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Abstract
We theoretically and experimentally verify that, the bidirectional hybrid-mode pumping scheme can address the optimization problem of trade-off between high gain and low differential modal gain (DMG) of four-mode erbium-doped fiber amplifier (4M-EDFA), in comparison with traditional both forward and backward hybrid-mode pumping scheme. It is noticed that, when the total pump power is fixed, the bidirectional hybrid-mode pumping scheme can not only achieve higher gain, but also suppress DMG due to different overlap integrals for the forward and backward pumping schemes. The bidirectional hybrid-mode pumped 4M-EDFA is developed with the forward pumping at LP02 mode and the backward pumping at LP21 mode, under a pump power ratio of 30%:70%. Thus, we can achieve an average gain of up to 21.16 dB and a low DMG of 0.43 dB at 1550 nm, and an average gain of up to 20.64 dB with a DMG of less than 1.6 dB over the C-band. In particular, the bidirectional hybrid-mode pumping scheme allows us to tailor the gain characteristics of the few-mode erbium-doped fiber amplifiers (FM-EDFAs), by adjusting the power ratio between forward and backward pumps.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Mode-division multiplexing (MDM) is a promising technique to overcome the capacity crunch of standard single-mode fibers (SSMF), because it can carry different data information on each spatial modes [1]. Thus, it becomes a worldwide research topic. As an important device to compensate for the long-haul MDM transmission loss [2–6], few-mode erbium-doped fiber amplifiers (FM-EDFAs) have been intensively explored over the past few years, owing to their low cost and energy consumption compared with multiple single-mode erbium-doped fiber amplifiers (SM-EDFAs) [7]. However, as for the few-mode erbium-doped fiber (FM-EDF), the overlapping difference among the signal mode profiles, the pump mode profiles, and the erbium-doping distribution leads to the occurrence of differential mode gain (DMG) [8], and simultaneously achieving high gain more than 20 dB and a DMG less than 1 dB becomes challenging for the FM-EDFA, especially when the number of guided modes is extended [9]. Currently, researchers suppress the DMG by optimizing either the erbium-doping distribution [10–12] or the refractive index (RI) distribution of the FM-EDF [13,14], as shown in Table 1. However, since the realization of specially designed RI distributions or erbium doping profile requires a complex fiber fabrication process, there is always a performance penalty between experimental validation and theoretical prediction. Meanwhile, some researchers propose to manipulate the mode profile of pump source, in order to fulfil such motivation [15]. It is noticed that, not only the mode profile but also the injection direction of pump light affect the performance of the FM-EDFA. It has been noticed that, the gain of SM-EDFA under the forward pump is less than that under the backward pump. However, the performance penalty associated with the backward pump is the higher noise figure (NF). It is found that the bidirectional pump can solve the optimization problem of trade-off between the high gain and the NF for FM-EDFA [16]. Nevertheless, the trade-off between the gain and DMG with respect to the pump light injection direction has not been investigated, when both the total pump power and the length of EDF are fixed.
Table 1. Recent experiment progress of FM-EDFA DMG suppression with various DMG optimization schemes
In the current submission, we demonstrate an all-fiber four-mode erbium-doped fiber amplifier (4M-EDFA) based on the bidirectional hybrid-mode pumping scheme, with both high gain and low DMG. By calculating the overlap integrals of the different pump combinations, we obtain the optimal pump combinations of LP21-mode and LP02-mode pump under the optimal power ratio of 70%:30%. After comparing the gain performance of the 4M-EDFA under different pump directions, we identify that the trade-off between high gain and low DMG can be well addressed, by the use of the scheme of combining LP02-mode forward pumping and LP21-mode backward pumping, i.e., the bidirectional hybrid-mode pumping scheme. Then, a low-DMG all-fiber 4M-EDFA is developed with the bidirectional hybrid-mode pumping scheme, in order to validate the simulation results. The experimental results show that, compared with all existing publications, the 4M-EDFA can achieve a gain of more than 20 dB at 1550 nm with DMG of 0.43 dB, when the power values of LP02 mode forward pumping and LP21 mode backward pumping are 91 mW and 179 mW, respectively, and the average gain over the C-band is 20.64 dB with DMG of less than 1.6 dB.
