Open Access
Add to BibSonomy
Abstract
We propose an adaptive optics (AO) pre-compensation scheme to improve the transmission quality of orbital angular momentum (OAM) beams in atmospheric turbulence. The distortion wavefront caused by atmospheric turbulence is obtained with the Gaussian beacon from the receiver. The AO system imposes the conjugate distortion wavefront onto the outgoing OAM beams at the transmitter, tto achieve the pre-compensation. Using the scheme, we conducted transmission experiments with different OAM beams in the simulated atmospheric turbulence. The experimental results indicated that the AO pre-compensation scheme can improve the transmission quality of the OAM beams in the atmospheric turbulence in real-time. It is found that the turbulence-induced crosstalk effects on neighboring modes are reduced by an average of 6 dB, and the system power penalty is improved by an average of 12.6 dB after pre-compensation.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
In theory, there are infinite mutually orthogonal orbital angular momentum modes, and different orbital angular momentum (OAM) modes can be used as independent carriers for transmitting information. The feature enables OAM multiplexed communication systems with large capacity and high spectral efficiency [1,2]. Therefore, in recent years, the OAM multiplexing communication technology has become an effective solution to improve the communication capability, and attracted widespread attention [3–6].
Many research efforts have been devoted to increasing the transmission capacity and spectral efficiency in free-space optical (FSO) communication system by employing OAM multiplexing [4,5]. For example, multiplexing 32 OAM beams has been demonstrated in a FSO link, providing a total 2.56 Tbit/s capacity and 95.7 bits/s/Hz efficiency [7]. Reference [8] has been reported that multiplexing 26 OAM modes achieves a communication capacity of 1.036Pbit/s and a spectrum efficiency of 112.6bits/s/Hz. However, the performance of FSO communication systems is limited by atmospheric turbulence effects [9–12]. The distortion wavefront caused by atmospheric turbulence will destroy the orthogonality of the different OAM beams, resulting in the OAM mode expand to neighbor modes. It will seriously affect the performance of the FSO communication system.
An important goal for achieving the high-capacity, and high-reliability OAM multiplexing communication links in free space is to solve the atmospheric turbulence effects [4]. Currently, several methods have been proposed to suppress atmospheric turbulence effects, which can be mainly classified into signal processing techniques and adaptive optics (AO) techniques [13–21]. Signal processing techniques use channel coding and equalization methods to mitigate the effects of signal degradation, but this method is generally suitable for the relatively weak turbulence conditions and has limited ability to suppress turbulence [14–18]. Regarding AO compensation techniques, one of the way is to use a wavefront sensor (WFS) to directly measure the wavefront of the input beam for compensation, and the other is to use a phase retrieval algorithm to recover the intensity profile of the wavefront beam for compensation, such as Gerchberg-Saxton (GS) algorithm and stochastic-parallel-gradient-descent (SPGD) algorithm. AO technology can actively correct distortion wavefront and is generally considered to be the best technology for solving atmospheric turbulence effects in FSO communication links [12,19–21].
In this paper, we describe a scheme to pre-compensating OAM beams using AO techniques. We solve the atmospheric turbulence effects by pre-imposing the conjugate distorted wavefront onto the outgoing OAM beams. This scheme overcomes the difficulty of the wavefront detection caused by the phase singularities in the OAM beam. In the scheme, we use a WFS and a deformable mirror (DM) we developed, so that it has better real-time compensation performance than the without WFS-based AO system. Based on this scheme, our experimental results on the OAM beams transmission in simulated atmospheric turbulence indicate that the crosstalk effect of the OAM modes is reduced by an average of 6 dB by AO pre-compensation. Meanwhile, our experimental results under dynamic turbulence also show that the scheme can suppress the atmospheric turbulence effects in real time and reduce the power loss of the system by an average of 12.6 dB.
