Rapid growth of global Internet traffic has driven significant research efforts to develop mode-division multiplexing (MDM) technology in the past decade [1–5]. High capacity and long distance have always been pursued for an MDM transmission system. At present, there have been quite a few reports on long-haul MDM transmission over thousands of kilometers, even with up to 15 modes [6–9]. However, in reported MDM transmissions, in-line few-mode erbium-doped fiber amplifiers (FM-EDFAs), which can simultaneously amplify multiple spatial channels with high energy efficiency, are often absent due to the relatively slow development of the FM-EDFAs. Instead, multiple commercially available single-mode EDFAs are used for long-haul transmission. Up to now, only three-mode in-line FM-EDFAs have exhibited transmission distances of >1000km [10–13], and those with three, six, and more modes have shown a relatively short reach of 180 km [14–17], as shown in Fig. 1. Thus, achieving a long-haul and high-mode-count transmission with in-line amplification would be of great interest.

In fact, it is quite difficult to achieve both long distance and high mode counts, which requires multifold innovations in optical fibers, FM-EDFAs, system architectures, and so on. In MDM transmissions via in-line amplification, high-performance FM-EDFAs become the key device to determine the longest distance achievable for MDM systems. Note that low differential modal gains (DMGs) are critical for FM-EDFAs, as a large DMG can cause large power imbalance among spatial modes after long-haul transmission. Although several control knobs, such as erbium doping profile [18–21], pump modal distribution [22–26], and index profile [27], have been proposed to reduce the DMG, the reported DMG values for six-mode erbium-doped fiber amplifiers (6M-EDFAs) are >2dB [16,17]. One possible reason is that the diffusion of erbium ions during the erbium-doped fiber drawing process makes real doping profiles drift away from their designed versions [28], which could introduce an additional DMG to FM-EDFAs. Minimizing DMG becomes urgent to achieve a six-mode transmission at a 1000-km level.

In this work, we propose a two-layer Gaussian-like erbium doping profile for a 6M-EDFA to achieve a DMG as low as 1.15 dB across the C-band, which represents the lowest DMG of 6M-EDFAs, to the best of our knowledge. Moreover, modal gains of >18dB and noise figures (NFs) of <8.4dB are simultaneously achieved for the 6M-EDFA. Using it, we demonstrate 28-GBaud dual-polarization QPSK six-mode transmission, greatly extending the world-record reach from 180 to 960 km and enriching the application scenarios of six-mode transmission.

The 6M-EDF supports six linear polarization modes, i.e., LP01, LP11a, LP11b, LP21a, LP21b, and LP02. It is fabricated by modified chemical vapor deposition [29]. The core diameter of the 6M-EDF is 20 μm, and its numerical aperture is 0.12. The effective mode areas of the six modes at 1550 nm are 206.7μm2, 210.1μm2, 210.2μm2, 218.9μm2, 219.0μm2, and 228.9μm2, respectively.

Often, the erbium dopant distribution is designed to have a perfect step multi-layer profile. However, due to erbium ions diffusion and other imperfections during fabrication, it is challenging to precisely control the erbium doping profile to be an ideally designed profile. That is why the erbium ions distribution in real EDFs exhibits a Gaussian-like distribution, greatly differing from the design. Thus, we propose a two-layer Gaussian-like erbium doping profile to minimize the influence of erbium ions diffusion on DMG. By doing this, we find that the tested erbium doping profile matches well with the designed, with an erbium doping concentration error of <10%, as shown in Fig. 3(a). Measured results are obtained by an electron probe micro-analyzer. Moreover, the total MDL of all passive components is ∼5dB, which directly contributes to the DMG of the 6M-EDFA. Here, two segments of 6M-EDF are used. To minimize the overall DMG of the two-stage 6M-EDFA, the modal gains of the LP21 and LP02 modes should be designed to ∼2.5dB higher than that of the LP01 mode for the 6M-EDF. By increasing the gains of the LP21 and LP02 modes appropriately, the difference in gains between these modes can be reduced. The simulation result of the 6M-EDF is shown in Fig. 3(b). Across the C-band, the modal gains of the LP21 and LP02 modes are about 2.5 dB higher than that of the LP01 mode.

Figure 4(a) shows the experimental setup to characterize the proposed 6M-EDFA. The six input signals are generated by a tunable laser source (TLS) and split into six beams via a 1×6 coupler. To avoid mode interference, single-mode fiber delay lines (DLs) with lengths of 10, 20, 30, 40, and 50 m are sequentially inserted into the last five paths, and six variable optical attenuators (VOAs) are employed to adjust the signal power. Finally, the signals of the six modes are fed into the 6M-EDFA through a commercial six-mode multiplexer (6M-Mux) based on the multi-plane light conversion technique [30,31]. The amplified signals from the proposed 6M-EDFA are demultiplexed into six fundamental modes by a six-mode demultiplexer (6M-DeMux) and then recorded by an optical spectrum analyzer (OSA). The 6M-Mux and 6M-DeMux are used to characterize the performance of each mode only and do not influence the amplification performance of the 6M-EDFA in real transmission systems.

