Second-order few-mode Raman amplifier for mode-division multiplexed optical communication systems

Jiaxiong Li; Jiangbing Du; Lin Ma; Ming-Jun Li; Ke Xu; Zuyuan He

doi:10.1364/OE.25.000810

1. Introduction

Mode-division multiplexing (MDM) based on few-mode fibers (FMF) has attracted extensive attention over the past few years and is now recognized as one of the most promising technologies that can overcome the capacity limit of single-mode fibers (SMF) [1–3]. To realize MDM transmission, a class of active and passive devices is needed [3–5]. Especially for the long-haul MDM transmission, suitable optical amplifiers used to compensate the fiber link loss are highly desired. Few-mode erbium-doped fiber amplifiers (FM-EDFA), which are an attractive amplification solution, have been intensively investigated. Some advanced techniques have been proposed to equalize the gain for different modes, including controlling the pumping mode content [6], tailoring the erbium-doping profiles [7], and employing cladding pumping [8]. Furthermore, few-mode [9–11] and even multicore few-mode [12] long-distance transmission experiments based on FM-EDFA have been demonstrated.

Compared with EDFA, distributed Raman amplifiers (DRA) have some fundamental advantages, such as simple architecture, broad gain bandwidth, flexible operation window, and low noise figure (NF) [13]. In particular, the merit of low NF becomes even more prominent for an MDM system, which relies heavily on digital signal processing (DSP) technique and has a more stringent requirement on noise performance [14]. In recent years, few-mode distributed Raman amplifiers (FM-DRA) have been theoretically [14–17] and experimentally [18–21] studied. FM-DRA based transmission experiment over 137-km FMF was firstly demonstrated in [20]. Recently, a wavelength-division and mode-division multiplexed combined optical transmission over 1050-km FMF based on FM-DRA has also been successfully demonstrated [21].

High-order DRA can provide a lower NF than conventional first-order DRA [22–24] and have been utilized in commercial SMF transmission systems. In a high-order DRA, additional pumps are added at wavelengths with one or several times of Stokes shifts below the conventional first-order pump [24]. These additional pumps are used to amplify the first-order pump to move gain for the signals farther from the pump input, which leads to the NF performance improvement. Therefore, for further improving the noise performance and constructing a better performed long-haul MDM transmission system, high-order FM-DRA is very appealing.

In this work, we experimentally demonstrate a second-order FM-DRA. The 1455 and 1360 nm pumps are both backward launched into the FMF in the forms of LP_11a and LP_11b modes. In the band from 1542 to 1558 nm, maximum on-off gains of 4 dB are achieved for both LP₀₁ and LP₁₁ modes, and the differential modal gain (DMG) is less than 0.4 dB. In comparison to the conventional first-order pumping scheme, the NFs at 1550 nm for LP₀₁ and LP₁₁ modes are improved by 1.2 dB and 1.1 dB, respectively. The lowest NFs of less than −2 dB are achieved for both modes. We also use an OTDR technique to measure the signal evolutions in the first-order and second-order pumping schemes. The signal power is comparably higher for both LP₀₁ and LP₁₁ modes at the same spatial location during the propagations in the second-order pumping configuration, which proves its contribution to the NF performance improvement. This work is the first demonstration of second-order FM-DRA, which can be used potentially in future high capacity MDM optical communication systems.

2. Second-order few-mode distributed Raman amplifier

Propagation equations governing forward and backward power evolutions of pumps, signals and amplified spontaneous emission (ASE) in conventional single-mode Raman amplifiers with Rayleigh scattering and temperature dependencies have been derived [25, 26]. We rewrite the equations for the FM-DRA as follows,

