Abstract

Twisted light carrying orbital angular momentum (OAM), which featuring helical phase front, has shown its potential applications in diverse areas, especially in optical communications in free space and specially designed fibers, e.g. a vortex fiber. Instead of specially designed fibers extensively used in the reported OAM-based fiber transmission experiments, here we demonstrate the viability of a conventional graded-index multi-mode fiber (MMF) for OAM multiplexing transmission with less digital signal processing (DSP) complexity. We demonstrate a 120-Gbit/s quadrature phase-shift keying (QPSK) signal transmission in an 8.8-km OM4 MMF by using OAM mode multiplexing with all the modes in the first two mode-groups (OAM01L, OAM01R, OAM+11L, OAM+11R, OAM11L, OAM11R) with only 2×2 and 4×4 multiple-input-multiple-output (MIMO) equalization. Moreover, we demonstrate the data-carrying two OAM mode groups multiplexing transmission over the 8.8-km MMF without MIMO equalization. These demonstrations may open up new perspectives to enable the realistic use of OAM-based MMF solution in data centers and super-computers.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Orbital angular momentum (OAM) beam, also called twisted light, is a helically phased beam comprising an azimuthal phase term exp(ilφ), carrying an OAM of lℏ per photon (: reduced Plank’s constant), where l is referred to topological charge and φ is the azimuthal angle [1]. Contrary to spin angular momentum (SAM), which is associated with photon spin and manifested as circular polarization, OAM is identified by the “twist” of a helical phase front [2–4]. Owing to the distinct helical phase structure, OAM beams can be quantified as different states for propagating coaxially [3]. As a natural property of various types of helically phased beams ranging from electron beams to radio waves, OAM has initiated vigorous interest in many applications such as optical manipulation, optical tweezers, sensor, imaging, metrology, astronomy, and quantum entanglement [2,5–12].

In addition to the above areas, very recently OAM has shown great potential both in free-space and fiber-based optical communications in terms of OAM modulation (encoding/decoding) and OAM multiplexing [13–21]. Using OAM multiplexing, independent data streams can be transported simultaneously by multiple OAM modes with increased aggregated transmission capacity. Hence, OAM multiplexing can provide an alternative approach to the well-established space-division multiplexing (SDM) using linearly polarized (LP) modes in fiber [22–24]. In 2004, G. Gibson first demonstrated a proof-of-concept experiment using OAM encoding/decoding for free-space data information transfer [13]. In 2012, J. Wang demonstrated free-space data transmission employing OAM multiplexing, achieving a 2.56-Tbit/s aggregated capacity [16]. Beyond free-space communications, fiber-based OAM communications are of great importance for long distance transmission thanks to the well-confined modes in fiber, which is a distinct advantage compared to free-space propagation with inevitable divergence. However, the specially designed fiber and mode crosstalk are the main challenges. In general, there are two categories of fiber-based OAM or spatial mode multiplexing communication systems. The first type is multiple input multiple output (MIMO)-free systems working in specially designed fibers and featuring weak coupling or low-level mode crosstalk [25–31]. Unfortunately, it might not be the best choice at present either for long-distance transmission due to relatively large loss or for short-reach optical interconnects due to increased complexity and cost of specialty fiber. The second type is MIMO-enabled systems working in fibers with strong mode coupling [32]. However, the challenge is the scalability of digital signal processing (DSP) when expanding the mode-division multiplexing system to higher-order spatial modes. In the full MIMO processing, assuming that the number of spatial modes used for multiplexing is N, the required number of MIMO-DSPs at the receiver side is N×N [33,34]. Moreover, high transceiver cost and power consumption make it still difficult at present to be employed in short-reach optical interconnects applications. Instead of few-mode fiber (FMF) and specially designed fibers, single-mode fiber (SMF) and multi-mode fiber (MMF) are the most widely deployed and commercially available fiber. Conventional MMFs are widespread use in short-reach optical interconnect applications such as data center networks and local access networks, due to their relaxed alignment tolerances and the low-cost high-speed transceivers [35–37]. Recently, many works about LP mode multiplexing and mode groups multiplexing transmission in conventional MMFs have been reported [38–40]. In particular, conventional MMF actually supports OAM modes [41]. In our previous work, two OAM mode groups multiplexing in a 2.6 km OM3 MMF was successfully demonstrated [19]. In this scenario, a laudable goal would be to exploit an OAM multiplexing scheme over conventional MMF with more modes and less DSP complexity.

In this paper, we demonstrate a 120-Gbit/s quadrature phase-shift keying (QPSK) signal transmission in an 8.8-km OM4 MMF by using OAM mode multiplexing with all the modes in the first two mode-groups (OAM01L, OAM01R, OAM+11L, OAM+11R, OAM11L, OAM11R, where L/R denotes left/right circular polarization) with only 2×2 or 4×4 MIMO equalization. Considering the low-level crosstalk between different mode groups in a convention MMF, we recover each mode group separately and partial MIMO scheme (2×2 or 4×4 MIMO-DSP) is employed to equalize intra-mode-group crosstalk. Moreover, we also demonstrate the two data-carrying OAM mode groups multiplexing transmission over the 8.8-km MMF even without MIMO equalization.

