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 (ℏ: 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$\times$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 ($OA{M}_{01}^L$, $OA{M}_{01}^R$, $OA{M}_{+11}^L$, $OA{M}_{+11}^R$, $OA{M}_{-11}^L$, $OA{M}_{-11}^R$, where L/R denotes left/right circular polarization) with only 2$\times$2 or 4$\times$4 MIMO equalization. Considering the low-level crosstalk between different mode groups in a convention MMF, we recover each mode group separately and partial MIMO scheme (2$\times$2 or 4$\times$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 ($OA{M}_{01}^L$, $OA{M}_{01}^R$, $OA{M}_{+11}^L$, $OA{M}_{+11}^R$, $OA{M}_{-11}^L$, $OA{M}_{-11}^R$) 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$\times$6 MIMO equalization, a 2$\times$2 or 4$\times$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 r_core = 25μm and r_cladding = 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 $n_{eff}$. Figure 2(a) shows the OAM modes in the first two mode groups and corresponding $n_{eff}$. Here OAM modes are denoted by ${\text{OAM}}_{\mathcal{l}m}$, where $\mathcal{l}$ 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 $n=\left|\mathcal{l}\right|+2m-1$. Note that the $n_{eff}$ differences between different OAM mode groups remain above $1.3\times {10}^{-3}$, while the $n_{eff}$ differences within the same OAM mode group are less than $3.8\times {10}^{-5}$, 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 n_eff in OM4 MMF. (b) Refractive index profiles of the mode coupler/filter. (c) Supported modes and corresponding n_eff 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 ($OA{M}_{+11}^L$, $OA{M}_{+11}^R$, $OA{M}_{-11}^L$, $OA{M}_{-11}^R$). 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 $OA{M}_{01}^L$ and $OA{M}_{01}^R$ 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$\times$4 MIMO time domain equalizer (TDE) with 25 half-symbol-spaced taps is performed for mitigation the intra-mode-group crosstalk between $OA{M}_{+11}^L$, $OA{M}_{+11}^R$, $OA{M}_{-11}^L$ and $OA{M}_{-11}^R$. By contrast, the heterodyne detection of OAM₀₁ modes group requires a 2$\times$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 $\mathcal{l}$ 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 $OA{M}_{01}^L$,$OA{M}_{01}^R$, $OA{M}_{+11}^L$, $OA{M}_{+11}^R$, $OA{M}_{-11}^L$, $OA{M}_{-11}^R$ modes at the input of MMF. (b) Demodulated Gaussian-like intensity profiles of $OA{M}_{01}^L$, $OA{M}_{01}^R$, $OA{M}_{+11}^L$, $OA{M}_{+11}^R$, $OA{M}_{-11}^L$, $OA{M}_{-11}^R$ at the output of MMF. (c) Interferograms of $OA{M}_{01}^L$,$OA{M}_{01}^R$,$OA{M}_{+11}^L$, $OA{M}_{+11}^R$, $OA{M}_{-11}^L$, $OA{M}_{-11}^R$ at the output of MMF.

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Then we measure the mode coupling between all the utilized modes ($OA{M}_{01}^L$, $OA{M}_{01}^R$, $OA{M}_{+11}^L$, $OA{M}_{+11}^R$, $OA{M}_{-11}^L$, $OA{M}_{-11}^R$). 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$\times$6 MIMO equalization, only 2$\times$2 or 4$\times$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 ($OA{M}_{01}^L$ or $OA{M}_{-11}^L$) 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 $OA{M}_{01}^L$ 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 ($OA{M}_{01}^L$ and $OA{M}_{-11}^L$ 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 $OA{M}_{01}^L$ and $OA{M}_{-11}^L$. It is observed that the average OSNR penalties at a BER of 3.8 × 10⁻³ for $OA{M}_{01}^L$ and $OA{M}_{-11}^L$ 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 $OA{M}_{01}^L$ and $OA{M}_{-11}^L$. (b) OAM mode group multiplexing ($OA{M}_{01}^L$ and $OA{M}_{-11}^L$) 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$\times$2 or 4$\times$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:

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$\times$2 or 4$\times$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.