\begin{array}{l} \frac{d P_{v, m}^{\pm}}{d z} = \mp α_{v, m} P_{v, m}^{\pm} \pm \sum_{n} η_{v, m, n} P_{v, n}^{\mp} \pm P_{v, m}^{\pm} \sum_{μ > ν} \sum_{n} \frac{g_{μ, ν}}{Γ} f_{m, n} (P_{μ, n}^{+} + P_{μ, n}^{-}) \\ \pm h v \sum_{μ > ν} \sum_{n} g_{μ, ν} f_{m, n} (P_{μ, n}^{+} + P_{μ, n}^{-}) [1 + {(e^{h (μ - ν) / k T} - 1)}^{- 1}] Δ ν \\ \mp P_{v, m}^{\pm} \sum_{μ < ν} \sum_{n} \frac{ν}{μ} \frac{g_{μ, ν}}{Γ} f_{m, n} (P_{μ, n}^{+} + P_{μ, n}^{-}) \\ \mp P_{v, m}^{\pm} \sum_{μ < ν} \sum_{n} \frac{ν}{μ} g_{μ, ν} f_{m, n} 2 h μ [1 + {(e^{h (ν - μ) / k T} - 1)}^{- 1}] Δ μ, \end{array}

where the + and - symbols denote the direction of propagations, P_v_,_m (P_v_,_n, P_μ_,_n) is the optical power at frequency v (v, μ) in mode m (n, n), α_v_,_m is the attenuation coefficient at frequency v for mode m, g_μ_,_v is the Raman gain coefficient between frequencies μ and v, f_m_,_n is the intensity overlap integral between modes m and n, η_v_,_m_,_n is the Rayleigh-backscattering coefficient at frequency v from mode n to mode m, ∆v and ∆μ represent the effective bandwidths at the frequencies v and μ, respectively, Г stands for the polarization factor between pump and signal, h is the Planck’s constant, k is the Boltzmann’s constant and T is the absolute temperature of the fiber. Equation (1) can characterize the second-order FM-DRA and even a FM-DRA with unlimited number of pumps and signals. The intensity overlap integral f_m,n between modes m and n is defined as [15]:

f_{m, n} = \frac{\int_{- \infty}^{+ \infty} \int_{- \infty}^{+ \infty} I_{m} (x, y) I_{n} (x, y) d x d y}{\int_{- \infty}^{+ \infty} \int_{- \infty}^{+ \infty} I_{m} (x, y) d x d y \int_{- \infty}^{+ \infty} \int_{- \infty}^{+ \infty} I_{n} (x, y) d x d y}

where I(x,y) is the mode profile and its wavelength dependence is assumed to be negligible. The difference in f_m_,_n for different modes will cause DMG, which can be minimized by controlling the pump mode content.

Figure 1(a) shows the configuration of our experimental setup. Two different pumping schemes are used in the experiments: first-order pumping and second-order pumping. The transmission line is 70-km long step-index 4-LP (LP₀₁, LP₁₁, LP₂₁, and LP₀₂) mode fiber, which is currently available for us. The parameters of the 4-LP mode fiber can be found in [27]. Table 1 presents some main characteristics, including modal effective areas, differential group delays (DGD) and (n_eff-n_cl) at 1550 nm, where n_eff is modal effective index and n_cl is cladding index. As shown in Table 1, the large n_eff difference (≥0.8 × 10⁻³) ensure low mode coupling [27], which can be neglected with a length of 70-km. Two mode-selective photonic lanterns (MSPL, Phoenix Photonic 3PL-MS1511200) are used as mode multiplexer and demultiplexer for the two LP modes (LP₀₁ and LP₁₁). The insertion losses of MSPL1 (MSPL2) for the LP₀₁ and LP₁₁ modes are 2.7 dB (1.4 dB) and 4.1 dB (1.7 dB), respectively. To make effective use of pump power, low-loss MSPL2 is chosen to couple 1455 and 1360 nm pumps, as shown in Fig. 1(a). Moreover, the mode selectivities of MSPL1 (MSPL2) for the LP₀₁ and LP₁₁ modes are 6.1 dB (1.9 dB) and 6.3 dB (5.7 dB), respectively. The advantage of using MSPL in the setup is that they can withstand the high power of the Raman pump laser, avoiding the problem of handling high power beams in free space [21]. The output pigtails of the MSPLs are 2-LP (LP₀₁ and LP₁₁) mode fibers, which are directly spliced to the 4-LP mode fiber, and the spliced point is provided in Fig. 1(b). These two types of fibers have similar core radius, as shown in Fig. 1(c). Moreover, the LP₀₁ and LP₁₁ mode effective areas of the 2-LP mode fiber are 130 and 113 μm², respectively, which are similar with the ones of the 4-LP mode fiber, as shown in Table 1. Therefore, we believe that the splice points have little effect on the mode propagation. The near field patterns (NFP) at 1550 nm after the first MSPL and after 70-km 4-LP mode fiber are also presented in Fig. 1(a). The cut-back method is used to measure the attenuation coefficients of the 4-LP mode fiber. We obtain losses of 0.212 dB/km and 0.214 dB/km at 1550 nm for the LP₀₁ and the LP₁₁ modes, respectively, and 0.277 dB/km and 0.349 dB/km at 1455 and 1360 nm, respectively, for the LP₁₁ mode.