2. Optimization and simulation
Based on parameters of the used four-mode EDF (4M-EDF), we carry out the corresponding FM-EDFA design and numerical optimization. As shown in Fig. 1, the used 4M-EDF has a core radius of about 9.5 µm and a cladding radius of 62.5 µm with a numerical aperture (NA) of around 0.14. Consequently, LP01, LP11, LP21 and LP02 modes can be successfully transmitted over the C-band. Erbium ions are uniformly doped at the core region with a doping concentration of about 1.1 × 1025 /m3, and the absorption at 980 nm is about 12 dB/m measured by the use of the cutback method under fundamental mode [15]. First, the overlap integrals of the 4M-EDF are compared, in order to determine the optimal pump mode profile, in relevant to the determined signal mode profile and the doping distribution. For the FM-EDFA, the gain of each guided mode is determined by the pump mode and the signal mode profiles within the doping region. Therefore, by comparing the overlap integrals of the signal and pump modes within the doping region, the optimal pump scheme to realize the lowest DMG can be identified. The overlap integrals between the signal and pump modes can be described as [17]
Fig. 1. (a) Refractive index distribution of FM-EDF, (b) intensity profiles of LP01, LP11, LP21 and LP02 at 1550 nm and 980 nm, together with Erbium doping concentration distribution.
Based on the Eq. (1) and the structure shown in Fig. 1, we can calculate the overlap integrals of the four guided modes under different pump schemes, as shown in Table 2. In the simulation, the LP11 and LP21 pump modes are denoted as the superposition of LP11a + LP11b and LP21a + LP21b, respectively, while for signal modes, “a” and “b” are separately calculated. It can be observed that the overlap integral difference among all guided modes is larger than 1 × 109, so it is challenging to obtain a low DMG under the single type of pump mode. Therefore, it is necessary to use two pump modes with a suitable power ratio, in order to suppress the DMG effectively.
Table 2. Overlap integrals of four guided modes under different pump schemes (units: a.u.)
Next, we intend to determine the optimal pump mode combination and the corresponding power ratio. Here, we numerically set the power ratio of one pump modes to be α, and the other pump power ratio is 1-α. Thus, the overlap integral for each guided modes and pump combinations can be expressed as
where k is order of the k-th signal mode, a and b are the orders of a-th and b-th pump mode, respectively. In order to realize low DMG, the differences of ${\Omega _k}$ among guided modes should be as low as possible, which is expressed asThe variation of η with respect to the pump power ratio α is shown in Fig. 2. It can be seen that, η is less than 1 × 109 only when the combination of LP02 and LP21 pump modes is employed In addition, lowest η of 3.97 × 108 is obtained when LP21 and LP02 modes are selected as the pump modes, and the pump power ratio between LP21 and LP02 modes is 70%:30%. Therefore, we choose LP21 and LP02 modes as the pump modes combination with a power ratio of 70%:30%.
Fig. 2. Variation of η with respect to the pump power ratio α for different combinations of pump modes.
Then we further compare the effect of various injection directions of the two pump modes on both gain and DMG, when the total pump power and the EDF length are fixed. The 4M-EDFA is modeled as a three-level system, considering amplified spontaneous emission (ASE) in the simulation. Meanwhile, we amplify the four-mode signals simultaneously [18,19]. For the ease of characterizing the performance of FM-EDFA, we utilize the fitness function $F = \frac{{{G_{\textrm{ave}}}}}{{DMG}}$ as the metric, where Gave is the average gain among all guided modes [20,21] and DMG is defined as the difference between the highest and lowest gain among all guided modes. A higher F indicates better performance of FM-EDFA with high gain and low DMG. Based on the above combination of LP21 and LP02 pump modes and the corresponding power ratio of 70%:30%, as shown in Fig. 3, we introduce two pump modes into the 4M-EDF under three schemes, in order to evaluate the corresponding F. Case i) both LP02 and LP21 pump modes are injected at the forward direction, case ii) both LP02 and LP21 pump modes are injected at the backward direction, and case iii) the LP02 pump mode is injected at the forward direction, while the LP21 pump mode is injected at the backward direction, which is defined as the bidirectional hybrid-mode pumping scheme. As shown in Fig. 4(a) and (b), the maximum F is less than 10 for the case of i) and ii). However, for the case iii), DMGs can be less than 1 dB over a wide range of total pump power and FM-EDF length. Since the DMG of less than 0.5 dB and an average gain of more than 20 dB can be simultaneously realized, an exponential DMG reduction leads to an order of magnitude reduction of F values, resulting in a singularity. Especially, when the LP02 mode used in forward pumping and the LP21 mode used in backward pumping are introduced into 4.2 m EDF simultaneously, under the fixed pump power of 260 mW, the maximum F can reach 401. As a result, the corresponding Gave is 20.50 dB and DMG is 0.05 dB. Therefore, none of the unidirectional pumping scheme is capable to realize the DMG mitigation, under the average gain of more than 20 dB. Moreover, the trade-off between the gain of more than 20 dB and a DMG of less than 1 dB can only be solved by the proposed bidirectional hybrid-mode pumping scheme.