2. Concept and principle

The concept and principle of OAM mode multiplexing in a conventional MMF with partial MIMO is illustrated in Fig. 1. All the OAM modes in the first two mode groups (OAM01L, OAM01R, OAM+11L, OAM+11R, OAM11L, OAM11R) are multiplexed and coupled into a conventional MMF for transmission. By using the self-made all-fiber mode coupler, one can easily couple the corresponding OAM mode groups in conventional MMF with high efficiency and reduce the crosstalk induced by the excitation of other OAM modes. After transmission through the conventional MMF, another self-made all-fiber mode filter is employed to suppress unwanted higher-order modes. The separate reception of mode group is possible for the negligible inter-mode-group crosstalk. Instead of using 6×6 MIMO equalization, a 2×2 or 4×4 MIMO would be only needed to equalize intra mode-group crosstalk. Moreover, the length of the tap required in MIMO equalization can be reduced significantly, because the differential mode delay (DMD) within the same mode group is much less than the differential mode group delay (DMGD) between mode groups. In this way, a full MIMO is divided into several partial MIMO modules in different mode groups, and both configuration of the receiver and computational load are greatly reduced.

 

Fig. 1 Concept and principle of OAM mode multiplexing transmission in a conventional MMF. Inset is the refractive index profile of an ideal conventional graded-index MMF.

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Inset of Fig. 1 depicts the refractive index profile of an ideal conventional graded-index MMF, e.g. an OM4 fiber. The radii of the fiber core and cladding are rcore = 25μm and rcladding = 62.5μm, respectively. The OM4 MMF supports 10 OAM mode groups in total at 1550 nm. Each mode group is formed by a set of degenerate OAM modes, which have nearly the same effective refractive index neff. Figure 2(a) shows the OAM modes in the first two mode groups and corresponding neff. Here OAM modes are denoted by OAMlm, where l is the topological charge of OAM and m is the number of concentric rings in the intensity profile. The OAM mode group number n fulfills the equation n=|l|+2m1. Note that the neff differences between different OAM mode groups remain above 1.3×103, while the neff differences within the same OAM mode group are less than 3.8×105, which means that the intra-group mode crosstalk is relatively large, and the inter-group mode crosstalk is negligible. These properties allow two OAM multiplexing approaches in the conventional MMF. First, we can use partial MIMO when multiplexing data-carrying different OAM modes. Instead of using full MIMO-DSP, only partial MIMO-DSP is required. Second, considering the low-level inter-group crosstalk, we can also employ a MIMO-free scheme when multiplexing data-carrying different OAM mode groups.

 

Fig. 2 (a) First two OAM mode groups and corresponding neff in OM4 MMF. (b) Refractive index profiles of the mode coupler/filter. (c) Supported modes and corresponding neff in mode coupler/filter.

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The mode coupler/filter is a short section of large-core fiber (~0.2 m). Figure 2(b) shows the refractive index profiles of the large-core fiber. The radii of the fiber core and cladding are 7.4 μm and 62.5 μm, respectively. The mode coupler/filter only supports the first two OAM mode groups. The effective refractive index difference of each mode group is shown in Fig. 2(c). As depicted in Fig. 2(c), the two groups have relatively large effective refractive index difference (>1.8 × 10−3). Accordingly, the mode coupler and filter can help to excite and select desired OAM modes in the conventional MMF and suppress unwanted high-order OAM modes.

3. Experimental setup

The experimental setup of OAM modes multiplexing in a conventional MMF with partial MIMO is in shown in Fig. 3. The setup for the generation of the QPSK signal is shown in Fig. 3(a). At the transmitter side, a light at 1550 nm is modulated with a 20-Gbit/s QPSK signal and split into 6 paths with a relative delay of about 100 of symbols between subsequent paths for decorrelation. The OAM multiplexer and de-multiplexer parts are shown in Fig. 3(c). The signals in Channels 1-4 (Ch. 1, Ch. 2, Ch. 3, Ch. 4) are sent to four spatial light modulators (SLM1, SLM2, SLM3, SLM4), which are loaded with complex phase patterns to generate desired QPSK-carrying OAM modes (OAM+11L, OAM+11R, OAM11L, OAM11R). The four OAM ± 11 modes are then combined by a beam splitter (BS) and two polarization beam splitters (PBSs). Channels 5 and 6 (Ch. 5, Ch. 6) of OAM01L and OAM01R are combined by a polarization beam combiner (PBC) and multiplexed with the four OAM ± 11 modes by another BS. After that, a quarter-wave plate (QWP) is used to convert the polarization of the multiplexed signals from linear to circular before coupling into the fiber. Then the multiplexed signal is coupled into the OM4 MMF via a self-made mode coupler. The coupling losses of OAM01 and OAM ± 11 mode groups are 3.16 dB and 3.39 dB, respectively. The transmission losses are 2.13 dB and 2.37 dB, respectively. After the multiplexing transmission over the 8.8-km MMF, the multiplexed OAM modes are coupled out via a self-made mode filter. Instead of demultiplexing all the 6 OAM modes simultaneously, each OAM mode group is demultiplexed separately, one for OAM ± 11 modes and another for OAM01 modes. In the OAM ± 11 modes demultiplexing, the output beam is split into 4 paths via a PBS and 2 BSs. Four SLMs (SLM5, SLM6, SLM7 and SLM8) are used to convert the output OAM ± 11 modes back to Gaussian-like mode resulting in four QPSK signals. As shown in Fig. 3(b), each resulting QPSK signal is heterodyne detected to reduce the number of photodetectors (PDs) and analog-to-digital converters (ADCs) into half [42]. The frequency offset between the local oscillator (LO) and the received optical signal is about 10 GHz. After optical-to-electrical conversion, the four generated electrical signals are simultaneously captured by a real-time oscilloscope (Keysight DSA-Z 204A), operating at 80 GS/s and a bandwidth of 20 GHz. For the OAM ± 11 modes group, a 4×4 MIMO time domain equalizer (TDE) with 25 half-symbol-spaced taps is performed for mitigation the intra-mode-group crosstalk between OAM+11L, OAM+11R, OAM11L and OAM11R. By contrast, the heterodyne detection of OAM01 modes group requires a 2×2 MIMO. Data-aided recursive least square (RLS) algorithm is used to update the MIMO tap coefficients. Subsequently the carrier recovery including frequency offset estimation and carrier phase recovery is performed to recover constellations. Finally, after symbol demapping and decision, bit-error rate (BER) is obtained.

