Space-division multiplexing allows unprecedented scaling of bandwidth density for optical communication. Routing spatial channels among transmission ports is critical for future scalable optical network, however, there is still no characteristic parameter to label the overlapped optical carriers. Here we propose a free-space optical flow routing (OFR) scheme by using optical orbital angular moment (OAM) states to label optical flows and simultaneously steer each flow according to their OAM states. With an OAM multiplexer and a reconfigurable OAM demultiplexer, massive individual optical flows can be routed to the demanded optical ports. In the routing process, the OAM beams act as data carriers at the same time their topological charges act as each carrier’s labels. Using this scheme, we experimentally demonstrate switching, multicasting and filtering network functions by simultaneously steer 10 input optical flows on demand to 10 output ports. The demonstration of data-carrying OFR with nonreturn-to-zero signals shows that this process enables synchronous processing of massive spatial channels and flexible optical network.
© 2016 Optical Society of America
With the increasing demands of emerging applications, such as intense social networking, ultra-high definition video, cloud computing, internet of things and so on, the network traffic will undoubtedly continue to dramatically grow in the foreseeable future [1–3]. However, the physical capacity (available spectrum) limits will soon be reached in the single-mode fiber (SMF) which is widely used in all kinds of today’s optical network [4, 5]. Thus, the optical transmission and network researchers have proposed various techniques to mitigate the capacity limitations. Space-division multiplexing (SDM) and flexible optical networking (FON) are considered as the two main promising techniques to override the current capacity crunch. The SDM refers to using multiple spatial channels co-propagating in the free space and waveguides to increase capacity for optical communication [6,7] and the FON dynamically assigns bandwidth to optimize the available wavelength-division multiplexing (WDM) network resources [8,9]. Recently, spectra and spatial flexible optical networks to utilize the aggregated residual bandwidth of multiple wavelengths across fibers/space-channels have captured the interests of many researchers’ [10–15]. Flexible routing of optical flows (or paths) at physical layer in different optical switch hierarchy is the foundation of network upper layers. However, the optical routing at this level is still an issue and becomes urgent with the aggregate network traffic and optical switching granularity increases especially in core, metro and future intra-datacenter optical interconnects [16–18]. Realizing a space-granular capacity or optical flow routing (OFR) and eliminating the WDM switching elements will significantly reduce the routing hardware and cost .
Free-space optical routing is a promising technology to be used in future SDM networks for OFR, because of its inherent advantages of low loss, low crosstalk, and expandability to guided-wave solid-state switches and compatible to SDM . The free-space optical switch core technologies mainly include optical shutter-based switches [21, 22] and holographic beam steering switches [23, 24]. However, because the optical flows (carriers) have no parameter to distinguish one from the others, the input beams must be individually selected and steered without spatial overlap in the switch process. To increase the routing port numbers and spatial port density, we must seek a parameter to label the different overlapped optical flows.
Optical vortex carrying orbital angular momentum (OAM) has a helical transverse phase in form of exp(ilφ), where l is the topological charge (TC) and φ is the azimuthal angle . In principle, the values of l are unlimited. These vortex beams with different OAM states are mutually orthogonal and can be efficiently separated from each other even after spatially overlapping and coaxially propagating [26, 27]. Thus, the OAM states could be used as an additional dimension to transfer information. There are two different ways to take advantage of the distinction between OAM states with different TC values in communication . One is encoding information into the spatial structure of the mixed vortex field where different OAM states act as different data symbols has been demonstrated [28–30]. The other, as a way of SDMs employed in the most recent demonstrations, is using each OAM beam as a carrier of a data stream [31–34]. These two communication ways could combine with each other to solve the “label” problem in the optical switching networks. In another word, the OAM beam could act as data carrier at the same time its TC act as each carrier’s “label” in the routing/switching process.
In this paper, we propose a free-space OFR scheme by using optical OAM states to label overlapped optical flows and simultaneously steer each flow according to their OAM states. With an OAM multiplexer and a reconfigurable OAM demultiplexer, massive individual input optical flows can be routed to any demanded output optical ports. We term this scheme as OAM-labeled OFR. In a concept proof experiment, 10 optical flows are labeled by 10 OAM states and multiplexed into a coaxial vortex beam. And then, each flow is discriminated and steered to one or more space output port by a designed reconfigurable demultiplexer. The switching, multicasting and filtering of the 10 input optical flows among 10 spatial output ports are demonstrated by a controllable SLM.
