Open Access
Add to BibSonomy
Abstract
Free space optical (FSO) communication has gained widespread attention due to its advantages, including high confidentiality, high communication capacity, and no limitation of spectrum. One of the great challenges in FSO communication is the transmission performance degradation in atmospheric turbulence channel due to wavefront distortion and scintillation. Here, we proposed and experimentally demonstrated a 120 Gbit/s vector beam multiplexed coherent optical communication system with turbulence-resilient capacity. Four multiplexed vector beams, each carrying a 30 Gbit/s quadrature phase-shift keying signal, propagate through different turbulence conditions. The influence of turbulence channel on the vector beam impairments is experimentally investigated. Under the weaker turbulence conditions, the system bit error rates are below the forward error correction threshold of 3.8 × 10−3. In comparison with the Gaussian mode, the communication interruption probability of the vector beams system decreases from 36% to 12%-18% under stronger turbulence conditions.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Compared with traditional radio frequency communication, free space optical (FSO) communication possesses unique and outstanding advantages such as heightened security, no spectrum limitations, and high data capacity [1–3]. However, the main challenge limiting the further development of FSO communication applications, such as unmanned aerial vehicles communication [4], satellite-terrestrial communication [5], and deep space exploration [6], is the inevitable transmission performance degradation impaired by atmospheric turbulence channel due to wavefront distortion and scintillation [7]. Therefore, turbulence-resistant communication techniques in free-space channels have garnered significant attention in recent years [8–12]. Traditional turbulence-resistant technologies comprise multiple-input-multiple-output (MIMO) electronic channel-equalization digital-signal-processing (DSP) algorithms [13,14], adaptive optics (AO) [15–17], and beam shaping [18–20]. Nevertheless, the practical implementation of MIMO and AO technologies is limited due to the complexity of system design and excessive cost involved. By the pre-modulation of phase and/or polarization distribution of transmitted light, beam shaping technology enables turbulence-resistant transmission through atmospheric turbulence link in a passive way.
Vector beams with spatially varying polarization distribution have been reported as exhibiting a unique polarization profile that enhances the beams’ resilience in atmosphere turbulence, enabling turbulence-resistant communication [21–26]. Specifically, the intensity distributions of vector light can be superimposed with two orthogonal polarized lights without interference. Given that turbulence may perturb one polarization more significantly than the orthogonal polarization, the stability of the intensity distribution in vector light is maintained [27–29]. While both scalar vortex beams and vector vortex beams are toroidal structures, it’s essential to note that vector vortex beams possess inhomogeneous polarization distribution properties, rendering them akin to partially coherent beams in their ability to withstand atmospheric turbulence [27,30]. Moreover, it has also been experimentally demonstrated that vector modes exhibit a higher overall fidelity than scalar modes, underscoring their superior resilience to atmospheric turbulence [31]. In recent years, there have been numerous studies and applications reported on vector optical fields in atmospheric turbulence. Particularly, radially polarized beams could exhibit lower scintillation rates than scalar vortex beams under turbulent conditions, suggesting the potential of vector vortex beams in mitigating the effects of atmospheric turbulence [32]. Furthermore, the orthogonal characteristics among cylindrical vector beams could enable the increase of communication capacity through mode division multiplexing (MDM) [33–41]. Despite related research conducted to expand communication capacity based on vector beam multiplexing, the impact of atmospheric turbulence on the performance of free-space multiplexed vector optical communication systems has rarely been reported.
In this paper, we proposed and experimentally demonstrated a free-space turbulence-resistant communication using MDM technology, specifically utilizing four cylindrical vector beams multiplexing within a single wavelength channel. In the experiment, each vector mode carried a 30 Gbit/s quadrature phase-shift keying (QPSK) signal, and the multiplexed beam was transmitted through a free-space channel over a distance of 10 m, with an atmospheric turbulence simulator placed between the transmitter and receiver. We experimentally investigated the effect of turbulence channels on vector beam degradation. Under weaker and stronger turbulence conditions, the system’s bit error rate (BER) is essentially below the forward error correction (FEC) threshold of 3.8 × 10−3. The experimental results demonstrate that the interruption probability of the Gaussian mode is two to three times greater than that of the vector mode under stronger turbulence conditions. Our results show communication stability under varying turbulence intensities, with the four vector modes exhibiting superior turbulence resistance when compared to the Gaussian mode under stronger turbulence.
