1. Introduction

With the rapid development over the past few decades, the transmission system based on single-mode fiber (SMF) has gradually reached its nonlinear Shannon capacity limit [1,2]. To further increase the transmission capacity and simultaneously keep more compact inline devices (e.g., optical fiber amplifier, etc.) for low cost and energy consumption per bit, mode division multiplexing (MDM) based on few-mode fiber (FMF)/ multimode fiber (MMF) has been proposed and extensively studied recently. The MDM systems make use of the fiber mode space to accommodate multiple independent mode channels and increase the transmission capacity in one fiber. However, the complexity of multi-input multi-output (MIMO) processing to cope with the inter-mode crosstalk and differential mode delay (DMD) will be significantly increased as the mode multiplexing scale or fiber transmission distance is further improved [3].

To cope with this problem, MDM schemes based on weakly-coupled FMFs have been proposed and demonstrated recently [4–9]. In these schemes, fibers with large relative refractive index differences (Δn_eff) are designed to maintain weak coupling among fiber modes or mode groups (MGs) so that MIMO-free [4,5] or partial-MIMO processing [6–8] can be adopted. As one special class of the weakly-coupled FMFs, ring-core optical fibers (RCFs) that can support both the linearly polarized (LP) and orbital angular momentum (OAM) mode basis have been increasingly studied over recent years [9–15]. With confinement of radial dimension, the RCFs exhibit good scalability towards high-order mode space as well as low mode-dependent gain in the fiber amplifiers [9]. Furthermore, efficient mode sorting of the OAM modes supported in the RCF can be achieved by only having to consider the azimuthal dimension in a relatively simple mode transform process [15]. Owing to these characteristics, data transmissions in RCF-based MDM systems over single-span fiber of 10 km [11], 18 km [12,13], 24 km [14], 50 km [15], and 100 km [16] have been achieved with aggregated capacity up to 10-Tbit/s level utilizing only partial MIMO or MIMO-free processing.

However, only two adjacent high-order MGs each carrying 4 mode channels (2 modes × 2 polarizations) are employed in most of the above-mentioned RCF-based MDM systems. In addition, relatively high coupling between adjacent low-order MGs (e.g., OAM MGs with topological charge |l| = 0 and 1) in RCFs of such schemes make them cannot be utilized in long-distance MDM transmission requiring only low-complexity MIMO equalization. Therefore, new solutions are desired to explore more multiplexed mode channels and thus further increase the capacity of the RCF-based MDM systems whilst keeping low MIMO complexity.

In this paper, we successfully demonstrate the OAM mode and wavelength division multiplexed (OAM-MDM-WDM) transmission utilizing 14 OAM mode channels (7 OAM modes × 2 polarizations) over a single-span 100-km RCF. The refractive-index profile (RIP) of RCF is specially designed so that four weakly-coupled OAM MGs with topological charge |l| = 0 to 3 can be supported. With each mode channel carrying 80 wavelengths modulated by 20-Gbaud QPSK signals, an aggregated (net) capacity of 44.8 (37.3) Tbit/s and a raw (net) spectral efficiency of 22.4 (18.7) bit/s/Hz can be achieved with bit error rates (BERs) of all channels below 20% soft-decision FEC threshold correcting BER of 2.4×10⁻². A record spectral-efficiency-distance product of 1870 (bit/s/Hz)·km is successfully realized for RCF-based MDM transmissions, only utilizing low-complexity 4${\times}$4 or 2${\times}$2 MIMO equalization with time-domain equalization tap number no more than 25 to deal with the intra-MG mode coupling.