2. Concept and principle
Figure 1(a) shows the schematic of the OAM-labeled optical flow routing process. There are two steps, the first step is labeling the different input optical flows and the second step is steering the flows to the needed output ports. Here, we design a Dammann optical vortex grating (DOVG) to convert Gaussian-shaped light beams into vortex beams with different l and form multiple coaxial OAM beams. Each of the coaxial OAM beams is unique and can be selected according to its l. We term the OAM carried optical flow as OAM-labeled optical flow. The label value l of each flow is determined by the DOVG’s structure and the relative angle between the input Gaussian beam and DOVG’s optical axis. Then, the multiple OAM-labeled and co-propagated optical flows incident on a specially designed computer-generated holograph (CGH) which act as a demultiplexer and flow helm. This CGH converts the multiple OAM beams back to multiple Gaussian-like beams and delivers them along different directions to the desired output ports. Figure 1(b) shows the OAM-labeled OFR functions of direct connection (reference), switch, multicast, and filter. Through reconstructing the CGH, these routing functions can be implemented. The labels of the optical flows in input and output domain are consistent.
The DOVG and CHG are the two key elements in this system. As described in our previous work [35–37], DOVGs can generate and multiplex OAM beams, and inversely can demultiplex and convert coaxial OAM beams into Gaussian beams at the corresponding diffraction directions. Here, we design a 2-D DOVG for multiplex and label the input optical flows with different OAM states. The pure phase structure of the DOVG can be described as:Eq. (1), the TC value l (l = mlx + nly) of the generated OAM beam is determined by the diffractive order, and can’t be changed. When it is used as a demultiplexer, the demultiplexed and converted Gaussian beam’s direction is fixed. This severely limits the flexibility of the demultiplexer. In order to break the dependency, we modify Eq. (1) as:Eq. (2), the value of lmn is independent of the diffractive order (m, n), and can be chosen as an arbitrary value. When it is used as a demultiplexer, the incident OAM beam with specific TC value can be chosen and demultiplexed in any diffractive order (direction). As a result, an incident OAM beam with l can be demultiplexed and steered to any diffraction order by correspondingly setting the lmn = - l or multicast to some selected diffraction orders or even broadcast to all the needed orders. When coaxial OAM beams labeled with different TC values incident on such phase structure, all of them can be demultiplexed and steer to different diffraction directions. If the phase structure of the CGH varied, the diffraction directions of the demultiplexed beams are changed.
We can generate desired CGHs as described in Eq. (2) by using our previous proposed high-efficiency iterative method [38, 39]. We set Eq. (2) as objective function to optimize phase-only transmittance and use relative root-mean-square error (R-RMSE) as a parameter to evaluate the CGH quality. The iterative process is ended when R-RMSE reaches a pre-defined limit and then the CGH is obtained. It should be specially mentioned that, in the iterative method, the weights of diffraction order am,n can be adjusted. Figure 2 shows the CGHs and intensity patterns generated by Gaussian beams and vortex beams irradiation. If we regard the Fig. 2(a) as a reference pattern, the Fig. 2(b) stands for function of switching, the Fig. 2(c) for multicasting and the Fig. 2(d) for filtering. The filtering is functioned by blocking the power (set am,n = 0) of the output port.