2. Principles and experimental setup
In our experiments, a vortex half-wave plate (VHP) made of liquid crystal polymer with birefringence is employed to generate vector beams. The fast-axis orientation is consistent along the radial direction of the substrate, with a continuous gradient along the angular direction of the substrate, which is specifically followed [23]:
where $\theta$ is the fast axis direction at a certain azimuth angle, m represents the order number, $\psi$ is the azimuth angle, and $\sigma$ indicates the fast axis direction when $\psi = 0$. The Jones matrix ${J_{m,\sigma }}$ of the VHP, with its fast axis oriented in the direction $\theta$, can be expressed as [42]:Here, cylindrical vector beams are generated using VHP with $m \in \{ 1,2\}$. When the incident beam is horizontally polarized with the Jones vector ${E_{/{/}}} = {[{1,0} ]^T}$, for the 1st-order VHP $({m = 1,\sigma = 0} )$ and the 2st-order VHP $({m = 2,\sigma = 0} )$, the Jones vectors of the transmitted beam are expressed as:
When the incident beam is vertically polarized with the Jones vector ${E_ \bot } = {[{0,1} ]^T}$, for the 1st-order VHP $({m = 1,\sigma = 0} )$ and the 2st-order VHP $({m = 2,\sigma = 0} )$, the Jones vectors of the transmitted beam are expressed as:
To clarify, we denote the above four cylindrical vector beams as VB1H, VB1V, VB2H and VB2V, respectively, in the following parts.
Figure 1 depicts the experimental setup of four cylindrical vector beams multiplexed turbulence-resistant FSO communication system. At the transmitter, an optical carrier from a continuous wave laser (1550 nm) is modulated by a 15 GBaud QPSK signal using an I-Q modulator. The QPSK signal is generated by an arbitrary waveform generator (AWG, Keysight, M8195A) operating at a sampling rate of 65 GSa/s. The optical signal is then amplified with an erbium-doped fiber amplifier (EDFA, OVERLINK, EDFA-C-LA-20-SM-B) to control the output power at the transmitter side. The optical signal is split into four paths using three fiber couplers (FC), and polarization controllers (PC) are utilized to control the power of each channel after passing through the linear polarizer (LP). Each optical signal then passes through varying lengths of fiber delay lines (DL) for decorrelation, which is then collimated into free space and converted into different cylindrical vector beams through collimator, LP, and VHP, respectively. Specifically, LP1, LP2, and VHP1 $({m = 1,\sigma = 0} )$ are employed to generate two first-order cylindrical vector beams, denoted as VB1H and VB1V with horizontal and vertical orthogonal polarizations. Similarly, LP3, LP4, and VHP2 $({m = 2,\sigma = 0} )$ are used to generate two second-order cylindrical vector beams, referred to as VB2H and VB2V, with horizontal and vertical orthogonal polarizations. The four vector light beams are then transmitted co-axially using beam splitter (BS). After a 20× beam expander, a collimated multiplexed vector beam with a beam waist D of 6 cm is emitted for transmission over a 10 m free-space channel.
Fig. 1. Experimental setup of vector multiplexing coherent communication: CW Laser, continuous wave laser; IQM, I-Q modulator; AWG, arbitrary waveform generator; EDFA, erbium-doped fiber amplifier; FC, fiber coupler; PC, polarization controller; DL, fiber delay line; Col, collimator; LP, linear polarizer; BS, non-polarizing beam splitter; VHP, vortex half-wave plate; Tel., telescope; Turb., hot air convection atmospheric turbulence simulator; VOA, variable optical attenuator; IQD., coherent receiver; DSP, offline digital signal processing; LO, local oscillation laser.