2. Methods
Atmospheric turbulence effects are caused by changes in the local temperature and pressure of the atmosphere, which leads to changes in the refractive index of the atmosphere. When the beam propagates in atmospheric turbulence, the wavefront will distort, causing dispersion, jitter, and drift of the light spot [11,22]. Atmospheric turbulence effects are extremely harmful to the OAM communication links that rely on different helical wavefront structures. Therefore, it is significance to compensate the distortion wavefront caused by atmospheric turbulence effects. Due to the OAM beam has a phase singularity, and the central intensity distribution of the spot is zero. It results in that the distorted wavefront cannot be directly obtained by using the traditional WFS [23,24]. The AO system without WFS seems to be able to resolve the phase singularity of the OAM beam, but the distortion wavefront caused by the atmospheric turbulence effects is random and variable. However, the AO system without WFS needs some iterative calculations, which will make it difficult to ensure the real-time performance of the system compensation [25,26]. To solve above problems, we have made some changes in the AO system based on the WFS, and proposed an AO pre-compensation scheme.
Figure 1 shows our scheme for turbulence pre-compensation of OAM beams. A Gaussian beacon beam is emitted at the receiver, which is transmitted through the free space with atmospheric turbulence and then enters the transmitter. At the transmitter, we build an AO pre-compensation system. It can detect the distorted Gaussian beacon wavefront through a WFS, and then uses a feedback controller to control the wavefront compensator in real time to generate a conjugated distorted wavefront. The outgoing OAM beam propagates in the opposite direction to the incident beacon, and after transmitting through the wavefront compensator, it will carry a conjugated distorted wavefront. After the preprocessed OAM beam is transmitted through the atmospheric turbulence, the distortion wavefront will cancel the turbulent effect. This not only solves the difficult problem of phase detection of the OAM beam’s wavefront, but also ensures the real-time performance of the system. Meanwhile, since the Gaussian beacon is independent from the OAM beams, it will not affect the reception and demultiplexing of the OAM beams. In addition, compensation of the OAM beams at the transmitter has certain advantages over compensation at the receiver, because the uncompensated OAM beams may become diffuse and tilted due to turbulence, and these will cause more trouble for the accurate reception of the OAM beam in the receiver.
An experimental setup of the scheme is shown in Fig. 2. In the transmitter, the AO module is used to achieve the pre-compensation of the OAM beams. The Gaussian beacon beam carrying the turbulent distortion wavefront enters to the AO pre-compensation system after passing through the Expander 2(Exp-2), and then passes through the fast mirror (FS), the wavefront compensator, the Expander 1(Exp-1), and the beam splitter (BS), and finally enters the WFS. For the WFS, we used a typical Shack-Hartmann sensor (SH-WFS) with 12 × 12 sub-aperture micro-lens array, which can detect the distorted wavefront of the Gaussian beacon at the frequency of 1.6kHz. The feedback controller controls the wavefront compensator to generate a conjugated distorted wavefront through the distorted wavefront information. Our wavefront compensator uses a continuous surface deformable mirror (DM) made by us with 137 separated piezoelectric actuators. The size of the wavefront compensator is 10 cm × 6 cm × 6 cm. The stroke of the DM is 2µm, and the wavefront compensation frequency can exceed 4 kHz. In addition, considering the small stroke of the DM, we added a fast mirror to compensate for the low-order tip-tilt error, and the low-order tip-tilt error can be obtained from the SH-WFS. The DM is mainly used to compensate for the other high-order errors.
Fig. 2. Optical layout of experimental setup. SLM: spatial light modulator, Pol.: polarizer, BS: beam splitter, Dia.: diaphragm, Col.: collimator, EXP: expander, M: mirror, FS: fast mirror, DM: deformable mirror, FC: Fiber coupler, SH-WFS: Shack Hartmann wavefront sensor, CAM: camera.
Another part of the transmitter is responsible for generating the OAM beams. After the laser in the single-mode fiber (SMF) passes through the collimator and aperture diaphragm, it outputs a collimated Gaussian beam with a diameter of 5 mm. After passing through a beam splitter (BS) and a polarizer, it is incident to the space light modulator (SLM) imposed with a specific blazed fork grating hologram. By the SLM, the Gaussian beam is converted into the OAM beam. Both the SLM-1 and the SLM-2 are reflective liquid crystal spatial light modulators with a resolution of 1920 × 1152 pixels. After the OAM beam enter the AO pre-compensation system, it will propagate in the opposite direction of the Gaussian beacon. Then the conjugated atmospheric turbulence distortion wavefront will be imposed, it enters the free space with atmospheric turbulence through the Exp-2 for transmission.