3. Experiments and discussion
3.1 Experiments setup
Figure 3 shows the experimental setup of 10 optical flows routing enabled by the DOVG and the reconfigurable CGH. The two lasers (both working at 1552.524 nm) are modulated into10 Gbps nonreturn-to-zero on-off keying (NRZ-OOK) signals, amplified by two erbium-doped fiber amplifiers (EDFAs) and equally divided into 4 (labeled by even l values) and 6 (labeled by odd l values) branches relatively delayed with fibers. The powers of the 10 channels are equalized to about 11 dBm by adjusting the two EDFAs. These 10 data-carried optical beams collimated with 10 fiber collimators are then projected onto our designed DOVG to multiplex and label the data channels. The diameters of collimated Gaussian beams are 3 mm. Through the DOVG, the beams with different angle are labeled with different OAM TC values in the zeroth order direction. The 10 optical flows are labeled by TC value of ± 2, ± 3, ± 7, ± 8, ± 13 (as shown in Fig. 4(b)) respectively. During the total experiments, the DOVG is fixed on the optical table with a lens holder and the input optical beams from the 10 fiber collimators are all fixed after their alignment. We placed an aperture after the DOVG to filter out the higher orders of the diffracted beams and ensure that only the zeroth order beams can pass through. After the aperture, the OAM-labeled optical flows incident on the designed CGH loaded on a Liquid crystal on Silicon (LCoS) spatial light modulator (SLM) to diffracts the coaxial beams into a 2 × 5 array as shown in Fig. 1(a). Then, the 2 × 5 array is focused by a lens with 35 mm focus length and each focused light spot can be coupled to an SMF for bit error rate (BER) measurements. The collected signal from the SMF is pre-amplified by a low noise EDFA to around 2 dBm. An optical spectrum analyzer (OSA) is used to monitor the signal to noise ratio of the routed channels. A variable optical attenuator (VOA) is employed to adjust the optical powers before the detector.
To clarify the routing functions, we first set an OAM channel networking case as the reference. When a Gaussian-shaped beam with plane wave front (l = 0) is incident on a reference CGH, an OAM beams array is generated as shown in Fig. 4(b) (the numbers denote the l values of the vortex beams). When the incident beams are coaxial OAM beams (as shown in Figs. 4(d), 4(g) and 4(j)), the conjugated OAM beams (the sum value of the two ls is 0) will be converted to Gaussian beams at the corresponding direction, and the other beams will be converted to other OAM beams, as shown in Figs. 4(e), 4(h) and 4(k). For detail, in Fig. 4(e), the point A is the beam with OAM value 8 converted, and the small donut B is not a point just because the same OAM beam converted to the OAM beam with l = 1 (−7 + 8 = 1). Figure 4(k) shows the case in which all of the 10 labeled coaxial optical flows pour onto the CGH simultaneously. The Roman numbers in Fig. 4(k) denote the output ports in this system.
Figure 4(c) shows the switched optical flow labels distribution in the 2 × 5 diffraction array which is generated by a Gaussian beam irradiate on the switch CGH. The arrow lines indicate the flow output port exchanges from the reference distribution on the output plane. Figure 4(d) shows the intensity profile of two coaxial optical flows labeled with TC values of 8 and −13.
When this two optical flows incident on the SLM with the switch CGH loaded, they are demultiplexed and located on I and VIII output ports as shown in Fig. 4(f). Compared with the reference case (in Fig. 4(e)), the input optical flow labeled with TC 8 is switched from output port II to output port I and the input flow labeled with TC −13 is switched from X to VIII. Figure 4(g) shows the intensity profile of four coaxial optical flows labeled with TC values of −3, ± 8 and 13. Figure 4(i) shows the demultiplexing of the flows with switch CGH. Compare with the reference case (in Fig. 4(h)), the two input optical flows labeled with TC 8 and 13 are mutual interchanged between output ports II and I; the two input flows labeled with TC ± 8 are switched from output ports II, IX to I, IV; the input flow labeled with TC −3 is switched from output port VIII to X. The intensity profile of the 10 OAM-labeled coaxial optical flows is shown in Fig. 4(j), and the corresponding demultiplexed and switched results are shown in Fig. 4(l). Compared with the reference case (as shown in Fig. 4(k)), all of the 10 labeled coaxial optical flows are switched simultaneously.
Figure 5(a) shows the measured bit-error ratio (BER) of the switched optical channels. We define (ipIʹ13, opII13) to denote the optical flow ports interconnect, where ipIʹ is the optical flow input port labeled as Iʹ and opII is the output port marked with II as shown in Fig. 1(b), the subscript number 13 represents the optical flow is labeled with TC value of 13. We first measured the back to back BER of our system as the curve labeled by the black dots. With the OAM-labeled routing involved, the BER curves of all the switch flows have a shift to high received power direction. The performance degradations induce less than 0.3dB power penalty for all the switch flows at the forward error correction (FEC) threshold of 3.8 × 10−3.
