly serious for multiplexed OAM beams, since the separation between different OAM beams relies on the helical phase front. Theoretical and experimental artworks have indicated that turbulence can cause fluctuations in power and inter-model crosstalk between multiple received OAM channels, increasing interruption probability and the average bit error ratio (BER) [21,22]. Therefore, mitigation techniques of atmospheric turbulence are key issues for practical OAM-based FSO communication links. Various techniques have been employed to mitigate the influence of turbulence, including adaptive optics compensation [23–26] and multiple-input-multiple-output (MIMO) equalization [27], but these approaches generally require more hardware complexity at the transmitter/receiver. Another approach is to use structured light beams carrying OAM for statable transmission under atmospheric turbulence, including the Bessel beam, vector vortex beam, and ring airy vortex beam [28–32]. In recent years, mode diversity has been proposed to reduce the turbulence effect and improve the FSO link reliability, which is considered as a complement to mode multiplexing [33–35]. It requires that different spatial modes experience turbulence differently, and so have the diversity gain, enabling a more robust system under turbulence. In our previous work, we experimentally demonstrated an OAM-based transmitter mode diversity scheme with a single phase-only element to mitigate the turbulence effect on OAM data transmission [36]. If mode diversity could be successfully used in the OAM-based multiplexed FSO link, then the transmission distance and system reliability might be increased under turbulence. In this scenario, a loadable goal would be to introduce mode diversity scheme in OAM mode multiplexing links to improve the communication performance under atmospheric turbulence.
In this paper, we experimentally demonstrate a novel OAM mode-group multiplexing (OAM-MGM) scheme with transmitter mode diversity in an OAM-multiplexed link to increase communication performance under atmospheric turbulence, in which all beams in each OAM mode group carry the same data stream for transmitter mode diversity, while different mode groups carry different data streams for mode multiplexing. Without adding extra system complexity, a system transmitting two OAM groups with a total of 144 Gbit/s discrete multi-tone (DMT) signal is demonstrated. In our experiment, the proposed scheme helps to achieve bit-error-rate (BER) mostly less than $3.8 \times {10^{ - 3}}$ for most of the 50 turbulence realizations under weak to moderate turbulence strength (D/r0 = 1 and 2) with a total transmitted power of 10 dBm. Compared with the conventional OAM multiplexed system, the interruption probability decreases from 28% to 4% under moderate turbulence strength D/r0 = 2.
2. Concept and principle
The concept and principle of the proposed OAM-MGM scheme are illustrated in Fig. 1. At the transmitter side, multiple OAM mode groups with sufficient mode interval are generated and multiplexed, in which each group consists of several adjacent OAM modes (e. g. OAM + 2,+3,+4 and OAM-2,-3,-4). One OAM mode group can be generated with a single phase-only element as our previous work demonstrated, which will not add extra system complexity compared with the conventional OAM multiplexing links [36,37]. Here all OAM modes in each group carry the same data stream, while different mode groups carry different data streams. In free-space transmission, the power of the transmitted OAM modes will be mainly coupled to their neighboring OAM modes randomly due to the turbulence, while little power will be coupled to the OAM modes with relatively large mode spacing. The crosstalk of the multiplexed OAM mode groups is mainly dependent on their mode spacing. Thus, we can get relatively low crosstalk by increasing the mode spacing of the central modes in each OAM mode group. Moreover, by using the OAM mode group with multiple modes carrying the same data, the transmitter mode diversity scheme is constructed. In the conventional single OAM transmission system, the power of the transmitted OAM mode will leak to other neighboring OAM modes randomly due to the turbulence. Thus, the received power would have a severe fluctuation, which may lead to the interruption of communication. In the OAM-MGM scheme with transmitter mode diversity, the power of the three transmitted modes will couple to each other. Considering the moderate to strong turbulence-induced mode coupling conditions, it is possible to achieve a relative stable received power with smaller standard deviation than conventional single OAM transmission, and reduce the interruption probability. Thus, one can improve the reliability of the FSO link by the use of OAM-MGM scheme with transmitter mode diversity, as demonstrated in our previous work [36]. At the receiver, only the intended OAM mode in the middle of each mode group (such as OAM + 3 and OAM-3) is detected. It should be noted that the total transmitted power of each OAM mode group should be the same as the conventional OAM multiplexed case which only uses the intended OAM modes for multiplexing. Compared to conventional OAM multiplexed links, our scheme can avoid increasing transmitter/receiver complexity. Considering the low-level inter-mode-group crosstalk under turbulence, we recover each mode group separately. In each mode group, the transmitter mode diversity scheme is employed to improve the system reliability under turbulence. When such a multiplexed OAM beam is transmitted through turbulence, the received power of the intended mode in each group might be higher and achieve a relatively stable condition due to the extra power coupled from the neighboring modes within each group. As a result, the received power of the intended OAM modes could potentially achieve a lower probability of system outage.