In the experiment, we placed a pseudo-random Kolmogorov phase plate in the main optical path to simulate atmospheric turbulence effects. The turbulence phase plate has several annular regions with different ${r_0}$ (atmospheric coherence length), and in our experiments we use the outermost ring area (${r_0}$= 1 mm). In order simulate the actual changing atmospheric turbulence environment, we mount the phase plate on a rotating device that can vary the speed.
The pre-compensated OAM beam is transmitted through the turbulence simulator and then enters the receiver. Part of the beam enters the camera after passing through the BS and the lens, and is used to observe the far-field image of the OAM beam. The other part of the beam is directly incident to the SLM imposed with the helical phase hologram opposite to the OAM beam to be back-converted after passing through the BS and polarizer, and finally enters the SMF through the fiber coupler (FC).
3. Experimental results
Using the experimental scheme described in Section 2, we performed separate transmission experiments for different OAM beams. Firstly, we conducted the experiment in a specific turbulent environment. The turbulence simulator remains stationary and the wavefront distortion of the beam is fixed. In this case, the cross-sectional diameter of the beams passing through the turbulence phase plate is about 10 mm ($D/{r_0}$ = 10), and the AO pre-compensation system can improve the root mean square (RMS) of the Gaussian beacon wavefront from 0.668λto 0.043λ. We monitored the far-field intensity distributions of the Gaussian beam(l = 0) and different OAM beams (l = 2,4,6,8,10) without and with pre-compensation in the receiver side. The results are shown in Fig. 3(b)(1)-b(6) and c(1)-c(6). In order to better illustrate the experimental effect, we also measured the beam generated by the SLM-1. The results are shown in Fig. 3(a)(1)-a(6). From the far-field images, it can be found that the quality of the beams is well improved after AO pre-compensation.
Fig. 3. Far-field intensity images of the Gaussian beam and OAM beams (l = 2,4,6,8,10) without turbulence a(1)-a(6), without pre-compensation b(1)-b(6), and with pre-compensation c(1)-c(6).
Furthermore, we also made some supplements to the above experiments. After propagating through the above static turbulence simulator, we back-converted above mentioned multiple OAM beams in the receiver by imposing the reversed helical phase through the SLM-2. The far-field intensity images of the back-converted OAM beams without pre-compensation are shown in Fig. 4(a1)-(a5), and the back-converted intensity images with pre-compensation are shown in Fig. 4(b1)-(b5). We can see that the pre-compensation effect is obviously. For instance, the intensity image of distorted back-converted beams without pre-compensation become very messy, while bright spots at the center can be clearly seen with the pre-compensated.
Fig. 4. Far-field intensity images of the back-converted OAM beams ($l = 2,\; 4,\; 6,\; 8,\; 10$) without pre-compensation a(1)-a(6) and with pre-compensation b(1)-b(6).
Figure 5(a) shows the normalized power of the OAM modes (l = 4 and 10) in the adjacent four modes (OAM + 4 and OAM + 10 transmitted separately). With the pre-correction, the normalized power of mode l = 4 is increased from 0.28 to 0.84, and the normalized power of mode l = 10 is increased from 0.27 to 0.78. Figure 5(b) further shows the crosstalk with adjacent modes for the above five OAM modes (l = 2,4,6,8,10). The crosstalk mentioned in this paper is the percentage of the power that the target OAM mode extends to adjacent four modes, and each OAM mode is also transmitted separately. For example, for OAM + 6, at the receiver, we counted the power of its extension to the four nearby modes (OAM + 4, OAM + 5, OAM + 7 and OAM + 6). The Crosstalk can be expressed as (P4 + P5 + P7 + P8) / PSUM(4,5,6,7,8). It can be seen that the crosstalk effect between adjacent OAM modes can be effectively reduced by pre-compensation. It is found that the crosstalk is reduced by an average of 6 dB with pre-compensation.