 

Fig. 3 Experimental setup of OAM mode multiplexing in a conventional MMF with partial MIMO. (a) Transmitter (Tx) for signal generation. (b) Receiver (Rx) for heterodyne coherent detection. (c) OAM mode multiplexing (Mux) and demultiplexing (Demux). ECL: external cavity laser; AWG: arbitrary waveform generator; IQ: in-phase/quadrature; EDFA: erbium-doped fiber amplifier; VOA: variable optical attenuator; OC: optical coupler; LO: local oscillator; PC: polarization controller; ADC: analog-to-digital converter; PD: photodetector; Col.: collimator; Pol.: polarizer; HWP: half-wave plate; QWP: quarter-wave plate; SLM: spatial light modulator; PBS: polarization beam splitter; BS: beam splitter; L: lens (f = 100 mm); OL: objective lens; MMF: multi-mode fiber; MIMO-DSP: multiple input multiple output digital signal processing; QPSK: quadrature phase-shift keying.

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4. Experimental results

We first characterize the transmission performance of OAM modes over the 8.8-km MMF. The measured intensity profiles at the input of MMF are shown in Fig. 4(a). The measured output OAM demodulated Gaussian-like intensity profiles and interferograms are shown in Figs. 4(b) and 4(c). The interferograms are obtained by using a reference Gaussian beam with the same polarization to interfere with the OAM modes. From the number of twists and the twist direction, one can get the topological charge value l with the sign of the OAM modes.

 

Fig. 4 Measured intensity profiles for OAM multiplexing transmission over 8.8-km MMF. (a) Intensity profiles of  OAM01L,OAM01R, OAM+11L, OAM+11R, OAM11L, OAM11R modes at the input of MMF. (b) Demodulated Gaussian-like intensity profiles of  OAM01L, OAM01R, OAM+11L, OAM+11R, OAM11L, OAM11R at the output of MMF. (c) Interferograms of  OAM01L,OAM01R,OAM+11L, OAM+11R, OAM11L, OAM11R at the output of MMF.

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Then we measure the mode coupling between all the utilized modes (OAM01L, OAM01R, OAM+11L, OAM+11R, OAM11L, OAM11R). To obtain the mode transfer matrix, we measure the power at each receiver for demultiplexing different mode when each single input mode is on. The power of the input mode is the same with each other. Figure 5 depicts the measured mode transfer matrix of the employed 6 modes. The measured inter-group crosstalk between the first two OAM mode groups is about −16 dB. It can be clearly seen that the mode coupling mostly occurs within the mode group, and the mode coupling between different mode groups is negligible. Consequently, instead of using the full 6×6 MIMO equalization, only 2×2 or 4×4 MIMO equalization is required to mitigate the intra mode-group crosstalk.

 

Fig. 5 Mode transfer matrix of the 8.8-km conventional MMF.

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In order to fully evaluate the feasibility of OAM modes multiplexing transmission over an 8.8-km MMF, bit-error rate (BER) performance is measured for three cases: (i) single OAM mode transmission; (ii) OAM mode group multiplexing transmission without using MIMO-DSP; (iii) OAM modes multiplexing transmission with partial MIMO.