3. Experimental setup
The experimental setup of the free-space OAM-MGM communication system is shown in Fig. 2. At the transmitter, a 72 Gbit/s 16-QAM-DMT signal is generated by an optical intensity modulator (IM) with an arbitrary waveform generator (Keysight M8196A). Then, the signal is amplified by an erbium-doped fiber amplifier (EDFA) and attenuated by a variable optical attenuator to control the transmitted optical power. Then the signal is equally split into 2 branches by a 50/50 coupler, and one of the branches is delayed by a ∼10 m length of single-mode fiber (SMF) for decorrelation. After being collimated and linearly polarized, the two generated Gaussian beams are directly converted to two data-carrying OAM mode groups (OAM + 2,+3,+4 and OAM-2,-3,-4) through spatial light modulator (SLM1). SLM1 is divided into two parts for loading the desired phase patterns, as shown in Fig. 2. Limited by the number of available SLMs, the phase pattern loaded on the SLM1 is the combination of a multi-OAM phase pattern and a pseudo-random phase mask that follows the Kolmogorov spectrum statistics. In general, turbulence strength can be characterized by the ratio D/r0, where D is the beam diameter, and r0 is the Fried parameter. In the experiment, the beam size of a set of OAM beams is 2.1 mm, and the turbulence strength D/r0 is set to 1, 2, and 4. Then, the two OAM mode groups are reflected by two mirrors, and combined by a beam splitter. After 1.5 m free-space transmission, only the intended mode (OAM + 3 or OAM-3) in each mode group is detected by SLM2, which is loaded with a specific fork grating phase pattern to convert the incoming beam to a Gaussian-like beam. An InGaAs camera is used to capture the intensity profile of the transmitted light beam. The back-converted Gaussian-like beam is coupled into SMF and sent to the photodetector for signal detection. The detected electrical signals are captured by a real-time oscilloscope (Tektronix DPO73304SX) with a sampling rate of 100 GSa/s and finally processed by offline digital signal processing.
Fig. 2. Experimental setup of free-space OAM-MGM communication system. (a) Loaded phase pattern for generating OAM mode group with turbulence phase. (b) Demultiplexing phase pattern OAM-3. IM: intensity modulator; AWG: arbitrary waveform generator. EDFA: erbium-doped fiber amplifier; PC: polarization controller; Col.: collimator; Pol.: polarizer; SLM: spatial light modulator; VOA: variable optical attenuator; PD: photodetector.
4. Results
Firstly, we show the intensity distribution of the transmitted OAM mode groups (OAM + 2,+3,+4 and OAM-2,-3,-4) and conventional OAM mode multiplexed transmission (OAM + 3 and OAM-3) under different turbulence. The captured intensity profiles are shown in Fig. 3. From the obtained results, it is clear that the mode distortion gets stronger with increasing of turbulence strength. When the turbulence strength increases to 4, it is hard to recognize the transmitted modes from the captured intensity distributions, which will have a great impact on the communication performance of the FSO link.
Fig. 3. Intensity distribution of the transmitted OAM mode groups (OAM + 2,+3,+4 and OAM-2,-3,-4) and conventional OAM mode multiplexed transmission (OAM + 3 and OAM-3) under different turbulence.