The data transmission performance degradations induced by the routing process mainly comes from the crosstalk with other optical channels. Here, the crosstalk is defined as the ratio of the power from all undesired flows (the desired channel is turned off) to the desire routed flow (all the undesired flows are turned off). Figure 5(b) shows the measured power distributions of the 10 output ports in the reference and the switch cases. To minimize the coupling loss or the biased projection, in the experiments, the lead out SMF’s orientation and position was carefully adjusted by using a precision 5-dimension micro displacement platform. Although, compared with the reference case, the crosstalk is larger, it is still less than −17dB in all the output ports (the maximum crosstalk is −19 dB in the reference case). The received power differences between the reference and switching case from output port I to X are 2.06, 0.10, 2.50, 2.51, −2.37, −1.10, 1.34, 0.71, −1.10, 0.90 dB. So, it is clear that the designed reconfigurable CGH can implement the massive individual OAM-labeled optical flows switch.
3.3 Multicast and filter
To illustrate the optical flows multicast and filter functions, we display the designed multicast and filter CGHs on the SLM. Figure 6(b) shows the multicast optical flows distributions in the 2 × 5 diffraction array which is generated by a Gaussian beam irradiate on the multicast CGH. The intensity distribution generated by an optical flow labeled with TC value of −2 incidents on the SLM is represented in Fig. 6(e). It is clear that the optical flow is demultiplexed and multicast to output ports IV, VI and X by the multicast CGH. Figure 6(g) shows the intensity profile if two coaxial optical flows labeled with TC values of −7 and 13. When this two optical flows incident on the multicast CGH, the output intensity distribution is formed as shown in Fig. 6(h), the flow labeled with TC value of −7 is multicast to output port I and V and the flow labeled with 13 is multicast to output ports III, VII and IX. Figure 6(k) shows the demultiplexed and multicast result which is produced by the 10 coaxial OAM-labeled optical flows incident on the multicast CGH. We also demonstrated a “port-block” filter, which blocks the output ports III and VI of the multicast case, as shown in Figs. 6(c), 6(f), 6(i) and 6(l).When an optical flow labeled with TC value of −2 incidents on the filter CGH, the flow was demultiplexed and steered to the output port VI is blocked as shown in Fig. 6(f). Figures 6(i) and 6(l) show the demultiplexed and filter intensity patterns with two and ten OAM-labeled optical flows incident on the filter CGH.
Figure 7(a) shows the measured BERs of the routed flows from III, VII and IX output ports with multicast and filter. The maximum power penalty is less than 0.4dB at the FEC threshold. We also characterize the power distributions of the multicast and filter flows in Fig. 7(b). The multicast power fluctuation is less than 1.7dB, and the two blocked output ports’ power is suppressed more than 23dB by the filter. These results verified the OAM-labeled OFR functions of multicast and filter.
In this paper, we propose and demonstrate the OAM-labeled free space OFR by introducing the OAM states into optical switching as labels for massive optical flows routing. The OAM states provide the TC of vortex beam as the characteristic parameter to the optical flows and given us the freedom to control the space overlapped optical flows in flexibility. We design the 2-D DOVG as optical multiplexer to label the input optical flows and the CGHs as demultiplexer to route the labeled optical flows. In order to get the desired CGHs, we modify the DOVG’s phase equation to broken the dependence of the lmn with the diffractive order. In the OAM-labeled OFR proof-of concept experiments, the 10 independent optical flows are parallel routed to the desired 10 output ports and their BER curves are measured. The experimental results indicate that the CGH implementation of the SLM provides a great degree of flexibility and allows the creation of arbitrary routing patterns. In addition, the output ports of this OAM-labeled OFR can be ports where wavelength-selective switches fan-out large number wavelength channels. Thus, OAM-labeled OFR enables synchronous processing of massive spatial channels and high-bandwidth, flexible optical network.