Fig. 1 (a) Configuration of experimental setup and NFPs at 1550 nm after MSPL1 and after 70 km 4-LP mode fiber. MSPL: mode-selective photonics lantern; WDM: wavelength-division multiplexer; OSA: optical spectrum analyzer. (b) Spliced point between the 2-LP mode and 4-LP mode fibers. (c) Relative index difference of the 2-LP mode and 4-LP mode fibers.

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Table 1. Characteristics of the 4-LP mode fiber from [27]

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In a typical step-index FMF, the LP mode profiles are not appropriate to describe the spatial intensity profiles in an optical fiber amplifier [15]. The intensity overlap integral f_m_,_n should be calculated based on real waveguide modes. We use the finite element method (FEM) to calculate f_m_,_n for the 4-LP mode fiber and the results are presented in Table 2, which can be used to calculate the Raman gains for different modes. Accordingly, we can minimize the DMG by tailoring the mode content of 1455 nm pump in the case of first-order pumping [15]. For the case of 2-LP modes, the perfectly equalized gain is obtained when 10.2% of pump power is launched into the LP₀₁ mode and 89.8% into the LP₁₁ mode. In the case of 4-LP modes, the optimum launch condition will be 69.5% of pump power injected into the LP₂₁ mode and 30.5% into the LP₀₂ mode, with a residual DMG of 0.19 dB for each 10 dB of Raman gain. It should be noted that no pump power is injected into LP₀₁ and LP₁₁ modes in this case. In the second-order pumping configuration, besides 1455 nm pump, the 1360 nm pump should also be subject to above launch conditions. It is because the Raman gain spectrum has a small peak at 24 THz, where the 1360 nm pump will work as first-order pump and amplify directly the signal around 1530 nm.

Table 2. Intensity overlap integral f_m,n (in 10⁹/m²) for the 4-LP mode fiber

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The Raman process is phase insensitive but depends on the relative polarization between the pump and the signal. To eliminate the polarization effect, the 1455 and 1360 nm pumps used in the experiments are both depolarized. The pumps are coupled by using low-loss wavelength-division multiplexers (WDM). In the experiments, the 1455 nm pump is launched in the backward direction, which can minimize the relative intensity noise (RIN) transferred from the 1455 nm pump. For the first-order pumping case, to equalize the gains for the LP₀₁ and LP₁₁ modes as far as possible, the 1455 nm pump is equally launched into the LP_11a and LP_11b ports of low-loss MSPL2, as shown in Fig. 1(a). However, MSPL2 has a limited mode selectivity for the LP₁₁ mode (5.7 dB), leading to 21% of pump power coupled into LP₀₁ mode. Thus, the DMG is still observed in the experiments, which will be discussed in Section 3. In the second-order pumping configuration, according to the above discussion, the 1455 and 1360 nm pumps are both equally injected into two degenerate LP₁₁ ports of MSPL2 in the backward direction, as shown in Fig. 1(a).