2. Characterization of the fiber

Figure 1(a) and 1(b) depict the cross section and RIP of the fabricated double-layer RCF, respectively. Different from the conventional RCF with both the inner and outer cladding, an inner-core layer with a refractive index relatively lower than that of the outer-core layer (still higher than the cladding refractive index) is designed to replace the inner cladding. This enables Δn_eff to be larger than 1.5×10⁻³ at 1550.12 nm among all the supported guide MGs so that the weak coupling between adjacent MGs can be maintained in the transmission link with a length scale up to one hundred kilometers, despite that the single-radial-order limitation is broken and the LP02 mode is involved, as shown in Fig. 1(c). Although the calculated results show that the OAM MG |l| = 4 can be supported, the attenuation of this MG is relatively large due to its very small refractive-index difference from that of the fiber cladding. Therefore, optical modes within the four OAM MGs with topological charge |l| = 0 to 3 are selected as transmission mode channels in our demonstration. The LP02 mode is not used for the MDM transmission due to the limitation of our mode generation setup even though its Δn_eff from the adjacent mode groups is large enough to maintain inter-mode-group weak coupling. The differential group delay (DGD) among the four OAM MGs after 100 km transmission are characterized using a vector network analyzer (VNA) [17] at the wavelength of 1550.12 nm, as shown in Table 1. Figure 1(d) illustrates the measured mode-dependent attenuation of the RCF utilizing an optical time-domain reflectometry (OTDR), whose value is around 0.21 dB/km on average with mode-dependent loss (MDL) of no more than 0.031 dB/km.

 

Fig. 1. (a) The cross section and (b) the RIP of the fabricated RCF. (c) The measured mode-dependent attenuation curves by OTDR.

Download Full Size | PDF

Table 1. Characterization of the OAM-WDM-MDM system after 100-km fiber transmission

View Table | View all tables in this article

3. Experimental setup

The experimental setup for the OAM-WDM-MDM transmission system is shown in Fig. 2, which contains five parts: a WDM signal transmitter with QPSK modulation, an OAM mode multiplexing (MUX) module, the single-span 100-km RCF, an OAM mode demultiplexing (DEMUX) module and coherent optical receivers followed by the offline digital signal processing (DSP).

 

Fig. 2. Experimental setup for OAM-WDM-MDM transmission system based on the 100-km RCF. AWG: arbitrary waveform generator; EA: electrical amplifier; ECL: external cavity laser; OP: optical processor; WDM: wavelength division multiplexer; DL: SMF-delay; EDFA: erbium-doped fiber amplifier; PC: polarization controller; Col.: collimator; LP: linear polarizer; SLM: spatial light modulator; QWP: quarter-wave plate; PBS: polarization beam splitter; PBC: polarization beam combiner; BS: beam splitter; VPP: vortex phase plate; ICR: integrated coherent receiver; LO: local oscillator; OSC: oscilloscope; DSP: digital signal processing. (The inset illustrates the intensity profiles of OAM MGs |l| = 0∼3 after 100-km transmission)

Download Full Size | PDF

3.1 WDM-QPSK transmitter

At the transmitter, five optical carriers from wavelength-tunable external cavity lasers (ECLs) are employed as the sliding test band, while a WDM carrier generator based on multiple seed light sources modulated by cascaded Mach-Zehnder modulator (MZM) and phase modulator is utilized as the light source of the dummy band. To avoid overlapping wavelengths, the dummy band is reshaped by a programmable optical processor (OP). After passing through a wavelength multiplexer, the test and dummy bands are combined together to form WDM carriers with 80 wavelength channels ranging from 1541.75 nm to 1557.57 nm at a 0.2 nm/25 GHz grid. Then the generated WDM carriers are modulated by 20-GBaud QPSK signals from an arbitrary waveform generator (AWG) through in-phase/quadrature (I/Q) modulators. Here the electrical QPSK signals are digitally shaped by a raised-cosine filter with a roll-off coefficient of 0.6 to maintain a large enough guard band and thus mitigate the insufficient decorrelation between adjacent WDM channels [18]. Finally, the generated WDM signals are amplified by a gain-flattened erbium-doped fiber amplifier (EDFA).