Fig. 3. Three injection cases of LP02 and LP21 pumping for the 4M-EDF: i) both LP02 and LP21 pump modes are injected at the forward direction, ii) both LP02 and LP21 pump modes are injected at the backward direction, and iii) bidirectional hybrid-mode pump scheme.
Fig. 4. The fitness value F varies with total pump power and FM-EDF length, when the pumping schemes are (a) forward, (b) backward, and (c) LP02 forward and LP21 backward, respectively.
In order to better explain the advantage of bidirectional hybrid-mode pumping scheme, we numerically investigate the impact of above-mentioned three cases on the characteristic of 4M-EDFA, when both 4.2 m 4M-EDF and total 260 mW pump power are utilized. For the case i), as shown in Fig. 5(a), the gain values of all four signal modes increase and eventually reach the saturation, leading to the average gain and DMG are 20.32 dB and 2.94 dB, respectively. However, since both two pump modes interact with the input signal at the same time, according to Eq. (2), LP01 signal mode has the largest overlap integral of Ω01 = 3.486 × 109 with two pump modes. Therefore, the LP01 signal can obtain the highest gain. In contrast, since the LP02 mode has the lowest overlap integral of Ω02 = 3.091 × 109, it has the lowest gain. Eventually the DMG among four guided modes becomes severe at the FM-EDF output. The same conclusion can be drawn for the case ii), as show in Fig. 5(b), and the average gain and DMG are 20.39 dB and 2.52 dB, respectively. Nevertheless, for the case iii), as shown in Fig. 5(c), the LP02 mode at the forward pump is dominant over the initial 2 m 4M-EDF, leading to the gain enhancement for the LP02 mode in comparison with the other guided modes. After the co-propagation over the initial 2 m FM-EDF, the LP21 pump mode at the backward direction starts to play an important role, instead of the LP02 pump mode at the forward direction. Consequently, the gain value of LP01, LP11 and LP21 signal modes is promoted, and finally the gain characteristic is equalized among LP01, LP11, LP21, and LP02 signal modes, under the condition of bidirectional hybrid-mode pumping scheme. In order to further examine the impact of signal wavelength on the performance of the bidirectional hybrid-mode pump scheme, we numerically calculate the 4M-EDFA performance with respect to the operation wavelength over the C-band. As shown in Fig. 5(d), the bidirectional hybrid-mode pumping 4M-EDFA can achieve an average gain of 20.72 dB over the C-band with DMG of less than 1.7 dB. Additionally, although we consider other signal wavelengths to optimize F, such as 1530 nm, the maximum DMG over the C-band is 2.9 dB, while it becomes 1.7 dB when the optimization is done at 1550 nm. Consequently, the optimization results at 1550 nm are ideally suitable, and then utilized in our further experimental verification.
Fig. 5. Variations of gains and DMGs along the position of FM-EDF, when the pumping schemes are (a) forward, (b) backward, and (c) LP02 forward and LP21 backward, respectively, and (d) variations of gains and DMGs over the C-band when the pump power ratio of LP02 forward pumping and LP21 backward pumping is 30%:70%.