3. Experimental results and discussion

As shown in Fig. 1(a), we use a broadband light source covering the C-band and an optical spectrum analyzer (OSA) to measure the Raman on-off gain G_on-off, which is defined as [24]:

G_{on-off} = \frac{P_{s}^{on} (L)}{P_{s}^{off} (L)}

where

P_{s}^{on}

(L) and

P_{s}^{off}

(L) are the signal power at the fiber output when the pumps are on and off, respectively. Figures 2(a) and 2(b) present the modal gains as a function of wavelength inthe cases of first-order (1455 nm, 260 mW) and second-order (1455 nm, 30 mW; 1360 nm, 1290 mW) pumping, respectively. The LP₁₁ modal gains in Figs. 2(a) and 2(b) are the average of the measured gains for LP_11a and LP_11b modes. It should be mentioned that because the currently used WDMs have a limited wavelength band from 1542 to 1558 nm, the spectral gain measurement for LP₁₁ mode cannot cover the full C-band. In both pumping schemes, within the band from 1542 to 1558 nm, maximum on-off gains of 4 dB are achieved for both LP₀₁ and LP₁₁ modes. Due to the small peak in the Raman gain spectrum at 24 THz, the 1360 nm pump will have a gain peak around 1530 nm and thus the second-order pumping scheme has flatter spectral gains for both LP₀₁ and LP₁₁ modes, as shown in Fig. 2(b). This is a significant advantage of the second-order FM-DRA, which can also be found in the second-order single-mode DRA [23]. Furthermore, it is anticipated that the advantage will also be observed in future second-order FM-DRA experiment extending to higher spatial modes such as LP₂₁ and LP₀₂.

Fig. 2 Measured Raman on-off gain as a function of wavelength in the cases of (a) first-order and (b) second-order pumping.

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In the wavelength range from 1542 to 1558 nm, the DMG is less than 0.2 dB for the case of first-order pumping. The gain for the LP₀₁ mode is slightly higher than that for the LP₁₁ mode, because a fraction (21%) of 1455 nm pump power launched into the LP_11a and LP_11b ports of MSPL2 will leak into LP₀₁ mode due to the crosstalk of MSPL2. According to Ref [21], we also calculate the DMG by using the data in Table 2:

\begin{array}{l} G_{on-off}^{11} = G_{on-off}^{01} (\frac{P f_{2 � 1} + (1 - P) f_{2 � 2}}{P f_{1 � 1} + (1 - P) f_{1 � 2}}) \\ = 4.2 dB (\frac{0.21 \times 5.34 + 0.79 \times 5.65}{0.21 \times 8.07 + 0.79 \times 5.34}) = 3.97 dB, \end{array}

where

G_{on-off}^{01}

and

G_{on-off}^{11}

represent the gain for LP₀₁ and LP₁₁, respectively, P is the fraction of pump power in LP₀₁ mode, f_m_,_n are shown in Table 2. The DMG illustrated in Eq. (4) agrees well with the experimental value. For a more detailed discussion, one can refer to [21]. In the second-order pumping configuration, both 1455 and 1360 nm pump power injected into the LP_11a and LP_11b ports of MSPL2 will leak partly into LP₀₁ mode because of the crosstalk. The leaked 1455 nm pump power in LP₀₁ mode will be amplified more strongly by the leaked 1360 nm pump power in LP₀₁ mode and eventually the DMG will be worsened. Within the band from 1542 to 1558 nm, the maximum DMG increases to 0.4 dB for the case of second-order pumping. Note that the DMG can be enhanced by using MSPL with lower crosstalk.

We also measure the ASE noise power for the two pumping configurations mentioned above. In the measurements, the OSA resolution bandwidth is set to 0.2 nm. The difference in the ASE power follows the gain measurement. As shown in Fig. 3(a), the ASE power for LP₀₁ mode is ~0.2 dB higher than that for LP₁₁ mode in the case of first-order pumping. For the second-order pumping scheme, the difference in the ASE power between LP₀₁ and LP₁₁ modes increases to ~0.4 dB, as shown in Fig. 3(b). Additionally, compared with first-order pumping scheme, the ASE noise performance for both LP₀₁ and LP₁₁ modes improves significantly in the second-order pumping configuration. Within the wavelength band from 1542 to 1558 nm, the ASE noise improvements for LP₀₁ and LP₁₁ modes are both above 2.5 dB, as shown in Figs. 3(a) and 3(b). Therefore, the use of second-order FM-DRA can provide a lower noise for MDM communication systems, which is similar to the second-order single-mode DRA [22–24]. As mentioned above, the Raman gain spectrum has a small peak at 24 THz so that the 1360 nm pump will work as first-order pump and amplify directly the signal around 1530 nm. Thus, there is a significant peak in the ASE spectrum at 1530 nm, as shown in Fig. 3(b).