National Natural Science Foundation of China (NSFC) (61138003, 61490712, 61427819, 61490715, 61435006, 61525502, 61405121, 11404007, 11604218), National High-tech R&D Program (863 Program) (No.2015AA015501), Science and Technology Innovation Commission of Shenzhen (KQCS2015032416183980, KQTD2015071016560101, KQJSCX20160226193555 889), Fundamental Research Foundation of Shenzhen (JCYJ20140418091413543), Natural Science Foundation of SZU (000011, 000075, 201454), Leading talents of Guangdong province program (00201505), Anhui Provincial Natural Science Foundation of China (1408085QF112).
The authors are very grateful to the reviewers for valuable comments.
References and links
1. C. V. N. Index, “Forecast and Methodology, 2014–2019 White Paper, Cisco, 2015.”
2. A. Al-Fuqaha, M. Guizani, M. Mohammadi, M. Aledhari, and M. Ayyash, “Internet of things: A survey on enabling technologies, protocols, and applications,” IEEE Commun. Surveys Tuts. 17(4), 2347–2376 (2015). [CrossRef]
3. D. Ckilper, K. Bergman, V. Schan, I. Monga, G. Porter, and K. Rauschenbach, “Optical Networks Come of Age,” Opt. Photonics News 25(9), 50–57 (2014). [CrossRef]
4. R. Essiambre and R. Tkach, “Capacity Trends and Limits of Optical Communication Networks,” Proc. IEEE 100(5), 1035–1055 (2012). [CrossRef]
5. P. Winzer, “Spatial multiplexing in fiber optics: The 10x scaling of metro/core capacities,” Bell Labs Tech. J. 19, 22–30 (2014). [CrossRef]
6. P. Winzer, “Making spatial multiplexing a reality,” Nat. Photonics 8(5), 345–348 (2014). [CrossRef]
7. G. Li, N. Bai, N. Zhao, and C. Xia, “Space-division multiplexing: the next frontier in optical communication,” Adv. Opt. Photonics 6(4), 413–487 (2014). [CrossRef]
8. I. Tomkos, S. Azodolmolky, J. Pareta, D. Careglio, and E. Palkopoulou, “A tutorial on the flexible optical networking paradigm: State of the art, trends, and research challenges,” Proc. IEEE 102(9), 1317–1337 (2014). [CrossRef]
9. B. Chatterjee, N. Sarma, and E. Oki, “Routing and spectrum allocation in elastic optical networks: a tutorial,” IEEE Commun. Surveys Tuts. 17(3), 1776–1800 (2015). [CrossRef]
10. L. Nelson, M. Feuer, K. Abedin, X. Zhou, T. Taunay, J. Fini, B. Zhu, R. Isaac, R. Harel, G. Cohen, and D. Marom, “Spatial superchannel routing in a two-span ROADM system for space division multiplexing,” J. Lightwave Technol. 32(4), 783–789 (2014). [CrossRef]
11. N. Zilberman, P. Watts, C. Rotsos, and A. Moore, “Reconfigurable Network Systems and Software-Defined Networking,” Proc. IEEE 103(7), 1102–1124 (2015). [CrossRef]
12. T. Xia, H. Fevrier, T. Wang, and T. Morioka, “Introduction of spectrally and spatially flexible optical networks,” IEEE Commun. Mag. 53(2), 24–33 (2015). [CrossRef]
13. D. Klonidis, F. Cugini, O. Gerstel, M. Jinno, V. Lopez, E. Palkopoulou, M. Sekiya, D. Siracusa, G. Thouenon, and C. Betoule, “Spectrally and spatially flexible optical network planning and operations,” IEEE Commun. Mag. 53(2), 69–78 (2015). [CrossRef]
14. R. Ryf, S. Chandrasekhar, S. Randel, D. Neilson, N. Fontaine, and M. Feuer, “Physical layer transmission and switching solutions in support of spectrally and spatially flexible optical networks,” IEEE Commun. Mag. 53(2), 52–59 (2015). [CrossRef]
15. S. Yan, E. Salas, V. Rancaňo, Y. Shu, G. Saridis, B. Rofoee, Y. Yan, A. Peters, S. Jain, T. Smith, P. Petropoulos, D. Richardson, and G. Zervas, “Archon: A Function Programmable Optical Interconnect Architecture for Transparent Intra and Inter Data Center SDM/TDM/WDM Networking,” J. Lightwave Technol. 33(8), 1586–1595 (2015). [CrossRef]