3.2 OAM mode multiplexing

The WDM signals are split into 7 branches, each of which is de-correlated using SMFs with different lengths and amplified separately by the high-power EDFAs. Then the 6 of the Gaussian-like beams from the SMFs are collimated, linear polarization filtered and finally converted into OAM beams employing 3 spatial light modulators (SLMs). Each SLM is partitioned into two halves for generating OAM modes with topological charges of + l and -l (l = 1, 2, 3). Then the generated OAM pairs in each OAM MG with topological charge |l| = 1, 2, and 3 are combined by polarization beam splitters (PBSs) or beam splitters (BSs). It is noted that to balance the MDL among all guided MGs, one more 3-dB BS is used to replace the PBS and the half-wave plate (HWP) in the optical paths of the OAM MG with topological charge |l| = 1, compared with that for OAM beams with topological charge |l| = 2 and 3, as shown in Fig. 2. Besides, the transmitting power of the EDFA for the mode l = 0 is appropriately reduced owing to the relatively low attenuation. The generated three OAM mode pairs can be expressed as < +l, x > and < -l, y >, where l = 1, 2, and 3, x and y present the x-polarization and y-polarization respectively. Particularly, the OAM mode with a topological charge of l = 0 is generated from the Gaussian-like beams after collimation and linear polarization filtering without using SLM. After being combined by the BSs and converted into circular polarizations, the OAM beams pass through a polarization multiplexed module including a PBS, an optical delay path and a polarization beam combiner (PBC) and are converted into circular polarizations to generate the mode space of lϵ $\langle{l, s}\rangle$, with ${l \in }$ [0, ±1, ±2, ±3] and polarization (spin) ${s \in }$ ±1 before being coupled into the 100-km RCF. Here noted that the multiplexing scheme used in our experiment with bulk elements can be replaced by more integrated optical modules with only several separate phase plates based on advanced spiral transformation [15] or multi-plane light conversion [19], even though efficient beam conversion from the densely packed single-mode fiber array to the RCF would be a challenge when many more mode channels are involved.

3.3 OAM mode demultiplexing and WDM-QPSK receiver

After 100-km RCF transmission, the optical intensity profiles of OAM MGs |l| = 0 to 3 can be observed at the end of the RCF, as shown in the inset of Fig. 2. Here note that an LP-mode-like intensity profile is formed by the coherent superposition of four intra-MG OAM modes [9], and the clear azimuthal distributions of the received intensity profiles indicate low inter-MG coupling. The spatial beams emitted from the RCF are restored into linearly-polarized states through a QWP and then they are split into two branches. For the detection of OAM mode l = 0, only one of the branches is coupled into an SMF directly. For the detection of high-order OAM MGs (|l| = 1, 2, 3), each of two branches passes through a vortex phase plate (VPP) with an opposite topological charge. Therefore, the OAM modes with topological charges of + l and -l are converted into Gaussian beams and subsequently coupled into the SMFs. Subsequently, they are amplified by the EDFAs used as pre-amplifiers and detected by two SMF-pigtailed integrated coherent receivers (ICRs). Finally, eight electrical waveforms generated by the two ICRs are sampled and stored by an 8-channel real-time oscilloscope operated at 50 GSa/s for offline DSP, which includes timing phase recovery, 4×4 MIMO equalization (for OAM MG |l| = 1, 2 and 3) or 2×2 MIMO equalization (for OAM MG |l| = 0) based on constant modulus algorithm, frequency offset estimation, and carrier phase estimation.

4. Results

We have experimentally characterized the inter-MGs crosstalk of the entire OAM-WDM-MDM transmission system at the wavelength of 1550.12 nm. As shown in Table 2, the crosstalk between adjacent MGs are around -11 dB, indicating that the inter-MG coupling coefficient of the RCF can be lower than -30 dB/km.