In the case of single OAM mode transmission, we transmit 20-Gbit/s QPSK on one OAM mode (OAM01L or OAM11L) individually. The measured BER performance for single OAM mode transmission is plotted in Fig. 6(a). It is observed that the measured average optical signal-to-noise ratio (OSNR) penalty at a BER of 3.8 × 10−3 (7% forward error correction (FEC) threshold) is about 1 dB. The constellation for OAM01L at OSNR of 15.5 dB is shown in the inset. In the case of OAM mode group multiplexing transmission without using MIMO-DSP, we demonstrate two data-carrying OAM modes (OAM01L and OAM11L from the first two mode groups) multiplexing transmission over the 8.8-km MMF. Due to the negligible mode coupling between the mode groups of a MMF, it is possible to allow independent detection of each channel without using MIMO-DSP. Figure 6(b) plots measured BER performance for OAM mode group multiplexing transmission using OAM01L and OAM11L. It is observed that the average OSNR penalties at a BER of 3.8 × 10−3 for OAM01L and OAM11L with crosstalk is about 1.3 dB.

 

Fig. 6 Measured BER curves versus received OSNR. (a) Single OAM mode transmission over the 8.8-km MMF using OAM01L and  OAM11L. (b) OAM mode group multiplexing (OAM01L and  OAM11L) transmission without using MIMO-DSP. Insets show constellations of QPSK signals.

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In the case of OAM mode multiplexing transmission with partial MIMO, we transmit QPSK signals on all 6 modes including 4 OAM ones simultaneously. As shown in Fig. 7, we measure the BER performance as a function of the received OSNR for the 6 modes with independent 2×2 or 4×4 MIMO equalization, and the observed OSNR penalties at a BER of 3.8 × 10−3 between each channel and a back-to-back channel are less than 2.5 dB. The insets in Fig. 7 show constellations of QPSK signals at OSNR of 15.7 dB. This favorable performance shows that it is possible to use partial MIMO scheme when the mode coupling between the mode groups of a MMF is relatively small. In this case, an aggregated capacity of 120-Gbit/s is achieved.

 

Fig. 7 Measured BER versus received OSNR for OAM modes (OAM01 and OAM ± 11 mode groups) multiplexing transmission over the 8.8-km MMF with partial MIMO. Insets show constellations of QPSK signals at OSNR of 15.7 dB after MIMO-DSP.

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5. Discussions

In optical fiber, both LP and OAM modes are formed from linear combinations of vector eigenmodes of the fiber. LP modes in MMF have similar characteristics with OAM modes. Here, we take OAM11/LP11 mode for example. The relationships of modes are shown in the equations below:

{OAM+11L=HE21oddiHE21evenOAM11L=TE01+iTM01OAM+11R=TE01iTM01OAM11R=HE21odd+iHE21even,{LP11ax=TM01HE21oddLP11bx=TE01+HE21evenLP11ay=TE01HE21evenLP11by=TM01+HE21odd.
For higher order modes (n>1), the equations are shown below,
{OAM+n1L=HE(n+1)1oddiHE(n+1)1evenOAMn1L=EH(n1)1odd+iEH(n1)1evenOAM+n1R=EH(n1)1oddiEH(n1)1evenOAMn1R=HE(n+1)1odd+iHE(n+1)1even,{LPn1ax=EH(n1)1evenHE(n+1)1oddLPn1bx=EH(n1)1odd+HE(n+1)1evenLPn1ay=EH(n1)1oddHE(n+1)1evenLPn1by=EH(n1)1even+HE(n+1)1odd.
From Eq. (2), we find that higher order LP modes are composed of two different fiber eigenmodes. In contrast, OAM modes can be obtained with odd/even eigenmodes. Therefore, OAM modes might better maintain the mode profile and have less mode walk-off after relatively long distance fiber propagation under an environment with less disturbances [43].

Generally, OAM offers an alternative mode base set for MDM. OAM based mode division multiplexing has been studied for years. A series of researches on OAM based MDM have been reported in both free space and optical fibers [15–19, 25, 32]. In the future, network operators may deploy different mode bases for MDM in fibers. The study of OAM mode based MDM in conventional MMF might complement the whole frame of OAM based optical communications.

6. Conclusions

In summary, we present a data-carrying OAM multiplexing scheme over conventional MMF with less DSP complexity. We demonstrate OAM multiplexing using 6 OAM modes each carrying 20-Gbit/s QPSK signal over 8.8-km OM4 MMF with only 2×2 or 4×4 MIMO-DSP, achieving an aggregated capacity of 120 Gbit/s. We also demonstrate MIMO-free OAM mode groups multiplexing transmission in 8.8-km MMF with two OAM modes belonging to different groups. The obtained favorable results show the viability of OAM modes multiplexing transmission over already existing conventional fibers.

The demonstrated OAM modes multiplexing transmission scheme with conventional MMF provides an attractive solution for short-reach optical interconnects applications. With future improvement of compact multiplexing and demultiplexing devices, OAM modes multiplexing systems over conventional MMF might enable realistic use of OAM-based MMF solution in data centers and super-computers.

Funding

National Basic Research Program of China (973 Program) (2014CB340004); National Natural Science Foundation of China (NSFC) (61761130082, 11574001, 11774116, 11274131, 61222502); Royal Society-Newton Advanced Fellowship; National Program for Support of Top-notch Young Professionals; Yangtze River Excellent Young Scholars Program; Program for HUST Academic Frontier Youth Team.