An enclosed hot air convection atmospheric turbulence simulator, measuring 3 m in length, is placed in the transmission link to simulate actual atmospheric turbulence. The temperature difference T between the upper layer and the lower layer of the simulator controls the changes in the Fried parameter r0 [43,44]. In our experiments, adjusting the temperature difference T from 20°C to 140°C resulted in a reduction of r0 from 6 cm to 1 cm. Therefore, the turbulence strength can be characterized by D/r0, corresponding to 1 to 6, where higher values indicate stronger turbulence intensity. After transmitting through a 10-m free-space link, the vector beam is collected by a 10× beam reduction telescope at the receiver. After beam splitting, the multiplexed vector beam is then demodulated with VHP and LP and coupled into a single-mode fiber (SMF). To demodulate the multiplexed beams, we use VHP1 for the demodulation of the 1st-order vector beams, and then use a linear polarizer to select one of the vector beams for coupling into the fiber. Similarly, the demodulation of the 2nd-order vector beam is realized with the use of VHP2. In our experiment, optical field capture and demodulation of a single vector beam are implemented by rotating the LP and replacing VHP1 and VHP2 one at a time, and the transmission performance of each vector beam is analyzed. After passing through a variable optical attenuator (VOA), the demodulated signal is received by a coherent receiver (IQD). It is then collected by a real-time oscilloscope and subsequently processed using DSP. Finally, the BER and error vector magnitude (EVM) of the system are calculated to evaluate the transmission performance of the system. Figure 2 presents the four captured vector light field profiles generated at the transmitter side in the experiment. Additionally, the light filed profiles of vector beams with different polarizations are also captured after passing through the linear polarizer (LP), which are shown in different columns of Fig. 2.
In the experiment, four vector beams were generated and multiplexed for transmission simultaneously. Figures 3(a) and 3(b) present the beam intensity profile after combining two first-order cylindrical vector lights and two second-order cylindrical vector lights, respectively, and Fig. 3(c) shows the image after combining all four cylindrical vector lights.
Fig. 3. Multiplexed light optical field for (a) two multiplexed first-order cylindrical vector light field; (b) two multiplexed second-order cylindrical vector light field, and (c) four multiplexed cylindrical vector light field images.
3. Results and discussion
To provide an intuitive characterization of the turbulence-resistant performance of the vector mode, we present an evaluation of the optical field distribution at the receiver side for four beam vectors multiplexed FSO communication under different turbulence conditions together with the comparison of Gaussian beam. Figure 4 displays the intensity distribution of the optical field captured by CCD. The results show that the optical fields of the vector mode and Gaussian mode are nearly unaffected in weaker turbulence (D/r0 ≈ 1), where the intensity distribution of the light field remains similar to that in the absence of turbulence. As turbulence intensity increases, the optical fields for all beams begin to deteriorate. However, under stronger turbulence (D/r0 ≈ 6), the four cylindrical vector fields are less affected and maintain the relatively stable distribution of the light field with hollow-hole type, while the Gaussian optical field suffers from severe deterioration. The variation of the optical field at the receiver side with different turbulence intensities verify the unique turbulence-resistant performance exhibited by the vector beams.
Fig. 4. Evolution of light optical fields for (a)VB1H, (b) VB1V, (c) VB2H, (d) VB2V, (e) Gauss in the experiment with different turbulence conditions.