To fully evaluate the performance of the OAM-MGM FSO link under atmospheric turbulence, we characterize the statistic distribution property of the OAM-MGM link and conventional OAM multiplexing link under different turbulence strengths D/r0 = 1, 2, and 4. The total transmitted power is 10 dBm for all the observed results. Figure 4 shows the distribution and corresponding cumulative probability of the received optical power and measured crosstalk of the detected mode OAM + 3 over 50 independent turbulence realizations under weaker turbulence condition (D/r0 = 1). From the obtained experimental results, we can find that the average received power of the conventional OAM multiplexing link is higher and the crosstalk is lower than the one of the OAM-MGM link under weaker turbulence condition. The main reason is due to the relatively weak turbulence strength, which introduces little mode coupling among the transmitted OAM modes. When the turbulence-induced mode coupling is weak, the power of transmitted OAM modes will mainly keep in the original modes. As shown in Figs. 4(a) and (b), the received power of both the OAM-MGM link and conventional OAM multiplexing link can achieve more than -25 dBm. The measured crosstalk of both the OAM-MGM link and conventional OAM multiplexing link are less than -15 dB. The obtained experimental results indicate that the OAM multiplexing and OAM-MGM links are little affected under weaker turbulence condition. In addition, we observe that the fluctuation range of the received power in the OAM-MGM link is lower than the conventional OAM multiplexing link, which means that by using the OAM-MGM scheme, one can mitigate random fluctuations in received power caused by atmospheric turbulence.
Fig. 4. Experimental results of the distribution and corresponding cumulative probability of the received optical power and measured crosstalk under weaker turbulence D/r0 = 1. (a) Received optical power of OAM + 3, (b) Ratio of measurements of optical power, (c) Cumulative probability of the received optical power, (d) Measured crosstalk from OAM-3 to OAM + 3, (e) Ratio of measurements of crosstalk, (f) Cumulative probability of measured crosstalk.
We then investigate the OAM-MGM link performance under moderate turbulence strength D/r0 = 2, as shown in Fig. 5. The received power and the corresponding cumulative probability of the received OAM + 3 beam for the OAM-MGM link are shown in Fig. 5(a). As shown in Fig. 5(a), we observe that OAM-MGM can improve the received power distribution and reduce the fluctuations of the receiver power, compared with the conventional OAM multiplexing links. The measured lowest received power of the OAM-MGM scheme is about 10 dB higher than that of the conventional OAM multiplexing link. In addition, we also measure the mode crosstalk and the corresponding cumulative probability of the crosstalk, as shown in Fig. 5(b). One can find that the fluctuations of the crosstalk are greatly reduced by employing OAM-MGM. Moreover, the highest crosstalk of the OAM-MGM with transmitter mode diversity is about -8 dB, which is much lower than the one without OAM mode group transmission. Thus, the proposed OAM-MGM link may have a lower interruption probability at a given detection threshold, as compared to the conventional OAM multiplexed link.
Fig. 5. Experimental results of the distribution and corresponding cumulative probability of the received optical power and measured crosstalk under moderate turbulence D/r0 = 2. (a) Received optical power of OAM + 3, (b) Ratio of measurements of optical power, (c) Cumulative probability of the received optical power, (d) Measured crosstalk from OAM-3 to OAM + 3, (e) Ratio of measurements of crosstalk, (f) Cumulative probability of measured crosstalk.
By increasing the turbulence strength to D/r0 = 4, we further characterize the statistic distribution property of the OAM-MGM link under stronger turbulence as shown in Fig. 6. From the experimental results, we can find that the average received power decreases and the crosstalk increases for both OAM-MGM and conventional OAM multiplexing links with the increasing of the turbulence strength. The received power ranges from -31 dBm to -15dBm for the OAM-MGM link, and -38 dBm to -12 dBm for the conventional OAM multiplexing link. The OAM-MGM link can still reduce the fluctuation range of the received power. However, for both two links, the average crosstalk is about -10 dB, which will cause serious degradation of the communication performance.