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33. B. Inan, B. Spinnler, F. Ferreira, D. van den Borne, A. Lobato, S. Adhikari, V. A. J. M. Sleiffer, M. Kuschnerov, N. Hanik, and S. L. Jansen, “DSP complexity of mode-division multiplexed receivers,” Opt. Express 20(10), 10859–10869 (2012). [CrossRef]   [PubMed]  

34. S. O. Arik and D. Askarov, znd J. M. KahnY, “MIMO DSP complexity in mode-division multiplexing,” in Proceedings of Optical Fiber Communication Conference (Optical Society of America, 2015), paper Th1D.1. [CrossRef]  

35. F. Karinou, L. Deng, R. Lopez, K. Prince, J. Jensen, and I. Monroy, “Performance comparison of 850-nm and 1550-nm VCSELs exploiting OOK, OFDM, and 4-PAM over SMF/MMF links for low-cost optical interconnects,” Opt. Fiber Technol. 19(3), 206–212 (2013). [CrossRef]  

36. J. M. Castro, R. Pimpinella, B. Kose, Y. Huang, B. Lane, K. Szczerba, P. Westbergh, T. Lengyel, J. S. Gustavsson, A. Larsson, and P. A. Andrekson, “48.7-Gb/s 4-PAM transmission over 200 m of high bandwidth MMF using an 850-nm VCSEL,” IEEE Photonics Technol. Lett. 27(17), 1799–1801 (2015). [CrossRef]  

37. K. Szczerba, P. Westbergh, M. Karlsson, P. A. Andrekson, and A. Larsson, “70 Gbps 4-PAM and 56 Gbps 8-PAM using an 850 nm VCSEL,” J. Lightwave Technol. 33(7), 1395–1401 (2015). [CrossRef]  

38. R. Ryf, N. K. Fontaine, H. Chen, B. Guan, B. Huang, M. Esmaeelpour, A. H. Gnauck, S. Randel, S. J. B. Yoo, A. M. J. Koonen, R. Shubochkin, Y. Sun, and R. Lingle Jr., “Mode-multiplexed transmission over conventional graded-index multimode fibers,” Opt. Express 23(1), 235–246 (2015). [CrossRef]   [PubMed]  

39. J. Carpenter, B. C. Thomsen, and T. D. Wilkinson, “Degenerate Mode-Group Division Multiplexing,” J. Lightwave Technol. 30(24), 3946–3952 (2012). [CrossRef]  

40. K. Benyahya, C. Simonneau, A. Ghazisaeidi, N. Barré, P. Jian, J. Morizur, G. Labroille, M. Bigot, P. Sillard, J. G. Provost, H. Debrégeas, J. Renaudier, and G. Charlet, “Multiterabit Transmission over OM2 Multimode Fiber with Wavelength and Mode Group Multiplexing and Direct Detection,” J. Lightwave Technol. 36(2), 355–360 (2018). [CrossRef]  

41. S. Chen and J. Wang, “Theoretical analyses on orbital angular momentum modes in conventional graded-index multimode fibre,” Sci. Rep. 7(1), 3990 (2017). [CrossRef]   [PubMed]  

42. H. Huang, Y. Cao, G. Xie, Y. Ren, Y. Yan, C. Bao, N. Ahmed, M. A. Neifeld, S. J. Dolinar, and A. E. Willner, “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]   [PubMed]  

43. Y. Yue, Y. Yan, N. Ahmed, J.-Y. Yang, L. Zhang, Y. Ren, H. Huang, K. M. Birnbaum, B. I. Erkmen, S. Dolinar, M. Tur, and A. E. Willner, “Mode properties and propagation effects of optical orbital angular momentum (OAM) modes in a ring fiber,” IEEE Photonics J. 4(2), 535–543 (2012). [CrossRef]  