To evaluate the communication performance of the system, we first measured the BER of four individual vector optical signals and Gaussian optical signal at different received optical power (ROP) in the absence of turbulence. All of the BER results were measured under multiplexing transmission conditions considering the influences of inter-modal crosstalk. In particular, to obtain the communication BER of the Gaussian beam as the reference, we multiplexed two Gaussian beams with polarizations orthogonal to each other and used a line polarizer to select one of the Gaussian beams at the receiver side. Comparison experiments are performed with four vector beams multiplexed communication. The ROP is controlled by adjusting the VOA at the receiver. As shown in Fig. 5, at a BER of approximately the hard-decision forward error correction (HD-FEC) threshold, the ROP between different modes does not precisely match, exhibiting a deviation of approximately 2 dB. This is owing to the random experimental measurement fluctuations caused by the instability of the measuring instruments and the environmental interference. Simultaneously, different vector beams have different degrees of pointing error at the receiver end, leading to inconsistent coupled power fluctuations. Therefore, there is a certain extent of variation in BER performance of each beam, but the overall trend of the data and the order of magnitude of the BER are consistent under no turbulence condition. The BERs of all cylindrical vector mode and Gaussian mode reached the HD-FEC threshold when ROP are around −35 dBm, which indicate that the communication performance of Gaussian mode and four cylindrical vector modes were essentially the same in the absence of turbulence. The insets in Fig. 5 depict the demodulated constellation diagram and their corresponding EVM values for different ROP cases. When ROP is approximately equal to −38 dBm, the BER reaches 0.3, and the EVM value exceeds 40%. At this point, normal communication cannot be achieved. In Fig. 5(b), for ROP around −35 dBm, the BER approaches the HD-FEC limit, and the EVM value is 35.77%. In Fig. 5(c), when ROP is approximately −28 dBm, the BER is in the order of 10−4, and the EVM value is 17.85%, which reveals excellent communication performance under this condition.
Next, we introduced different simulated turbulence strengths into the transmission link to validate the turbulence-resistant performance of the generated four cylindrical vector beams. Figures 6(a-e) show the measured BER values for the four cylindrical vector beams and Gauss beam under 100 random realizations without turbulence and with weaker turbulence. The experimental results indicate that the Gaussian and four vector modes have similar transmission performance in both turbulence-free and weaker turbulence conditions. Figure 6(f) presents the statistical results of BER fluctuations for these beams under weaker turbulence conditions. Among them, the longer the green box section, the more instability of the communication performance. It can be observed that in weaker turbulence, the measured BERs for all beams are always below FEC threshold, with an average value of approximately 1.8 × 10−4 for all realizations. The statistical results indicate that under weaker turbulence conditions, the turbulence has an ignorable impact on the communication performance of both vector and Gaussian modes.
Fig. 6. Experimentally measured BER under weaker turbulence (D/r0 ≈ 1) over 100 different emulated turbulence random realizations for (a) VB1H, (b) VB1V, (c) Gauss, (d) VB2H, (e) VB2V. (f) Statistical distribution of BER for all beams.
Figure 7 shows the BER fluctuations for the Gaussian and vector modes in both turbulence-free and stronger turbulent conditions under 100 random turbulence realizations. The distribution of BERs for all beams among the 100 groups indicates that the performance of these beams is degraded due to the stronger atmospheric turbulence, while Gaussian mode has the highest probability of BER values that above the HD-FEC threshold out of 100 measurements. The probability statistics of BER distribution in Fig. 7(f) show that the fluctuation range of BER for vector mode communication is much smaller than that of Gaussian mode communication under stronger turbulence, indicating that the vector mode has better turbulence-resistance ability. Figure 7(g) presents a comparison of probability statistics among different cylindrical vector modes, revealing that these modes exhibit similar communication transmission performance under stronger turbulence conditions.
Fig. 7. Experimentally measured BER under stronger turbulence (D/r0 ≈ 6) over 100 different emulated turbulence random realizations for (a) VB1H, (b) VB1V, (c) Gauss, (d) VB2H, (e) VB2V. (f) Statistical distribution of BER for all beams; (g) Comparison of vector modes probability statistics.
Subsequently, we quantitatively evaluated the turbulence resistance of the vector beams by calculating the probability of communication interruption for each beam with the turbulence strength at D/r0 ≈ 4 and D/r0 ≈ 6. Here, communication with a BER higher than the HD-FEC threshold is considered as an interruption, and the interruption probability is calculated as the ratio of the times of interruptions over the total number of measurements. As depicted in Fig. 8, at moderate strong turbulence (D/r0 ≈ 4), the interruption probabilities for vector mode communication are 4%, 5%, 3%, and 6%, respectively, while the interruption probability for Gaussian mode communication is raised to 20%. Furthermore, at stronger turbulence (D/r0 ≈ 6), the communication interruption rations for the four vector modes are increased to 18%, 12%, 12%, and 11%, respectively, compared to a 36% interruption rate for Gaussian communication. The communication interruption probability of four vector beams remains lower than that of the Gaussian beam even in the presence of stronger turbulence, indicating that the vector mode demonstrates greater robustness for turbulence-resistant communication.