16. J. Pedro and B. Gangopadhyay, “Prospects for transparent handover between the metro and core segments of next-generation transport networks,” In Transparent Optical Networks (ICTON), 2015 17th International Conference on. IEEE, 1–5 (2015). [CrossRef]
17. K. Kitayama, Y. Huang, Y. Yoshida, R. Takahashi, T. Segawa, S. Ibrahim, T. Nakahara, Y. Suzaki, M. Hayashitani, Y. Hasegawa, Y. Mizukoshi, and A. Hiramatsu, “Torus-topology data center network based on optical packet/agile circuit switching with intelligent flow management,” J. Lightwave Technol. 33(5), 1063–1071 (2015). [CrossRef]
18. R. Cessa, Y. Kaymak, and Z. Dong, “Schemes for Fast Transmission of Flows in Data Center Networks,” IEEE Commun. Surveys Tuts. 17(3), 1391–1422 (2015). [CrossRef]
19. D. Marom and M. Blau, “Switching solutions for WDM-SDM optical networks,” IEEE Commun. Mag. 53(2), 60–68 (2015). [CrossRef]
20. L. Lin, E. Goldstein, and R. Tkach, “Free-space micromachined optical switches for optical networking,” IEEE J. Sel. Top. Quantum Electron. 5(1), 4–9 (1999). [CrossRef]
21. T. Wilkinson, B. Crossland, N. Collings, F. Zhang, and M. Fan, “Reconfigurable free-space optical cores for storage area networks,” IEEE Commun. Mag. 43(3), 93–99 (2005). [CrossRef]
22. F. Zhang, H. Chou, and W. A. Crossland, “PLZT-based Shutters for Free-Space Optical Fiber Switching,” IEEE Photonics J. 8(1), 7800512 (2016). [CrossRef]
23. W. Crossland, I. Manolis, M. Redmond, K. Tan, T. Wilkinson, M. Holmes, T. Parker, H. Chu, J. Croucher, V. Handerek, S. Warr, B. Robertson, I. Bonas, C. Stace, H. White, R. Woolley, and G. Henshall, ““Holographic optical switching: the” ROSES” demonstrator,” J. Lightwave Technol. 18(12), 1845–1854 (2000). [CrossRef]
24. B. Lynn, P. Blanche, A. Miles, J. Wissinger, D. Carothers, L. LaComb, R. Norwood, and N. Peyghambarian, “Design and Preliminary Implementation of an N × N Diffractive All-Optical Fiber Optic Switch,” J. Lightwave Technol. 31(24), 4016–4021 (2013). [CrossRef]
25. A. Yao and M. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011). [CrossRef]
26. I. Djordjevic, J. Anguita, and B. Vasic, “Error-correction coded orbital-angular-momentum modulation for FSO channels affected by turbulence,” J. Lightwave Technol. 30(17), 2846–2852 (2012). [CrossRef]
27. A. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. Lavery, M. Tur, S. Ramachandran, A. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
28. Z. Bouchal and R. Celechovský, “Mixed vortex states of light as information carriers,” New J. Phys. 6(1), 131 (2004). [CrossRef]
29. G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12(22), 5448–5456 (2004). [CrossRef] [PubMed]
31. J. Shapiro, S. Guha, and B. Erkmen, “Ultimate channel capacity of free-space optical communications [Invited],” J. Opt. Netw. 4(8), 501–516 (2005). [CrossRef]
32. J. Lin, X. C. Yuan, S. H. Tao, and R. E. Burge, “Multiplexing free-space optical signals using superimposed collinear orbital angular momentum states,” Appl. Opt. 46(21), 4680–4685 (2007). [CrossRef] [PubMed]
33. J. Wang, J. Yang, I. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012). [CrossRef]
34. N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013). [CrossRef] [PubMed]
35. T. Lei, M. Zhang, Y. Li, P. Jia, G. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light Sci. Appl. 4(3), e257 (2015). [CrossRef]
38. J. Lin, X. C. Yuan, S. H. Tao, and R. E. Burge, “Collinear superposition of multiple helical beams generated by a single azimuthally modulated phase-only element,” Opt. Lett. 30(24), 3266–3268 (2005). [CrossRef] [PubMed]