1. Introduction

The ever-growing demand for data traffic coming from the Internet of Things (IOT), cloud services, online game, video and business etc., is driving the modern data centers (DC), as one kind of short-reach optical interconnect systems, to increase the transmission data rate and capacity timely [1,2]. In general, there are technologically numerous methods to meet the bandwidth and density requirements of short-reach datacenter optical interconnect. For instance, rising the symbol rate, adopting multi-level modulation formats, and polarization multiplexing etc [3–5]. Meanwhile, the wavelength division multiplexing (WDM) for short-reach optical interconnect has also been researched by some groups [6,7]. Besides, since the low cost and power consumption are the most important concern on the short reach optical interconnection systems, a concept of modular DC design has been proposed to ensure the better scalability, faster deployment, and higher cost and energy efficiency when compared with the conventional designs [8]. In this proposal, the optical spatial division multiplexing (SDM), which is regarded as the last unexplored physical dimension to improve the capacity of optical communication [9–12], has been studied in modular data center for high capacity optical interconnects. They showed that the SDM-based architecture can provide best cost-performance tradeoff depend on the network load and DC size.

SDM-based technologies are involved the use of fiber bundle with multiple parallel optical fibers together, coupled or uncoupled multi-core fiber (MCF), and few-mode or multi-mode fiber (FMF/MMF). The later one is also categorized as the mode division multiplexing (MDM) technology because the multiple orthogonal fiber modes are used as the individual channels to transmit optical signal [13]. MDM technique has been demonstrated in short-reach optical interconnects by means of mode-group division multiplexing (MGDM) [14–16], linearly polarized mode (LPM) [17–19], orbital angular momentum (OAM) [20–23], and vector mode (VM) [24–29]. As one kind of the VMs, the cylinder vector beam (CVB) with the properties of polarization singularity and cylindrically symmetric electric field, has attracted much research attention [30–34]. However, the studies on data transmission over optical fiber based on CVBs have not been demonstrated widely so far. In the previous work, it has been demonstrated that CVBs can be generated and propagated in optical fibers with good performance [35]. Recently, 4 × 10 Gb/s CVB-based (the order of ± 2) multiplexing transmission with the on-off keying (OOK) signal over 5-km link FMF has been demonstrated [36]. Researchers also use compact, integrated optics to realize the 2 × 20 Gb/s eigenmode multiplexing communication in 2-km circular optical fiber [37]. However, most of these newly employed MDM transmissions are based on the coherent detection which is not the best choice for the short-reach optical interconnect systems.

In this paper, we demonstrate the CVB-based MDM transmission over 4-mode FMF with the aim to further improve the data rate and transmission capacity. The beam quality of CVB generated by the used Q-plate (QP) and the induced mode crosstalk have been analyzed. Although the lower mode isolation existed in the two orthogonal 1st-order CVBs (TE₀₁ and TM₀₁ modes), the transmissions of 95.16 Gb/s over 5 m and 47.58 Gb/s over 100 m have been realized by using the modulation of direct-detection (DD) orthogonal-frequency-division-multiplexing (OFDM) without multiple-input multiple-output (MIMO) digital signal processing (DSP). To the best of our knowledge, this is the first demonstration of CVB-based DD-OFDM-MDM transmission over FMF. The results show that the CVB-based MDM technology could be a good candidate for large-capacity short-reach optical interconnects, such as the board-to-board or rack-to-rack interconnect in future large capacity data centers or super-computing centers.

2. Transmission setup

The experimental setup of CVB-based DD-OFDM-MDM transmission over FMF link for short reach optical interconnect is shown in Fig. 1. The external cavity laser (ECL, 1550 nm, 16 dBm) at transmitter is launched into an intensity modulator (IM, Photoline MX-LN-40) which is modulated by a quadrature phase shift keying (QPSK)-OFDM signal generated by an arbitrary waveform generator (AWG, Tektronix AWG 70002A) with a 25 Gs/s sample rate. The direct-current (DC) bias is employed to make IM work at the optimal operating point and electrical amplifier (EA) is used to amplify the signal generated by AWG. After amplified by a low noise erbium-doped fiber amplifier (EDFA), the optical signal is divided into two branches by a 3-dB optical coupler (OC). Two polarization controllers (PCs) are used to maximize output power of horizontal and vertical polarization light from polarization beam splitter (PBS). After passing through QP1, two collimated light beams are converted to the cylinder vector beams (TE₀₁ mode and TM₀₁ mode) which are coupled into the FMF link as two independent channels for data transmission. Insets (i) and (ii) in Fig. 1 show the intensity profiles of the unconverted fundamental mode and the converted CVBs.