The modal crosstalk between the 6M-Mux and 6M-DeMux is <−15dB. The insertion losses of individual modes are <3.8dB for 6M-Mux or 6M-DeMux. At the two splicing points, A and B, the insertion losses are <0.3dB. The modal gain and NF are measured by comparing the input and output spectra of the 6M-EDFA. The insertion losses of passive components and the splice losses are excluded from the calculation. Figure 4(b) shows the modal profiles of signals before and after amplification, under the condition where individual modes are amplified separately by the 6M-EDFA. Before characterizing the gain and NF of the 6M-EDFA, the modal crosstalk of the whole setup should be measured first, because mode coupling among the signal modes may lead to measurement errors [32]. Figure 4(c) shows that the crosstalk introduced by the 6M-EDFA is <−12.37dB. This crosstalk level will not severely deteriorate signal quality as the multi-input multi-output (MIMO) technique can be used to recover the signals [2]. In order to accurately characterize the modal gain, the output signal powers should be corrected according to the crosstalk matrix [12,20,32].

We first use the cutting-back method to test the optimized length of the 6M-EDF for a single-stage 6M-EDFA. Figure 5(a) shows the modal gain and DMG of the single-stage amplifier at different EDF lengths with a forward pumping power of 600 mW and the input signal power of −10dBm. The signal wavelength is 1550 nm. The length ranges from 5 to 8 m with a step of 0.5 m. The modal gains gradually increase with fiber length. Limited by the maximum output power of the pump LD, the modal gains approach saturation of 12.45 dB at the length of 7.5 m. On the other hand, the DMG gradually decreases with fiber length to a minimum of 1.12 dB. Thus, the length of the 6M-EDF for the first-stage amplifier is set to 7.5 m. Subsequently, the length of the 6M-EDF for the second-stage amplifier is optimized in the same way. Figure 5(b) shows the modal gain and DMG of a dual-stage amplifier at different second-stage EDF lengths. Both the forward and backward pumping powers are 600 mW. We find that the modal gains first increase and then decrease with the length of the second 6M-EDF. The saturated modal gains are >19.3dB at the second-stage EDF length of 7 m, and the DMG is 1.02 dB.

Figure 6 shows the modal gain, DMG, and NF as a function of forward pump power (FPP) of the first-stage amplifier when the backward pump power (BPP) of the second-stage amplifier is set to 600 mW and the input signal power for each mode is −10dBm. FPP ranges from 100 to 600 mW with a step of 100 mW. The modal gains increase with FPP and start to saturate when the FPP is >400mW. Meanwhile, the DMG decreases from 1.5 to 1.02 dB and then remains almost unchanged after the modal gains become saturated. The NFs decrease as FPP increases and reach a minimum of about 7.3–8.15 dB for the six modes when the FPP is 600 mW. The higher NFs for the higher-order modes partially arise from the higher insertion losses of passive components. Besides, the NF difference between the degenerate LP11 and LP21 modal groups originates from the MDL of passive components. Figure 7 shows the modal gain, DMG, and NF as a function of BPP when the FPP is set to 600 mW. The maximum modal gains are 19.35–20.12 dB, with a minimum DMG of 1.04 dB, when the BPP is increased to 600 mW. The NFs keep almost unchanged with the aid of a 6M-ISO in the middle of the two-stage amplifier, which prevents the backward ASE power from returning into the first stage. It is observed that the pump power of the second-stage amplifier has a larger influence on the modal gains and the DMG than that of the first stage. On the other hand, the NFs are mainly affected by the pump power of the first-stage amplifier. Slightly higher modal gains and lower DMG could be achieved if a pump LD with a larger output power is available.

Figure 8 shows the modal gain, DMG, and NF as a function of the input signal power, which ranges from −25 to −5dBm for individual mode. Both FPP and BPP are 600 mW. It is observed that the modal gains increase to a maximum of 25 dB when the input power is −25dBm. The DMG still remains <1.13dB over a wide range of input power, with the fluctuations of NFs within 0.35 dB.

Figure 9(a) shows modal gain and DMG across the C-band, where a flattened amplified spontaneous emission (ASE) source is used as the signal source. We test the setup again and find that the crosstalk is still <−8.7dB, which has little influence on the characterization and sequent applications in the strongly coupled MDM transmission systems. Both FPP and BPP are 600 mW. The total input power of individual mode over the wide band is −10dBm. It is observed that modal gains and the DMG across the C-band are >17.6dB and <1.15dB, respectively, as shown in Fig. 9(a). Compared with our previous work with a step erbium doping profile [33], the DMG is significantly reduced by more than 4.8 dB, which proves the effectiveness of the Gaussian-like erbium doping profile for gain equalization. Besides, eight equalized signals with a total power of −10dBm/mode are selected to characterize NFs. The wavelength ranges from 1530 to 1565 nm with a step of 5 nm. The NFs are <8.4dB across the C-band, as shown in Fig. 9(b). Compared to single-mode EDFAs, the additional NF of the 6M-EDFA can be mainly attributed to the insertion losses of six-mode passive components and the mode mismatch induced losses between the 6-mode fiber (6MF) and the 6M-EDF. The NFs are expected to be further reduced, if passive components with lower insertion losses and MDL are available. The difference in noise figures resulting from the MDL of six-mode components used in the 6M-EDFA would cause different signal-to-noise ratios (SNRs) across modes, which degrades signal quality after long-haul transmission.