Fig. 3 Measured ASE noise power as a function of wavelength in the cases of (a) first-order and (b) second-order pumping. The OSA resolution bandwidth is set to 0.2 nm.

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The light source in Fig. 1(a) is then turned to an external cavity laser (ECL) working at 1550 nm, which is used to investigate the effective NF of the FM-DRA in different pumping cases. The effective NF is defined as [28]:

NF = \frac{1}{G_{on - off}} (1 + \frac{P_{ASE}}{E_{ph} B_{0}})

where E_ph is the signal photon energy, and P_ASE is the ASE noise power measured in a bandwidth B₀. The measured values of effective NFs for the LP₀₁ and LP₁₁ modes are provided in Figs. 4(a) and 4(b), respectively. The 1455 nm pump power launched into the 4-LP mode fiber are 260, 175, 110, 65 and 30 mW at different points in both Figs. 4(a) and 4(b). Moreover, the Raman on-off gains are fixed to 4 dB for the LP₀₁ mode and 3.8 dB for the LP₁₁ mode. The effective NF improves along with the decrease of 1455 nm pump power, as shown in Figs. 4 (a) and 4(b). We obtain maximum NF improvements of 1.2 dB and 1.1 dB for the LP₀₁ and LP₁₁ modes, respectively. The lowest effective NF achieved here is −2.3 dB (−2.1 dB) for LP₀₁ (LP₁₁) mode with 1290 mW (1310 mW) 1360 nm pumping and 30 mW 1455 nm pumping. Note that the effective NF could be further improved by employing a weaker 1455 nm pumping and simultaneously a stronger 1360 nm pumping. The obvious negative side here is that the better NF performance is at the expense of higher pump power consumption, as shown in Figs. 4(a) and 4(b). Moreover, we believe that the NF improvements for all modes will also be obtained in future second-order FM-DRA experiment extending to higher spatial modes such as LP₂₁ and LP₀₂.

Fig. 4 Effective NF and total pump power as a function of 1455 nm pump power: (a) LP₀₁ mode, gain is fixed to 4 dB. (b) LP₁₁ mode, gain is fixed to 3.8 dB.

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We then replace the ECL by building an OTDR in the FMF operating at 1550 nm to investigate the signal power evolutions for the LP₀₁ and LP₁₁ modes in the cases of no pumping, first-order pumping and second-order pumping. In the measurements for both modes, the 1455 nm pump power launched into the fiber is 260 mW (30 mW) in the case of first-order (second-order) pumping. In the second-order pumping configuration, 1360 nm pump has a power of 1290 mW (1310 mW) in the measurement for the LP₀₁ (LP₁₁) mode. The measured OTDR traces for the LP₀₁ and LP₁₁ modes are shown in Figs. 5(a) and 6(a), respectively. We also use commercial MATLAB package to solve Eq. (1) numerically to obtain signal power evolutions. In the numerical calculations, the terms in Eq. (1) standing for Rayleigh-backscattering and ASE noise are neglected and the polarization factor Г is assumed to be 2. The 4-LP mode fiber is Ge-doped and the relative index difference is 0.67%. According to Ref [29], the Raman gain coefficient g_μ,v is assumed to be 0.8 × 10⁻¹³ m/W in the calculations. The simulated signal power evolutions for the LP₀₁ and LP₁₁ modes are presented in Figs. 5(b) and 6(b), respectively, which are in good agreement with the experimental results. It should be noted that we neglect the crosstalk of MSPL2 in the simulation and the pump power is assumed perfectly injected into LP₁₁ mode. Thus, the simulated Raman gains for the LP₀₁ mode in both pumping cases are slightly lower than the measured ones.