Table 2. Measured inter-MG crosstalk (dB) in the OAM-WDM-MDM system after 100-km RCF transmission

View Table | View all tables in this article

In order to evaluate the transmission performance of this system, BERs at different OSNR are evaluated in a single-wavelength transmission scenario. The measured curves between BER and OSNR of all OAM guided modes are illustrated in Fig. 3(a), where the BER values of two orthogonal polarizations with the same topological charges are averaged for simplicity. The inset depicts the recovered QPSK constellation of OAM mode l = +2 with x-polarization at an OSNR of 22 dB after 100 km RCF transmission. The BERs of all mode channels are all below the 20% soft-decision FEC threshold of 2.4 × 10⁻² with the presence of XT when the OSNR is higher than 14 dB. Compared with the case without any inter-MG crosstalk, the OSNR penalty of OAM MG |l| = 3 is about 4 dB after 100 km transmission with all inter-MG crosstalk at the 7% hard-decision FEC threshold of 3.8 × 10⁻³. Meanwhile, these values become about 10 dB for all the three OAM MG |l| = 0, 1, and 2. This is mainly because relatively larger crosstalk for the OAM MGs |l| = 1 and 2 comes from their two adjacent MGs, while such inter-MG crosstalk for the OAM MG |l| = 3 is only from one adjacent MG. As for the OAM mode l = 0, its relatively high OSNR penalty between the cases with and without inter-MG crosstalk might be resulted from the high crosstalk from the LP02 mode due to inaccurate mode excitation in the RCF. Figure 3(b) presents the corresponding 4 × 4 absolute-valued tap diagram of OAM mode l = +2 with x-polarization at an OSNR of 22 dB. In the process of the 4 × 4 equalization, the number of iterations is set to 50 for convergence and the number of taps is only set to 25 due to the high degeneracy and strong coupling among the intra-MG modes.

 

Fig. 3. (a) The measured BER-OSNR curves of all guided modes in the case with crosstalk and without crosstalk, and the inset plots the recovered QPSK signal constellation of OAM mode l = +2 with x-polarization at an OSNR of 22 dB. (b) The absolute values of 16 complex-valued FIR filters in the 4×4 MIMO equalizer of OAM mode MG |l| = 2 at an OSNR of 22 dB after 100-km RCF transmission.

Download Full Size | PDF

The BERs of all 1120 transmission channels in the OAM-WDM-MDM system are also evaluated experimentally, as the results illustrated in Fig. 4(a). All the BERs are measured below the 20% soft-decision FEC threshold of 2.4×10⁻². Figure 4(b) depicts the spectrum of the 80 WDM channels from 1541.75 nm to 1557.57 nm, each carrying 14 OAM mode channels modulated with 20-GBaud QPSK signals. As a result, a successful data transmission with a total capacity of 44.8 Tbit/s, a spectral efficiency of 22.4 bit/s/Hz, and a capacity-distance product of 4.48 (Pbit/s)·km over a 100-km RCF is achieved.

 

Fig. 4. (a) The measured BER of all 1120 mode channels of the OAM-WDM-MDM system after 100-km RCF transmission. (b) The optical spectrum of the WDM signal from 1541.75 nm to 1557.57 nm.

Download Full Size | PDF

5. Summary

In this paper, an OAM-WDM-MDM transmission system supporting total 1120 channels (7 OAM modes × 2 orthogonal polarizations × 80 wavelengths) over a 100-km single-span distance has been successfully demonstrated, achieving a raw (net) capacity of 44.8 (37.3) Tbit/s and a raw (net) spectral efficiency of 22.4 (18.7) bit/s/Hz. BERs below the 20% soft-decision FEC threshold of 2.4×10⁻² have been achieved from all data streams based on low-complexity 4 ${\times}$ 4 or 2 ${\times}$ 2 MIMO equalization with time-domain equalization tap number no more than 25, realizing a record capacity-distance product of 4.48 (Pbit/s)·km for RCF based OAM-MDM transmission.