Fig. 5. (a) Normalized power spectrum of the OAM modes (l = 4and 10) between the adjacent four modes. (b) Crosstalk of OAM modes (l = 2,4,6,8,10) onto the adjacent modes.
Because the actual atmospheric turbulence effect is not static, but changes randomly. In order to further verify the effectiveness of the scheme in the actual atmospheric turbulence environment, we also carried out the transmission experiment of the OAM beams in the simulated dynamic turbulent environment. We let the turbulence simulator rotate at 500 rpm to represent the dynamically changing turbulence. At this point, the AO pre-compensation system can reduce the RMS of the Gaussian beacon from 0.856λ to 0.072λ Then, we respectively performed real-time pre-compensation for the modes l = 6 and l = 10. The experimental results are shown in Fig. 6. After the pre-compensation, the power of modes l = 6 and l = 10 both are significantly improved. The loss of power is reduced by an average of 12.6 dB, indicating that the pre-compensation scheme can effectively correct the atmospheric turbulence in real time.
Fig. 6. (a) Received power variation of the OAM mode l = 6 before and after pre-compensation. (b) Received power variation of the OAM mode l = 10 before and after pre-compensation.
4. Conclusion
In conclusion, an AO pre-compensation scheme is suggested to correct the atmospheric turbulence effects for the OAM beams, in which a Gaussian beacon beam is used to get the distortion wavefront of the atmospheric turbulence. Then the conjugate distortion wavefront will be pre-imposed on the outgoing OAM beams in transmitter to cancel the turbulent effect during the transmission. By using the scheme, we conducted experiments on the various OAM beams in the simulated atmospheric turbulent environment. The experimental results show that the scheme has significant effect. After pre-compensation, the crosstalk between adjacent modes of the OAM beam is reduced by an average of 6 dB, and the power loss is reduced by an average of 12.6 dB. The scheme is very useful for the future high-speed OAM communication links to ensure their reliability.
Funding
National Natural Science Foundation of China (61901449).
Acknowledgments
The authors acknowledge the support from the National Science Foundation of China (grant number 61901449).
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.
References
1. Y. J. Shen, X. J. Wang, and Z. W. Xie, “Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities,” Light: Sci. Appl. 8(1), 29 (2019). [CrossRef]
2. L. Zhu and J. Wang, “A review of multiple optical vortices generation: methods and applications,” Front. Optoelectron. 12(1), 17–68 (2019). [CrossRef]
3. A. E. Willner, Y. X. Ren, and G. D. Xie, “Recent advances in high-capacity free-space optical and radio-frequency communications using orbital angular momentum multiplexing,” Philos. Trans. R. Soc., A 375(2087), 20150439 (2017). [CrossRef]
4. A. Trichili, K. H. Park, and M. Zghal, “Communicating Using Spatial Mode Multiplexing: Potentials, Challenges and Perspectives,” IEEE Commun. Surv. Tutorials 21(4), 3175–3203 (2019). [CrossRef]
5. A. E. Willner, Z. Zhao, and C. Liu, “Perspectives on advances in high-capacity, free-space communications using multiplexing of orbital-angular-momentum beams,” APL Photonics 6(3), 030901 (2021). [CrossRef]
6. J. Liu, J. Zhang, and J. Liu, “1-Pbps orbital angular momentum fibre-optic transmission,” Light: Sci. Appl. 11(1), 202 (2022). [CrossRef]
7. J. Wang, J. Y. Yang, and I. M. Fazal, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012). [CrossRef]
8. J. Wang, S. H. Li, and M Luo, “N-dimentional multiplexing link with 1.036-Pbit/s transmission capacity and 112.6-bit/s/Hz spectral efficiency using OFDM-8QAM signals over 368 WDM pol-muxed 26 OAM modes,” European Conference on Optical Communication (ECOC, 2014), pp. 1–3.