Fig. 8. Interruption probability at turbulence intensities of (a) moderate turbulence (D/r0 ≈4), (b) stronger turbulence (D/r0 ≈ 6).
4. Conclusion
In this paper, a 120 Gbit/s-QPSK optical transmission system employing four vector beams multiplexed is successfully demonstrated under different atmospheric turbulence conditions in a 10-m free-space channel. By applying vector beams, the transmission performance of the FSO system in atmospheric turbulence is enhanced. The communication BERs are measured for each beam in 100 consecutive times under the same turbulence condition. As the turbulence intensity increased, the BER of Gaussian beam fluctuated the most and the average BER was higher than that of all the four vector beams. Moreover, under stronger turbulence condition, the communication interruption probability for the Gaussian mode is 36%, which is two to three times higher than that for the four vector beams. Finally, the optical field analysis further corroborates the good turbulence stability of vector mode compared to Gaussian mode. Compared with other turbulence-resistant techniques, vector optical field manipulation can not only improve the communication quality of the system in atmospheric turbulence, but also enhance the transmission capacity of the communication system by spatial mode multiplexing, which provides a new way for the development of high-speed FSO systems.
In the future, it is still necessary to explore the effect of turbulence-resistant communication with different modes of vector beam in long-range real atmospheric turbulence environment. Different modes of vector light can be generated by vector light field modulation [45], and their different anti-turbulence capabilities show great potential for application in FSO communication systems. Combined with large-aperture optical systems, such as planar digital optics [46], it is expected to realize the verification of long-distance and large-capacity vector multiplexing turbulence-resistant communication under real atmospheric turbulence environment.
Funding
National Natural Science Foundation of China (62105338, U20A20217); Sichuan Science and Technology Program (2021ZYCD001).
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. V. W. S. Chan, “Free-space optical communications,” J. Lightwave Technol. 24(12), 4750–4762 (2006). [CrossRef]
2. M. A. Khalighi and M. Uysal, “Survey on free space optical communication: A communication theory perspective,” IEEE Commun. Surv. Tutorials 16(4), 2231–2258 (2014). [CrossRef]
3. K. Anbarasi, C. Hemanth, and R. G. Sangeetha, “A review on channel models in free space optical communication systems,” Opt. Laser Technol. 97, 161–171 (2017). [CrossRef]
4. J. H. Lee, K. H. Park, Y. C. Ko, et al., “A UAV-mounted free space optical communication: Trajectory optimization for flight time,” IEEE Trans. Wirel. Commun. 19(3), 1610–1621 (2020). [CrossRef]
5. Z. Hu, D. Jiang, X. Liu, et al., “Performance research on flat-topped beam-based small satellites free space optical communication,” Opt. Commun. 487, 126802 (2021). [CrossRef]
6. W. Wu, M. Chen, Z. Zhang, et al., “Overview of deep space laser communication,” Sci. China Inf. Sci. 61(4), 040301 (2018). [CrossRef]
7. H. Kaushal and G. Kaddoum, “Optical communication in space: Challenges and mitigation techniques,” IEEE Commun. Surv. Tutorials 19(1), 57–96 (2017). [CrossRef]