References

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  4. A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photonics 8(2), 200–227 (2016).
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  26. S. Li and J. Wang, “A compact trench-assisted multi-orbital-angular-momentum multi-ring fiber for ultrahigh-density space-division multiplexing (19 rings × 22 modes),” Sci. Rep. 4(1), 3853 (2015).
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  29. G. Milione, E. Ip, Y. Huang, P. Ji, T. Wang, M. Li, J. Stone, and G. Peng, “1.2-Tb/s MIMO-less transmission over 1 km of four-core elliptical-core few-mode fiber with 125-μm diameter cladding,” in Proceedings of Opto-Electronics and Communications Conference (OECC, 2016), paper PD2–1.
  30. L. Wang, R. M. Nejad, A. Corsi, J. Lin, Y. Messaddeq, L. A. Rusch, and S. LaRochelle, “MIMO-Free transmission over six vector modes in a polarization maintaining elliptical ring core fiber,” in Proceedings of Optical Fiber Communication Conference (Optical Society of America, 2017), paper Tu2J.2.
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  33. B. Inan, B. Spinnler, F. Ferreira, D. van den Borne, A. Lobato, S. Adhikari, V. A. J. M. Sleiffer, M. Kuschnerov, N. Hanik, and S. L. Jansen, “DSP complexity of mode-division multiplexed receivers,” Opt. Express 20(10), 10859–10869 (2012).
    [Crossref] [PubMed]
  34. S. O. Arik and D. Askarov, znd J. M. KahnY, “MIMO DSP complexity in mode-division multiplexing,” in Proceedings of Optical Fiber Communication Conference (Optical Society of America, 2015), paper Th1D.1.
    [Crossref]
  35. F. Karinou, L. Deng, R. Lopez, K. Prince, J. Jensen, and I. Monroy, “Performance comparison of 850-nm and 1550-nm VCSELs exploiting OOK, OFDM, and 4-PAM over SMF/MMF links for low-cost optical interconnects,” Opt. Fiber Technol. 19(3), 206–212 (2013).
    [Crossref]
  36. J. M. Castro, R. Pimpinella, B. Kose, Y. Huang, B. Lane, K. Szczerba, P. Westbergh, T. Lengyel, J. S. Gustavsson, A. Larsson, and P. A. Andrekson, “48.7-Gb/s 4-PAM transmission over 200 m of high bandwidth MMF using an 850-nm VCSEL,” IEEE Photonics Technol. Lett. 27(17), 1799–1801 (2015).
    [Crossref]
  37. K. Szczerba, P. Westbergh, M. Karlsson, P. A. Andrekson, and A. Larsson, “70 Gbps 4-PAM and 56 Gbps 8-PAM using an 850 nm VCSEL,” J. Lightwave Technol. 33(7), 1395–1401 (2015).
    [Crossref]
  38. R. Ryf, N. K. Fontaine, H. Chen, B. Guan, B. Huang, M. Esmaeelpour, A. H. Gnauck, S. Randel, S. J. B. Yoo, A. M. J. Koonen, R. Shubochkin, Y. Sun, and R. Lingle., “Mode-multiplexed transmission over conventional graded-index multimode fibers,” Opt. Express 23(1), 235–246 (2015).
    [Crossref] [PubMed]
  39. J. Carpenter, B. C. Thomsen, and T. D. Wilkinson, “Degenerate Mode-Group Division Multiplexing,” J. Lightwave Technol. 30(24), 3946–3952 (2012).
    [Crossref]
  40. K. Benyahya, C. Simonneau, A. Ghazisaeidi, N. Barré, P. Jian, J. Morizur, G. Labroille, M. Bigot, P. Sillard, J. G. Provost, H. Debrégeas, J. Renaudier, and G. Charlet, “Multiterabit Transmission over OM2 Multimode Fiber with Wavelength and Mode Group Multiplexing and Direct Detection,” J. Lightwave Technol. 36(2), 355–360 (2018).
    [Crossref]
  41. S. Chen and J. Wang, “Theoretical analyses on orbital angular momentum modes in conventional graded-index multimode fibre,” Sci. Rep. 7(1), 3990 (2017).
    [Crossref] [PubMed]
  42. H. Huang, Y. Cao, G. Xie, Y. Ren, Y. Yan, C. Bao, N. Ahmed, M. A. Neifeld, S. J. Dolinar, and A. E. Willner, “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] [PubMed]
  43. Y. Yue, Y. Yan, N. Ahmed, J.-Y. Yang, L. Zhang, Y. Ren, H. Huang, K. M. Birnbaum, B. I. Erkmen, S. Dolinar, M. Tur, and A. E. Willner, “Mode properties and propagation effects of optical orbital angular momentum (OAM) modes in a ring fiber,” IEEE Photonics J. 4(2), 535–543 (2012).
    [Crossref]

2018 (1)

2017 (4)

2016 (5)

J. Wang, “Advances in communications using optical vortices,” Photon. Res. 4(5), B14–B28 (2016).
[Crossref]

A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photonics 8(2), 200–227 (2016).
[Crossref]

L. Zhu, J. Liu, Q. Mo, C. Du, and J. Wang, “Encoding/decoding using superpositions of spatial modes for image transfer in km-scale few-mode fiber,” Opt. Express 24(15), 16934–16944 (2016).
[Crossref] [PubMed]

A. Wang, L. Zhu, S. Chen, C. Du, Q. Mo, and J. Wang, “Characterization of LDPC-coded orbital angular momentum modes transmission and multiplexing over a 50-km fiber,” Opt. Express 24(11), 11716–11726 (2016).
[Crossref] [PubMed]

S. Chen, J. Liu, Y. Zhao, L. Zhu, A. Wang, S. Li, J. Du, C. Du, Q. Mo, and J. Wang, “Full-duplex bidirectional data transmission link using twisted lights multiplexing over 1.1-km orbital angular momentum fiber,” Sci. Rep. 6(1), 38181 (2016).
[Crossref] [PubMed]

2015 (9)

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

A. Wang, L. Zhu, J. Liu, C. Du, Q. Mo, and J. Wang, “Demonstration of hybrid orbital angular momentum multiplexing and time-division multiplexing passive optical network,” Opt. Express 23(23), 29457–29466 (2015).
[Crossref] [PubMed]

H. Huang, G. Milione, M. P. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. An Nguyen, D. A. Nolan, M.-J. Li, M. Tur, R. R. Alfano, and A. E. Willner, “Mode division multiplexing using an orbital angular momentum mode sorter and MIMO-DSP over a graded-index few-mode optical fibre,” Sci. Rep. 5, 14931 (2015).
[Crossref] [PubMed]