To show superior performance of the proposed 6M-EDFA, we set up a six-mode recirculating loop system, as shown in Fig. 10. An external cavity laser with a linewidth of ∼100kHz at 1550 nm is modulated with a 28-GBaud QPSK signal. The modulated signal is split into six tributaries, decorrelated with the length of delay lines of 0 m, 400 m, 800 m, 1200 m, 1600 m, and 2000 m for the LP01, LP11a, LP11b, LP21a, LP21b, and LP02 modes, respectively. The 6M-EDFA, as an in-line amplifier, is used to compensate for the loop transmission loss of a 60-km six-mode fiber (6MF), while six single-mode EDFAs have to be used to compensate for losses from 6M-Mux, 6M-DeMux, acousto-optic modulators (AOMs), and VOAs due to the absence of six-mode AOMs [16]. For the 6MF, the differential mode delay (DMD) is ∼468ps/km, as determined by the spatial and spectral imaging method [34]. Meanwhile, the fiber loss and mode-dependent loss (MDL), determined by the cut-off method [35], are ∼0.26dB/km and ∼0.06dB/km, respectively. The launched powers of individual modes are 4 dBm. A cyclic mode permutation (CMP) scheme is applied to suppress DMD-induced pulse spreading [7]. A time-division multiplexing scheme is applied to the reception of all signals by two coherent receivers [36]. The electrical signals are digitized in a real-time oscilloscope with 36-GHz electrical bandwidth at 80 GSamples/s, and a frequency-domain 12×12 MIMO equalization is used to recover the data.

Figure 11(a) shows the impulse responses averaged over all modes at 240, 600, and 960 km with the CMP scheme. The corresponding response widths are 41.72 ns, 60.42 ns, and 79.13 ns, respectively. Note that the relative delay between the six parallel single-mode loops is within 1 cm, corresponding to a time delay of 50 ps. This 50-ps delay is significantly smaller than the overall DMD-induced delay over the 60-km span. Therefore, the measured signal spread is primarily determined by the 6MF’s properties rather than loop misalignments. We obtain the impulse responses by Gaussian fitting the normalized transmission matrix, and then the necessary equalizer windows required for full MIMO digital signal processing can be calculated. In a transmission system without mode permutation, signal broadening is significant as the transmission reach increases due to slight inter-modal mixing. However, when the permutation scheme is applied, the impulse spreading could be compressed [7], which could mitigate the DMD impact. The impulse response at 240 km still has many spikes, indicating insufficient mode coupling, while those at 600 and 960 km take on a bell-shaped distribution, showing considerable mode coupling. As a result, it exhibits a nonlinear relationship between equalizer window and transmission distance, as shown in Fig. 11(b).

Figure 12(a) gives the bit error rate (BER) as a function of transmission distance. The constellations of six channels after 960-km transmission are in Fig. 12(b), averaged in the two polarization states. After 960-km transmission, an averaged BER over six modes of ∼7.21×10−3 is obtained, with the BER of individual modes below the forward error correction (FEC) limit [37]. Despite the coupling enhancement brought by the CMP scheme, the BER difference between the best and worst channels remains a major obstacle in achieving longer transmission distances. This BER difference mainly arises from the varying signal-to-noise ratios (SNRs) among the six modes. These varying SNRs are caused by two factors: the mode-dependent loss/gain induced by few-mode devices within the link and the difference in noise figures induced by the 6M-EDFA. We expect that, if additional mode exchange [33] could be introduced in the dual-stage 6M-EDFA to enable more frequent mode mixing for mitigating the DMD- and MDL-induced degradation, transmission reach can be extended. Besides, it is noted from the above that the NFs are also mode-dependent due to the MDLs of the passive components, and thus a 6M-EDFA with more uniform noise properties could reduce the BER difference. Additionally, a gain flattening filter can be employed to further flatten the gain spectrum of the 6M-EDFA, thereby enabling the system to effectively support more wavelength channels.

For the first time, we have experimentally demonstrated an in-line integrated 6M-EDFA in a long-haul six-mode transmission system, showing a 5× reach extension from 180 to 960 km. This is enabled by a greatly reduced DMG, benefiting from a Gaussian-like erbium doping profile, with the minimized erbium concentration errors between the designed and tested erbium doping profiles. Importantly, the modal gains of >17.6dB, DMG of <1.15dB, and NFs of <8.4dB over the C-band are simultaneously achieved by the proposed 6M-EDFA. After 960-km transmission, the averaged BER for the six modes is around 7.21×10−3. The overall performance of the proposed 6M-EDFA can be further improved with a well-matched erbium doping profile, which indicates a potential application in integrated MDM systems supporting more linear polarization modes and a longer transmission distance.