Appendix

According to the results of OAM MG |l| = 2 shown in Fig. 4(a) and (b), the recovered QPSK constellations of OAM mode l = 0, +1 and +3 at an OSNR of 22 dB are illustrated in Fig. 5(a), and the corresponding MIMO matrix of OAM MG |l| = 0, +1 and +3 are given in Fig. 5(b), (c) and (d), respectively.

 

Fig. 5. (a) The constellations of recovered QPSK signals of OAM mode (i) l = 0, (ii) l = +1 and (iii) l = +3 with x polarization at an OSNR of 22 dB after 100-km RCF transmission. (b) The modulus of 4 complex-valued FIR filters in a 2×2 equalizer at an OSNR of 22 dB for OAM mode l = 0. The modulus of 16 complex-valued FIR filters in a 4×4 MIMO equalizer at an OSNR of 22 dB for OAM mode (c) l = 1 and (d) l = 3.

Download Full Size | PDF

Funding

National Key Research and Development Program of China (2018YFB1801800); National Natural Science Foundation of China-Guangdong Joint Fund (U2001601); National Natural Science Foundation of China (61875233), (62101602); The Key Research and Development Program of Guangdong Province (2018B030329001), Guangdong Provincial Pearl River Talents Program (2017BT01X121).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

References

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

2. B. J. Puttnam, G. Rademacher, and R. S. Luís, “Space-division multiplexing for optical fiber communications,” Optica 8(9), 1186–1203 (2021). [CrossRef]  

3. S. O. Arik, D. Askarov, and J. M. Kahn, “Effect of mode coupling on signal processing complexity in mode-division multiplexing,” J. Lightwave Technol. 31(3), 423–431 (2013). [CrossRef]  

4. T. Hu, J. Li, D. Ge, Z. Wu, Y. Tian, L. Shen, Y. Liu, S. Chen, Z. Li, Y. He, and Z. Chen, “Weakly-coupled 4-mode step-index FMF and demo of IM/DD MDM transmission,” Opt. Express 26(7), 8356–8363 (2018). [CrossRef]  

5. L. Shen, D. Ge, Y. Liu, L. Xiong, S. Chen, H. Zhou, R. Zhang, L. Zhang, J. Luo, and J. Li, “MIMO-free 20 Gb/s×4×2 WDM-MDM transmission over 151.5-km single-span ultra low-crosstalk FMFs,” in Proceedings of 2018 European Conference on Optical Communication (ECOC), pp. 1–3.

6. D. Soma, S. Beppu, Y. Wakayama, K. Igarashi, T. Tsuritani, I. Morita, and M. Suzuki, “257-Tbit/s Weakly Coupled 10-Mode C + L-Band WDM Transmission,” J. Lightwave Technol. 36(6), 1375–1381 (2018). [CrossRef]  

7. S. Beppu, D. Soma, S. Sumita, Y. Wakayama, H. Takahashi, T. Tsuritani, I. Morita, and M. Suzuki, “402.7-Tb/s MDM-WDM Transmission Over Weakly Coupled 10-Mode Fiber Using Rate-Adaptive PS-16QAM Signals,” J. Lightwave Technol. 38(10), 2835–2841 (2020). [CrossRef]  

8. K. Ingerslev, P. Gregg, M. Galili, F. Da Ros, H. Hu, F. Bao, M. A. Usuga Castaneda, P. Kristensen, A. Rubano, L. Marrucci, K. Rottwitt, T. Morioka, S. Ramachandran, and L. K. Oxenløwe, “12 mode, WDM, MIMO-free orbital angular momentum transmission,” Opt. Express 26(16), 20225–20232 (2018). [CrossRef]  

9. J. Liu, G. Zhu, J. Zhang, Y. Wen, X. Wu, Y. Zhang, Y. Chen, X. Cai, Z. Li, Z. Hu, J. Zhu, and S. Yu, “Mode division multiplexing based on ring core optical fibers,” IEEE J. Quantum Electron. 54(5), 6300413 (2018). [CrossRef]  