9. A. Belmonte and J. M. Kahn, “Capacity of coherent free-space optical links using diversity-combining techniques,” Opt. Express 17(15), 12601–12611 (2009). [CrossRef]
10. M. Malik, M. O’Sullivan, and B. Rodenburg, “Influence of atmospheric turbulence on optical communications using orbital angular momentum for encoding,” Opt. Express 20(12), 13195–13200 (2012). [CrossRef]
11. Y. Ren, H. Huang, and G. Xie, “Atmospheric turbulence effects on the performance of a free space optical link employing orbital angular momentum multiplexing,” Opt. Lett. 38(20), 4062–4065 (2013). [CrossRef]
12. C. Liu, M. Chen, and S. Q. Chen, “Adaptive optics for the free-space coherent optical communications,” Opt. Commun. 361, 21–24 (2016). [CrossRef]
13. S. H. Li, S. Chen, and C. Q. Gao, “Atmospheric turbulence compensation in orbital angular momentum communications: Advances and perspectives,” Opt. Commun. 408, 68–81 (2018). [CrossRef]
14. I. B. Djordjevic and M. Arabaci, “LDPC-coded orbital angular momentum (OAM) modulation for free-space optical communication,” Opt. Express 18(24), 24722–24728 (2010). [CrossRef]
15. Y. Zhang, P. Wang, and L. Guo, “Performance analysis of an OAM multiplexing-based MIMO FSO system over atmospheric turbulence using space-time coding with channel estimation,” Opt. Express 25(17), 19995–20011 (2017). [CrossRef]
16. E. M. Amhoud, A. Trichili, and B. S. Ooi, “OAM Mode Selection and Space–Time Coding for Atmospheric Turbulence Mitigation in FSO Communication,” IEEE Access 7, 88049–88057 (2019). [CrossRef]
17. H. Song, L. Li, and K. Pang, “Demonstration of using two aperture pairs combined with multiple-mode receivers and MIMO signal processing for enhanced tolerance to turbulence and misalignment in a 10 Gbit/s QPSK FSO link,” Opt. Lett. 45(11), 3042–3045 (2020). [CrossRef]
18. L. Li, H. Song, and R. Zhang, “Increasing system tolerance to turbulence in a 100-Gbit/s QPSK free-space optical link using both mode and space diversity,” Opt. Commun. 480, 126488 (2021). [CrossRef]
19. M. Chen, C. Liu, and D. M. Rui, “Experimental results of 5-Gbps free-space coherent optical communications with adaptive optics,” Opt. Commun. 418, 115–119 (2018). [CrossRef]
20. H. C. Zhan, L. Wang, and Q. Peng, “Progress in adaptive optics wavefront correction technology of vortex beam,” Infrared Laser Eng. 50(9), 20210428 (2021).
21. L. Jiang, Z. S. Dai, and X. Yu, “Experimental Demonstration of a Single-Mode Fiber Coupling Over a 1 km Urban Path with Adaptive Optics,” J. Russ. Laser Res. 42(3), 363–370 (2021). [CrossRef]
22. G. A. Tyler and R. W. Boyd, “Influence of atmospheric turbulence on the propagation of quantum states of light carrying orbital angular momentum,” Opt. Lett. 34(2), 142–144 (2009). [CrossRef]
23. K. Murphy, D. Burke, and N. Devaney, “Experimental detection of optical vortices with a Shack-Hartmann wavefront sensor,” Opt. Express 18(15), 15448 (2010). [CrossRef]
24. C. Huang, H. Huang, and H. Toyoda, “Correlation matching method for high-precision position detection of optical vortex using Shack-Hartmann wavefront sensor,” Opt. Express 20(24), 26099–26109 (2012). [CrossRef]
25. G. Xie, Y. Ren, and H. Huang, “Phase correction for a distorted orbital angular momentum beam using a Zernike polynomials-based stochastic-parallel-gradient-descent algorithm,” Opt. Lett. 40(7), 1197–1200 (2015). [CrossRef]
26. X. Z. Ke and X. Y. Wang, “Experimental Study on the Correction of Wavefront Distortion for Vortex Beam,” Guangxue Xuebao 38(3), 0328018 (2018). [CrossRef]