 

Fig. 1 The experimental setup of the CVB-based DD-OFDM-MDM transmission over FMF link. AWG: arbitrary waveform generator; EA: electrical amplifier; ECL: external cavity laser; MZM: Mach-Zehnder modulator; EDFA: erbium-doped fiber amplifier; PC: polarization controller; SMF: single mode fiber; COL: collimator; PBS: polarization beam splitter; QP: Q-plate; FMF: four-mode fiber; PC-FMF: polarization controller based on four-mode fiber; ATT: attenuator; TOF: tunable optical filter; PD: photo-detector; OSC: oscilloscope; DSP: digital signal processing. Recorded intensity profiles of (i) the unconverted fundamental mode, (ii) the converted CVBs, (iii) output CVBs after transmission 100m FMF, (iv) the de-multiplexed CVBs.

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After transmission over the FMF link, an FMF-based PC (PC-FMF) is employed to adjust the polarization and intensity pattern of the output beams. Inset (iii) in Fig. 1 shows the intensity profile after transmission over 100 m FMF. Then, the output beams are collimated and pass through the second Q-plate (QP2) to realize the conversion of CVBs to fundamental mode. Inset (iv) illustrates the image of the de-multiplexed CVBs. Subsequently, the two orthogonal polarizations of demodulated beams are split by the PBS. At receiver, the optical signals are amplified by another EDFA and then attenuated by a variable optical attenuator (VOA). After being filtered by a 1nm bandwidth tunable optical filter (TOF) and received by a photo-detector (PD, u2t XPDV2120R), the generated electrical signal is then demodulated using real-time oscilloscope (OSC, LecroyLabMaster 10-36Zi) and further processed by the off-line digital signal processing (DSP).

3. Results and discussions

3.1 CVB Mode characterization during the FMF propagation

According to the higher-order Poincaré spheres analysis [38], the generated CVBs based on the Q-plate can be mapped by the points of equators on the higher-order Poincaré spheres, such as the first-order Poincaré sphere in Fig. 2(a). θ and ϕ are the colatitude and azimuth angles over the Poincaré sphere, which determine the polarization distribution of certain vector mode on the sphere (θ ∈ [0, π], ϕ ∈ [0, 2π]). For example, the transverse mode is a radially polarized mode (θ = π/2, $\varphi =0$) or an azimuthally polarized mode (θ = π/2, $\varphi =\pi$). In general, the description of an arbitrary point on the surface of Poincaré sphere can be expressed as follows,

 

Fig. 2 (a) The four typical polarization distributions on the first-order Poincaré sphere, (b) the index profile of the used FMF and (c) the simulated mode fields and effective refractive index of the used vector modes of the FMF at 1550 nm wavelength.

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where $|L_l〉=(\widehat{x}+i\widehat{y})e^{-il\phi }/\sqrt{2}$ and $|R_l〉=(\widehat{x}-i\widehat{y})e^{il\phi }/\sqrt{2}$ stand for the left- and right-handed polarization states respectively, and the term e^ilφ is the characteristic of a helical phase wave-front for the orbital angular momentum (OAM) mode, namely, vortex beams. Then, the point located at the equators of higher-order Poincaré spheres, namely corresponding to the CVBs, can be represented as follows,

Thus, the CVBs can be projected to two basis states of the left- and right-handed polarization states with the helical phase e^ilφ. For instance, the radially polarized mode TM₀₁ (point A in Fig. 2(a)) can be treated as a superposition of the ± 1 order vortex modes (point C, D in Fig. 2(a)).