8. H. Song, H. Song, R. Zhang, et al., “Experimental mitigation of atmospheric turbulence effect using pre-signal combining for uni- and bi-directional free-space optical links with two 100-Gbit/s OAM-multiplexed channels,” J. Lightwave Technol. 38(1), 82–89 (2020). [CrossRef]
9. Z. Zhu, M. Janasik, A. Fyffe, et al., “Compensation-free high-dimensional free-space optical communication using turbulence-resilient vector beams,” Nat. Commun. 12(1), 1666 (2021). [CrossRef]
10. H. Zhou, R. Zhang, H. Song, et al., “Demonstration of turbulence resiliency in a mode-, polarization-, and wavelength-multiplexed free-space optical link using pilot-assisted optoelectronic beam mixing,” J. Lightwave Technol. 40(3), 588–596 (2022). [CrossRef]
11. R. Zhang, N. Hu, H. Zhou, et al., “Turbulence-resilient pilot-assisted self-coherent free-space optical communications using automatic optoelectronic mixing of many modes,” Nat. Photonics 15(10), 743–750 (2021). [CrossRef]
12. I. Nape, K. Singh, A. Klug, et al., “Revealing the invariance of vectorial structured light in complex media,” Nat. Photonics 16(7), 538–546 (2022). [CrossRef]
13. H. Huang, Y. Cao, G. Xie, et al., “Crosstalk mitigation in a free-space orbital angular momentum multiplexed communication link using 4×4 MIMO equalization,” Opt. Lett. 39(15), 4360–4363 (2014). [CrossRef]
14. L. Li, R. Zhang, P. Liao, et al., “Mitigation for turbulence effects in a 40-Gbit/s orbital-angular-momentum-multiplexed free-space optical link between a ground station and a retro-reflecting UAV using MIMO equalization,” Opt. Lett. 44(21), 5181–5184 (2019). [CrossRef]
15. Y. Ren, G. Xie, H. Huang, et al., “Adaptive optics compensation of multiple orbital angular momentum beams propagating through emulated atmospheric turbulence,” Opt. Lett. 39(10), 2845–2848 (2014). [CrossRef]
16. Y. Ren, G. Xie, H. Huang, et al., “Adaptive-optics-based simultaneous pre- and post-turbulence compensation of multiple orbital-angular-momentum beams in a bidirectional free-space optical link,” Optica 1(6), 376–382 (2014). [CrossRef]
17. Y. Guo, L. Zhong, L. Min, et al., “Adaptive optics based on machine learning: a review,” Opto-Electron. Adv. 5(7), 200082 (2022). [CrossRef]
18. J. Nie, L. Tian, H. Wang, et al., “Adaptive beam shaping for enhanced underwater wireless optical communication,” Opt. Express 29(17), 26404–26417 (2021). [CrossRef]
19. Y.-H. Huang, S.-W. Ko, M.-S. Li, et al., “Modulation of shape and polarization of beam using a liquid crystal q-plate that is fabricated via photo-alignment,” Opt. Express 21(9), 10954–10961 (2013). [CrossRef]
20. F. Bouchard, H. Larocque, A. M. Yao, et al., “Polarization shaping for control of nonlinear propagation,” Phys. Rev. Lett. 117(23), 0031–9007 (2016). [CrossRef]
21. E. Snitzer, “Cylindrical dielectric waveguide modes,” J. Opt. Soc. Am. B 51(5), 491–498 (1961). [CrossRef]
22. A. Klug, C. Peters, and A. Forbes, “Robust structured light in atmospheric turbulence,” Adv. Photonics 5(1), 016006 (2023). [CrossRef]
23. J. Qi, W. Wang, B. Shi, et al., “Concise and efficient direct-view generation of arbitrary cylindrical vector beams by a vortex half-wave plate,” Photonics Res. 9(5), 803–813 (2021). [CrossRef]
24. C. Rosales-Guzmán, B. Ndagano, and A. Forbes, “A review of complex vector light fields and their applications,” J. Opt. 20(12), 123001 (2018). [CrossRef]
25. J. Wang, “Advances in communications using optical vortices,” Photonics Res. 4(5), B14–B28 (2016). [CrossRef]