Fig. 6. Experimental results of the distribution and corresponding cumulative probability of the received optical power and measured crosstalk under stronger turbulence D/r0 = 4. (a) Received optical power of OAM + 3, (b) Ratio of measurements of optical power, (c) Cumulative probability of the received optical power, (d) Measured crosstalk from OAM-3 to OAM + 3, (e) Ratio of measurements of crosstalk, (f) Cumulative probability of measured crosstalk.
To evaluate the communication performance of the OAM-MGM link, we measure the BER values of the received OAM + 3 for the OAM-MGM link over 50 random turbulence realizations with a total transmitted power of 10 dBm under turbulence strength D/r0 = 1, 2, and 4. For comparison, we conduct the same measurements for the conventional OAM multiplexing link. In addition, to further investigate the system performance, we measure the BER performance as a function of the transmitted power under one example of turbulence realization for each turbulence strength. The obtained experimental results are shown in Fig. 7. Under weaker turbulence D/r0 = 1 as shown in Figs. 7(a) and (b), we find that the BER value for both the OAM-MGM link and conventional OAM multiplexing link can achieve less than the 7% forward error correction (FEC) threshold (3.8 × 10−3).
Fig. 7. (a, c, e) Measured the BER values of the received OAM + 3 for the OAM-MGM link over 50 random turbulence realizations with a total transmitted power of 10 dBm under turbulence strength D/r0 = 1, 2, and 4, respectively. (b, d, f) Measured the BER performance as a function of the transmitted power under one example turbulence realization for turbulence strength D/r0 = 1, 2, and 4, respectively.
Figure 7(c) shows the measured BER performance for the OAM-MGM link under moderate turbulence strength D/r0 = 2. One can find that the OAM-MGM link has a better BER performance and lower interruption probability compared with the conventional OAM multiplexing link. The interruption probability corresponds to the ratio where the BER exceeds the 7% FEC threshold. As shown in Fig. 7(c), compared with the conventional OAM multiplexing link, the interruption probability decreases from 28% to 4% in the OAM-MGM link. Figure 7(d) shows BER performance versus transmitted power for the OAM-MGM link and conventional OAM multiplexing link under one example of turbulence realization. By using the OAM-MGM scheme, the required transmitter power at the BER of 3.8 × 10−3 for OAM + 3 and OAM-3 is relaxed by 2 dB and 3.5 dB compared with the conventional OAM multiplexing link. Under stronger turbulence D/r0 = 4 as shown in Fig. 7(e), the interruption probability of OAM-MGM link increases to 50%, which is 4% lower than that of the conventional OAM multiplexing link. The obtained results indicate that the stronger turbulence-induced mode coupling has a serious impact on the BER performance of both OAM-MGM and conventional OAM multiplexing links.
5. Conclusion
In summary, we have proposed and demonstrated a novel OAM mode-group multiplexing scheme to increase the communication performance of FSO mode multiplexing links under turbulence without adding extra system complexity. 144 Gbit/s DMT signals are successfully transmitted with two OAM mode groups multiplexing in the FSO link under turbulence strength D/r0 = 1, 2, and 4. In our experiments, the proposed scheme helps to achieve bit-error-rate (BER) mostly less than 3.8 × 10−3 for most of the 50 turbulence realizations under weak to moderate turbulence strength (D/r0 = 1 and 2) with a total transmitted power of 10 dBm. Compared with the conventional OAM multiplexed system, the interruption probability decreases from 28% to 4% under moderate turbulence strength D/r0 = 2. The obtained simulation results show that the OAM-MGM scheme can improve the system reliability of the high-capacity mode multiplexed FSO link under atmospheric turbulence.
Funding
National Natural Science Foundation of China (12104078, 62001072); China Postdoctoral Science Foundation (2021M700561); Natural Science Foundation of Chongqing (cstc2021jcyj-bshX0223); Science and Technology Research Program of Chongqing Municipal Education Commission (KJQN201900637, KJQN202000622).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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