Subsequently, according to the feature of CVBs, there is a non-separable coupling between the spatial and polarization degrees of freedom [39–41]. This coupling will result in the mode crosstalk when the CVBs propagated through the optical fiber. Besides, optical fiber’s imperfection and perturbation may impact the spatial and polarization distribution of CVBs, which may further lead to the inter-mode crosstalk when we use these modes as independent channels to carry data for transmission over fiber. Thus, the performance of these modes propagated in the used optical fiber should be characterized before implementing the data transmission. Figure 2(b) shows the index profile of the used four-mode fiber (4-mode FMF) with a core diameter 2a = 19 μm, a cladding diameter 2b = 125 μm, a core index of 1.449 and a cladding index of 1.444, which can support the linearly polarized modes of LP₀₁, LP₁₁, LP₂₁ and LP₀₂, or correspondingly, the vector modes of HE₁₁, TE₀₁, HE₂₁, TM₀₁, HE₃₁, EH₁₁ and HE₁₂ at 1550 nm wavelength. Figure 2(c) theoretically illustrates the effective refractive index (n_eff) of the multiplexed vector modes in the VMDM transmission system. The effective refractive index difference between the TM₀₁ and the TE₀₁ modes of the used fiber is around 3.4e-6.

The experimental setup used to characterize the CVB mode performance is shown in Fig. 3(a). The output light from laser is collimated (COL) and transformed to uniform linearly polarized beam by a linear polarizer (LP). Then, we employ the Q-plate with a topological charge q = 1/2 (QP, Arcoptix) to generate radially polarized vector mode TM₀₁ (inset 3(i)), which is launched into the 4-mode FMF link for transmission. By rotating the PC-FMF, we obtain the optimal output pattern. The polarization constituents of output beams are separated by a polarization grating (PG), which can diffract the input beams into the left- and right-handed polarization beams with the opposite order. In our experiment, TM₀₁ (Inset Fig. 3c(A)) and TE₀₁ modes (Inset Fig. 3c(B)) are decomposed to two basis states of the opposite circular polarization with helical phase e ^{± iφ}. The power of the divided two parts (I_L and I_R) are detected by the spatial optical power meter. According to Eq. (2), I_L and I_R should have the same weight to form a pure TM₀₁ and TE₀₁ modes under the ideal condition. We measured the separated power in the cases of transmissions in free space, 5 m FMF and 100 m FMF respectively. The normalized results are shown in Fig. 3(b), which indicates the performance degradation of CVBs during the fiber propagation. We can see that the generated TM₀₁ and TE₀₁ modes by the QP are not so pure since the imperfect conversion resulted in that other modes have been included. Thus, after transmission over the FMF, the scale of the two components of TM₀₁ and TE₀₁ modes become further imbalanced due to the mode coupling. Figures. 3(c)-3(A1) and 3(c)-3(A2) / Figs. 3(c)-3(B1) and 3(c)-3(B2) depict the intensity patterns of separated two parts after transmission over 5 m FMF. Finally, a quarter-wave plate (QWP) is employed to adjust the polarization of the divided vortex beams for interference. Figures. 3(c)-3(A3) and 3(c)-3(A4) /Figs. 3(c)-3(B3) and 3(c)-3(B4) depict their interference patterns of the clockwise spiral and the counter clockwise spiral with the reference Gaussian beam. These interference patterns clearly showed that the radially and azimuthally polarized vector modes TM₀₁ and TE₀₁ after transmission over FMF can be projected to two basis states of the left- and right-handed polarization states with the first-order OAM. Then, the mode crosstalk induced by the imbalanced two states can be further verified by the measured power difference.

 

Fig. 3 (a) The experiment setup for characterizing CVB performance. COL: collimator; LP: linear polarizer; QP: q-plate; FMF: four-mode few-mode fiber; PC-FMF: polarization controller based on four-mode fiber; PG: polarization grating; QWP: quarter-wave plate; CCD: charged-coupled device camera. (b) the measured power differences under different conditions. (c) Insets (A) and (B) depict the used vector modes. Insets (A₁) and (A₂) / (B₁) and (B₂) illustrate the separated left- and right-handed polarization intensity patterns corresponding to the insets (A) / (B) after transmission over 5 m FMF. Insets (A₃) and (A₄) / (B₃) and (B₄) show the interference patterns of the clockwise spiral and the counter clockwise spiral corresponding to the insets (A₁) and (A₂) / (B₁) and (B₂), respectively.

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Figure 4 illustrates the comparison of the intensity profiles before (insets (A) and (B)) and after (insets (C) and (D)) transmission over 100 m FMF. By rotating the linear polarizer (LP) placed in front of the charged-coupled device (CCD) camera, we obtain the polarization distribution of CVBs channels which are shown in the Figs. 4(a)-4(d). Obviously, the property of polarization patterns of CVBs becomes worse after transmission over FMF, which may be caused by the fiber perturbation and strong mode coupling. Figures 4(E) and 4(F) show the profiles of the demultiplexed CVBs corresponding to the output TM₀₁ and TE₀₁ channels at the end of 100 m FMF, respectively.