S. Li and J. Wang, “A compact trench-assisted multi-orbital-angular-momentum multi-ring fiber for ultrahigh-density space-division multiplexing (19 rings × 22 modes),” Sci. Rep. 4(1), 3853 (2015).
[Crossref] [PubMed]

E. Ip, G. Milione, M. J. Li, N. Cvijetic, K. Kanonakis, J. Stone, G. Peng, X. Prieto, C. Montero, V. Moreno, and J. Liñares, “SDM transmission of real-time 10GbE traffic using commercial SFP + transceivers over 0.5km elliptical-core few-mode fiber,” Opt. Express 23(13), 17120–17126 (2015).
[Crossref] [PubMed]

S. Li and J. Wang, “Supermode fiber for orbital angular momentum (OAM) transmission,” Opt. Express 23(14), 18736–18745 (2015).
[Crossref] [PubMed]

J. M. Castro, R. Pimpinella, B. Kose, Y. Huang, B. Lane, K. Szczerba, P. Westbergh, T. Lengyel, J. S. Gustavsson, A. Larsson, and P. A. Andrekson, “48.7-Gb/s 4-PAM transmission over 200 m of high bandwidth MMF using an 850-nm VCSEL,” IEEE Photonics Technol. Lett. 27(17), 1799–1801 (2015).
[Crossref]

K. Szczerba, P. Westbergh, M. Karlsson, P. A. Andrekson, and A. Larsson, “70 Gbps 4-PAM and 56 Gbps 8-PAM using an 850 nm VCSEL,” J. Lightwave Technol. 33(7), 1395–1401 (2015).
[Crossref]

R. Ryf, N. K. Fontaine, H. Chen, B. Guan, B. Huang, M. Esmaeelpour, A. H. Gnauck, S. Randel, S. J. B. Yoo, A. M. J. Koonen, R. Shubochkin, Y. Sun, and R. Lingle., “Mode-multiplexed transmission over conventional graded-index multimode fibers,” Opt. Express 23(1), 235–246 (2015).
[Crossref] [PubMed]

2014 (2)

R. G. H. van Uden, R. Amezcua Correa, E. Antonio Lopez, F. M. Huijskens, C. Xia, G. Li, A. Schülzgen, H. de Waardt, A. M. J. Koonen, and C. M. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fiber,” Nat. Photonics 8(11), 865–870 (2014).
[Crossref]

H. Huang, Y. Cao, G. Xie, Y. Ren, Y. Yan, C. Bao, N. Ahmed, M. A. Neifeld, S. J. Dolinar, and A. E. Willner, “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] [PubMed]

2013 (4)

F. Karinou, L. Deng, R. Lopez, K. Prince, J. Jensen, and I. Monroy, “Performance comparison of 850-nm and 1550-nm VCSELs exploiting OOK, OFDM, and 4-PAM over SMF/MMF links for low-cost optical interconnects,” Opt. Fiber Technol. 19(3), 206–212 (2013).
[Crossref]

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]

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibers,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341(6145), 537–540 (2013).
[Crossref] [PubMed]

2012 (6)

A. Anhäuser, R. Wunenburger, and E. Brasselet, “Acoustic rotational manipulation using orbital angular momentum transfer,” Phys. Rev. Lett. 109(3), 034301 (2012).
[Crossref] [PubMed]

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-division multiplexing over 96 km of few-mode fiber using coherent 6×6 MIMO processing,” J. Lightwave Technol. 30(4), 521–531 (2012).
[Crossref]

J. Carpenter, B. C. Thomsen, and T. D. Wilkinson, “Degenerate Mode-Group Division Multiplexing,” J. Lightwave Technol. 30(24), 3946–3952 (2012).
[Crossref]

B. Inan, B. Spinnler, F. Ferreira, D. van den Borne, A. Lobato, S. Adhikari, V. A. J. M. Sleiffer, M. Kuschnerov, N. Hanik, and S. L. Jansen, “DSP complexity of mode-division multiplexed receivers,” Opt. Express 20(10), 10859–10869 (2012).
[Crossref] [PubMed]

Y. Yue, Y. Yan, N. Ahmed, J.-Y. Yang, L. Zhang, Y. Ren, H. Huang, K. M. Birnbaum, B. I. Erkmen, S. Dolinar, M. Tur, and A. E. Willner, “Mode properties and propagation effects of optical orbital angular momentum (OAM) modes in a ring fiber,” IEEE Photonics J. 4(2), 535–543 (2012).
[Crossref]

2011 (3)

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5(6), 335–342 (2011).
[Crossref]

M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5(6), 343–348 (2011).
[Crossref]

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[Crossref]

2008 (1)

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2(4), 299–313 (2008).
[Crossref]

2005 (2)

S. Fürhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “Spiral phase contrast imaging in microscopy,” Opt. Express 13(3), 689–694 (2005).
[Crossref] [PubMed]

D. Cojoc, V. Garbin, E. Ferrari, L. Businaro, F. Romanato, and E. Di Fabrizio, “Laser trappping and micro-manipulation using optical vortices,” Micro. Eng. 78, 125–131 (2005).
[Crossref]

2004 (1)

2001 (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[Crossref] [PubMed]

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Adhikari, S.