Fig. 5 (a) Measured and (b) simulated signal power evolutions for LP₀₁ mode in the cases of no pumping, first-order pumping and second-order pumping.

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Fig. 6 (a) Measured and (b) simulated signal power evolutions for LP₁₁ mode in the cases of no pumping, first-order pumping and second-order pumping.

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As shown in Figs. 5 and 6, the signal power is comparably higher for both LP₀₁ and LP₁₁ modes at the same spatial location during the propagations in the second-order pumping configuration, which proves its contribution to the NF performance improvement. Furthermore, one can obtain a quasi-constant transmission for both modes by using second-order bi-directional pumping scheme, which is the best trade-off between the NF and the nonlinear penalty [22].

4. Summary

In this paper, we have demonstrated experimentally a second-order FM-DRA. The 1455 and 1360 nm pumps are both equally backward injected into two degenerate LP₁₁ modes. Within the wavelength band from 1542 to 1558 nm, maximum on-off gains of 4 dB are obtained for both LP₀₁ and LP₁₁ modes, and the DMG is less than 0.4 dB. Compared with the first-order pumping configuration, the NF improvements at 1550 nm for LP₀₁ and LP₁₁ modes are 1.2 dB and 1.1 dB, respectively. The lowest NFs of less than −2 dB are achieved for both modes. The signal evolutions in the cases of first-order and second-order pumping are also measured by an OTDR. This work is the first demonstration of second-order FM-DRA, which can be used potentially in future high capacity MDM optical communication systems.

Funding

National Natural Science Foundation of China (NSFC) (61675128, 61307107, 61327812, 61405113). Science and Technology Commission of Shanghai Municipality (STCSM) (13ZR1456200, 15511103102).

Acknowledgments

We would like to thank Shoulin Jiang, Guangyao Yang and Yangtze Optical Fiber Company for their help in the experiments.

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	LP₀₁	LP₁₁	LP₂₁	LP₀₂
A_eff (μm²)	124	118	133	127
DGD vs. LP₀₁ (ps/m)	–	4.4	8.5	7.2
(n_eff - n_cl) at 1550 nm ( × 10⁻³)	8.3	6.0	3.2	2.4

f_m,n	LP₀₁: HE₁₁	LP₁₁: TE₀₁, TM₀₁, HE₂₁	LP₂₁: HE₃₁, EH₁₁	LP₀₂: HE₁₂
LP₀₁: HE₁₁	8.07	5.34	3.72	5.99
LP₁₁: TE₀₁, TM₀₁, HE₂₁	5.34	5.65	4.96	3.04
LP₂₁: HE₃₁, EH₁₁	3.72	4.96	5.01	2.77
LP₀₂: HE₁₂	5.99	3.04	2.77	7.88

	LP₀₁	LP₁₁	LP₂₁	LP₀₂
A_eff (μm²)	124	118	133	127
DGD vs. LP₀₁ (ps/m)	–	4.4	8.5	7.2
(n_eff - n_cl) at 1550 nm ( × 10⁻³)	8.3	6.0	3.2	2.4

f_m,n	LP₀₁: HE₁₁	LP₁₁: TE₀₁, TM₀₁, HE₂₁	LP₂₁: HE₃₁, EH₁₁	LP₀₂: HE₁₂
LP₀₁: HE₁₁	8.07	5.34	3.72	5.99
LP₁₁: TE₀₁, TM₀₁, HE₂₁	5.34	5.65	4.96	3.04
LP₂₁: HE₃₁, EH₁₁	3.72	4.96	5.01	2.77
LP₀₂: HE₁₂	5.99	3.04	2.77	7.88

Second-order few-mode Raman amplifier for mode-division multiplexed optical communication systems

Abstract

1. Introduction

2. Second-order few-mode distributed Raman amplifier

3. Experimental results and discussion

4. Summary

Funding

Acknowledgments

References and links

Cited By

Figures (6)

Tables (2)

Equations (5)

Optics Express