10. X. Jin, A. Gomez, K. Shi, B. C. Thomsen, F. Feng, G. S. D. Gordon, T. D. Wilkinson, Y. Jung, Q. Kang, P. Barua, J. Sahu, S. Alam, D. J. Richardson, D. C. O’Brien, and Frank P. Payne, “Mode Coupling Effects in Ring-Core Fibers for Space-Division Multiplexing Systems,” J. Lightwave Technol. 34(14), 3365–3372 (2016). [CrossRef]  

11. G. Zhu, Z. Hu, X. Wu, C. Du, W. Luo, Y. Chen, X. Cai, J. Liu, J. Zhu, and S. Yu, “Scalable mode division multiplexed transmission over a 10-km ring-core fiber using high-order orbital angular momentum modes,” Opt. Express 26(2), 594–604 (2018). [CrossRef]  

12. L. Zhu, G. Zhu, A. Wang, L. Wang, J. Ai, S. Chen, C. Du, J. Liu, S. Yu, and J. Wang, “18 km low-crosstalk OAM + WDM transmission with 224 individual channels enabled by a ring-core fiber with large high-order mode group separation,” Opt. Lett. 43(8), 1890–1893 (2018). [CrossRef]  

13. L. Zhu, J. Li, G. Zhu, L. Wang, C. Cai, A. Wang, S. Li, M. Tang, Z. He, S. Yu, C. Du, W. Luo, J. Liu, J. Du, and J. Wang, “First demonstration of orbital angular momentum (OAM) distributed Raman amplifier over 18-km OAM fiber with data-carrying OAM multiplexing and wavelength-division multiplexing,” in Proceedings of Optical Fiber Communication Conference (OFC) (OSA, 2018), paper W4C.4.

14. F. Feng, Y. Jung, H. Zhou, R. Zhang, S. Chen, H. Wang, Y. Yang, S. U. Alam, D. J. Richardson, and T. D. Wilk, “High-order mode-group multiplexed transmission over a 24 km ring-core fibre with OOK modulation and direct detection,” in Proceedings of 2017 European Conference on Optical Communication (ECOC), pp. 1–3.

15. Y. Wen, I. Chremmos, Y. Chen, G. Zhu, J. Zhang, J. Zhu, Y. Zhang, J. Liu, and S. Yu, “Compact and high-performance vortex mode sorter for multi-dimensional multiplexed fiber communication systems,” Optica 7(3), 254–262 (2020). [CrossRef]  

16. J. Zhang, J. Liu, L. Shen, L. Zhang, J. Luo, J. Liu, and S. Yu, “Mode-division multiplexed transmission of wavelength-division multiplexing signals over a 100-km single-span orbital angular momentum fiber,” Photonics Res. 8(7), 1236–1242 (2020). [CrossRef]  

17. J. Zhang, J. Zhu, J. Liu, S. Mo, J. Zhang, Z. Lin, L. Shen, L. Zhang, J. Luo, J. Liu, and S. Yu, “Accurate Mode-Coupling Characterization of Low-Crosstalk Ring-Core Fibers Using Integral Calculation Based Swept-Wavelength Interferometry Measurement,” J. Lightwave Technol. 39(20), 6479–6486 (2021). [CrossRef]  

18. Liang B. Du and Arthur J. Lowery, “The validity of “Odd and Even” channels for testing all-optical OFDM and Nyquist WDM long-haul fiber systems,” Opt. Express 20(26), B445–B451 (2012). [CrossRef]  

19. N. K. Fontaine, R. Ryf, H. Chen, D. T. Neilson, K. Kim, and J. Carpenter, “Laguerre-Gaussian mode sorter,” Nat. Commun. 10(1), 1–7 (2019). [CrossRef]