26. J. Qi, W. Yi, M. Fu, et al., “Practical generation of arbitrary high-order cylindrical vector beams by cascading vortex half-wave plates,” Opt. Express 29(16), 25365–25376 (2021). [CrossRef]
27. Y. Gu, O. Korotkova, and G. Gbur, “Scintillation of nonuniformly polarized beams in atmospheric turbulence,” Opt. Lett. 34(15), 2261–2263 (2009). [CrossRef]
28. C. Wei, D. Wu, C. Liang, et al., “Experimental verification of significant reduction of turbulence-induced scintillation in a full Poincaré beam,” Opt. Express 23(19), 24331–24341 (2015). [CrossRef]
29. P. Lochab, P. Senthilkumaran, and K. Khare, “Designer vector beams maintaining a robust intensity profile on propagation through turbulence,” Phys. Rev. A 98(2), 023831 (2018). [CrossRef]
30. Y. Gu and G. Gbur, “Reduction of turbulence-induced scintillation by nonuniformly polarized beam arrays,” Opt. Lett. 37(9), 1553–1555 (2012). [CrossRef]
31. M. A. Cox, N. Mphuthi, I. Nape, et al., “Structured light in turbulence,” IEEE J. Sel. Top. Quant. Electron. 27(2), 1–21 (2021). [CrossRef]
32. W. Cheng, J. W. Haus, and Q. Zhan, “Propagation of vector vortex beams through a turbulent atmosphere,” Opt. Express 17(20), 17829–17836 (2009). [CrossRef]
33. L. Zhu, M. Deng, B. Lu, et al., “Turbulence-resistant high-capacity free-space optical communications using OAM mode group multiplexing,” Opt. Express 31(9), 14454–14463 (2023). [CrossRef]
34. H. Tan, J. Deng, R. Zhao, et al., “A free-space orbital angular momentum multiplexing communication system based on a metasurface,” Laser Photonics Rev. 13(6), 1800278 (2019). [CrossRef]
35. S. N. Khonina, N. L. Kazanskiy, M. A. Butt, et al., “Optical multiplexing techniques and their marriage for on-chip and optical fiber communication: a review,” Opto-Electron. Adv. 5(8), 210127 (2022). [CrossRef]
36. D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013). [CrossRef]
37. G. Milione, M. P. J. Lavery, H. Huang, et al., “4 × 20 Gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer,” Opt. Lett. 40(9), 1980–1983 (2015). [CrossRef]
38. K. Pang, H. Song, Z. Zhao, et al., “400-Gbit/s QPSK free-space optical communication link based on four-fold multiplexing of Hermite-Gaussian or Laguerre-Gaussian modes by varying both modal indices,” Opt. Lett. 43(16), 3889–3892 (2018). [CrossRef]
39. Y. Lu, Y. Xu, X. Ouyang, et al., “Cylindrical vector beams reveal radiationless anapole condition in a resonant state,” Opto-Electron. Adv. 5(4), 210014 (2022). [CrossRef]
40. Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009). [CrossRef]
41. Z. Wang, N. Zhang, and X. C. Yuan, “High-volume optical vortex multiplexing and de-multiplexing for free-space optical communication,” Opt. Express 19(2), 482–492 (2011). [CrossRef]
42. J. Qi, W. Yi, M. Fu, et al., “Continuously adjustable cylindrical vector and vortex beams by programming vortex half-wave plates and detection based on coaxial or small-angle interference,” Phys. Rev. Appl. 18(3), 034086 (2022). [CrossRef]
43. L. C. Andrews, Field guide to atmospheric optics (SPIE Press, 2019).
44. Y. Zhang, M. Xu, M. Pu, et al., “Experimental demonstration of an 8-Gbit/s free-space secure optical communication link using all-optical chaos modulation,” Opt. Lett. 48(6), 1470–1473 (2023). [CrossRef]
45. X. Luo, M. Pu, F. Zhang, et al., “Vector optical field manipulation via structural functional materials: Tutorial,” J. Appl. Phys. 131(18), 181101 (2022). [CrossRef]
46. X. Luo, “Multiscale optical field manipulation via planar digital optics,” ACS Photonics 10(7), 2116–2127 (2023). [CrossRef]