 

Fig. 4 The intensity profiles of the 2 CVB channels before (insets A and B) and after (insets C and D) transmission over 100 m FMF, respectively. The arrows indicate the orientations of the transmission axis of the LP. Insets (a) ~(d) show the property of the polarization distribution of the corresponding channels. Insets (E) and (F) depict the intensity profiles of the demultiplexed CVBs corresponding to TM₀₁ and TE₀₁ channels, respectively.

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3.2 Transmission results

The crosstalk of between CVBs channels (TE₀₁ and TM₀₁) in this experiment is shown in the Fig. 5, in which a mode isolation (MI) has been used to measure the crosstalk when the two orthogonal modes are transmitted simultaneously. As can be seen from Fig. 5, the respective minimum MI are about 16.8 dB after transmitting over 5 m FMF and 12.5 dB over 100 m FMF. There is no doubt that MI has a significant impact on the transmission performance of this CVB-based MDM system. Thus, based on the MI achieved in the experimental condition, we demonstrate the VMDM-DD-OFDM transmission with 16QAM modulation format over 5 m FMF link and QPSK modulation format over 100 m FMF respectively.

 

Fig. 5 Modal isolation for CVBs transmission over the used FMF after (a) 5 m and (b) 100 m respectively.

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In the experiment, the IFFT size for OFDM signal generation is 512, in which 246 low positive frequency subcarriers carry data and another 246 low negative frequency subcarriers are set as the complex conjugate of the positive frequency subcarriers to generate real-value OFDM signal. The first subcarrier is set to zero for DC-bias. The rest 19 null subcarriers at the edge of high frequency are also set zeros for oversampling. A 32-sample cyclic prefix (CP) is added to the 512 samples, giving 544 samples per OFDM symbol. One training sequence (TS) is inserted in the front of 100 OFDM signal symbols to realize time synchronization and channel estimation. Thus, the aggregate raw bit rate of 5 m FMF link system is 25 × 246/512 × 100/101 × 4 × 2 ≈95.16 Gb/s. Accordingly, the total raw bit rate of 100 m FMF link is 25 × 246/512 × 100/101 × 2 × 2 ≈47.58 Gb/s.

Figure 6 shows the measured bit-error-ratio (BER) property versus the received optical power for the above two cases. When 16QAM is employed, there are 1.7 dB, 1.9 dB power penalties between the back-to-back (B2B) and CVB channels respectively under the forward error correction (FEC) threshold of 3.8 × 10⁻³ when the propagation distance is 5 m. In principle, the 16QAM modulation format is more sensitive to the mode crosstalk which becomes larger with propagation through the FMF. Meanwhile, there is no MIMO DSP algorithm used to compensate the signal impairment in our experiment. As a result, the BER of DD-OFDM-16QAM signal cannot reach the error-free after transmission 100 m FMF. However, only 0.6 dB and 0.55 dB power penalties are induced when the length of link is 100 m with the modulation format of QPSK. This is obviously benefit from the lower-order modulation format. In addition, the received power is much lower than that of 16QAM transmission. This meant that the higher data rate or longer transmission distance can be realized provided that the more power penalty be acceptable. Therefore, the demonstrations of 5 m and 100 m VMDM transmission have the potential applications in the short-reach optical interconnect [42].

 

Fig. 6 The BER performances of CVB-based DD-OFDM-MDM transmission over FMF link of distance (a) 5 m with 16QAM; (b) 100 m with QPSK. B2B: back to back.

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4. Conclusions

In conclusion, the fiber vector eigenmode based mode division multiplexing transmission system over few-mode fiber has been demonstrated. We use a modal decomposition scheme based on polarization grating to analyze the mode inter-coupling and the variation of spatial and polarization distribution when the CVBs propagate in the few-mode fiber. By using the 1st-order CVBs, namely, the eigenmode of TM₀₁ and TE₀₁ modes, the 95.16 Gb/s over 5 m FMF and 47.58 Gb/s over 100 m FMF transmissions have been realized with the DD-OFDM technology. The experimental results show that the CVB-based MDM technique has the potential in the large-capacity short-reach optical interconnects.