Ahmed, N.

H. Huang, G. Milione, M. P. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. An Nguyen, D. A. Nolan, M.-J. Li, M. Tur, R. R. Alfano, and A. E. Willner, “Mode division multiplexing using an orbital angular momentum mode sorter and MIMO-DSP over a graded-index few-mode optical fibre,” Sci. Rep. 5, 14931 (2015).
[Crossref] [PubMed]

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

H. Huang, Y. Cao, G. Xie, Y. Ren, Y. Yan, C. Bao, N. Ahmed, M. A. Neifeld, S. J. Dolinar, and A. E. Willner, “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] [PubMed]

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Figures (7)

Fig. 1
Fig. 1 Concept and principle of OAM mode multiplexing transmission in a conventional MMF. Inset is the refractive index profile of an ideal conventional graded-index MMF.
Fig. 2
Fig. 2 (a) First two OAM mode groups and corresponding neff in OM4 MMF. (b) Refractive index profiles of the mode coupler/filter. (c) Supported modes and corresponding neff in mode coupler/filter.
Fig. 3
Fig. 3 Experimental setup of OAM mode multiplexing in a conventional MMF with partial MIMO. (a) Transmitter (Tx) for signal generation. (b) Receiver (Rx) for heterodyne coherent detection. (c) OAM mode multiplexing (Mux) and demultiplexing (Demux). ECL: external cavity laser; AWG: arbitrary waveform generator; IQ: in-phase/quadrature; EDFA: erbium-doped fiber amplifier; VOA: variable optical attenuator; OC: optical coupler; LO: local oscillator; PC: polarization controller; ADC: analog-to-digital converter; PD: photodetector; Col.: collimator; Pol.: polarizer; HWP: half-wave plate; QWP: quarter-wave plate; SLM: spatial light modulator; PBS: polarization beam splitter; BS: beam splitter; L: lens (f = 100 mm); OL: objective lens; MMF: multi-mode fiber; MIMO-DSP: multiple input multiple output digital signal processing; QPSK: quadrature phase-shift keying.
Fig. 4
Fig. 4 Measured intensity profiles for OAM multiplexing transmission over 8.8-km MMF. (a) Intensity profiles of   O A M 01 L , O A M 01 R , O A M + 11 L , O A M + 11 R , O A M 11 L , O A M 11 R modes at the input of MMF. (b) Demodulated Gaussian-like intensity profiles of   O A M 01 L , O A M 01 R , O A M + 11 L , O A M + 11 R , O A M 11 L , O A M 11 R at the output of MMF. (c) Interferograms of   O A M 01 L , O A M 01 R , O A M + 11 L , O A M + 11 R , O A M 11 L , O A M 11 R at the output of MMF.
Fig. 5
Fig. 5 Mode transfer matrix of the 8.8-km conventional MMF.
Fig. 6
Fig. 6 Measured BER curves versus received OSNR. (a) Single OAM mode transmission over the 8.8-km MMF using O A M 01 L and   O A M 11 L . (b) OAM mode group multiplexing ( O A M 01 L and   O A M 11 L ) transmission without using MIMO-DSP. Insets show constellations of QPSK signals.
Fig. 7
Fig. 7 Measured BER versus received OSNR for OAM modes (OAM01 and OAM ± 11 mode groups) multiplexing transmission over the 8.8-km MMF with partial MIMO. Insets show constellations of QPSK signals at OSNR of 15.7 dB after MIMO-DSP.

Equations (2)

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{ O A M + 11 L = H E 21 o d d i H E 21 e v e n O A M 11 L = T E 01 + i T M 01 O A M + 11 R = T E 01 i T M 01 O A M 11 R = H E 21 o d d + i H E 21 e v e n , { L P 11 a x = T M 01 H E 21 o d d L P 11 b x = T E 01 + H E 21 e v e n L P 11 a y = T E 01 H E 21 e v e n L P 11 b y = T M 01 + H E 21 o d d .
{ O A M + n 1 L = H E ( n + 1 ) 1 o d d i H E ( n + 1 ) 1 e v e n O A M n 1 L = E H ( n 1 ) 1 o d d + i E H ( n 1 ) 1 e v e n O A M + n 1 R = E H ( n 1 ) 1 o d d i E H ( n 1 ) 1 e v e n O A M n 1 R = H E ( n + 1 ) 1 o d d + i H E ( n + 1 ) 1 e v e n , { L P n 1 a x = E H ( n 1 ) 1 e v e n H E ( n + 1 ) 1 o d d L P n 1 b x = E H ( n 1 ) 1 o d d + H E ( n + 1 ) 1 e v e n L P n 1 a y = E H ( n 1 ) 1 o d d H E ( n + 1 ) 1 e v e n L P n 1 b y = E H ( n 1 ) 1 e v e n + H E ( n + 1 ) 1 o d d .

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