3. Experiment setup
We start to develop an all-fiber 4M-EDFA. As shown in Fig. 6, the signal to be amplified is generated by a C-band tunable laser source (TLS) with the SSMF pigtail. As one of the essential components for the implementation of an all-fiber FM-EDFA, the self-fabricated mode-selective photonic lantern1 (MSPL1) is used to individually generate LP01, LP11, LP21 and LP02 modes. Moreover, we use a single-mode wavelength division multiplexer (SM WDM) to combine the 980 nm pump and the signal, and introduce to the designated input port of the MSPL1, leading to the generation of LP02 mode. Thus, simultaneous conversion of pump and signal fundamental modes to their LP02 mode can be realized. The variable optical attenuator (VOA) is used to equalize the mode dependent loss (MDL) arising in the mode selective conversion, in order to fix the power of each mode at the 4M-EDF input. Meanwhile, at the 4M-EDF output, we use another self-fabricated MSPL2 to convert another 980 nm pump light at fundamental mode to the LP21 mode and introduce it backwards into the 4M-EDF via four-mode WDM (YX-WDM-SI-4-FA, Esonphotonics). Finally, the amplified signal light is output from the four-mode WDM, for the subsequent monitoring by an optical spectrum analyzer (OSA, AQ6370D). The signal modes prior to (point A) and after the optical amplification (point C), together with the pump mode profile are captured, by the use of charge-coupled device cameras (CCDs, BM-USB-SP928-1550-OSI, and BGS-USB3-SP932U). Because of the degeneracy for the mode group LPmn (m≠0), the modal gain characteristics for the odd mode and even mode are the same [6]. Therefore, only LP11a and LP21a are measured in the experiment.
Fig. 6. Experimental setup of all-fiber FM-EDFA. TLS, tunable laser source; VOA, variable optical attenuator; PC, polarization controller; MSPL, mode-selective photonic lantern; SM ISO, single-mode isolator; SM WDM, single-mode wavelength division multiplexer; Four-Mode WDM, four-mode wavelength division multiplexer; OSA, optical spectrum analyzer.
Figure 7(a) shows the measured near-field signal mode profiles before and after the optical amplification. According to the theory in [22], The intensity profile correlation coefficients of LP01, LP11, LP21, and LP02 at points A and C are evaluated as 93%, 79%, 73% and 80%, respectively, indicating that the mode profiles of four amplified signals are well preserved at the output of the EDFA. In addition, the mode profiles of pump signals are presented in Fig. 7(b), and we use the theory in [22] to evaluate the intensity profile correlation coefficient of the LP02 pump mode as 92%. The MDL of each passive device is also summarized in Table 3, and cross-talk of MSPL1 is shown in Table 4. By adjusting the VOA and the bias current of pump source, the launch power of involved signal and pump lights can be managed.
Fig. 7. Near-field mode profiles of (a) signal modes measured before (point A) and after optical amplification (point C), and (b) pump modes at points A and B, respectively.
Table 3. Insertion losses of passive fiber-optic devices (units: dB)
Table 4. Cross-talk of Self- Fabricated MSPL1 (units: dB)
4. Results and discussions
Based on the experimental setup, we start to characterize the gain characteristic of 4M-EDFA, under different pump combinations, where the pump power ratio is defined as P(LP02)/Pp. In the experiment, the signal power of each mode is set as −10 dBm and the FM-EDF length is 4.2 m. Here, the total pump power Pp is defined as the sum of the LP02 pump power P(LP02) and the pump power P(LP21) after considering the spatial degeneration of LP21a and LP21b mode. In order to further investigate the impact of the pump injection direction on the performance of FM-EDFA, we fix the FM-EDF length and the total pump power in the experiments, based on the optimization results obtained from the simulation, and analyze them according to the three cases shown in Fig. 3.Considering the splice loss of four-mode fiber and 4M-EDF, we fix the total pump power at 270 mW, and then change the LP02 pump power from 31 mW to 141 mW with the step of 10 mW.
When the total pump power and the EDF length are fixed, the gain characteristic of the 4M-EDFA is experimentally characterized under the above-mentioned three case. As shown in Fig. 8(a), when the forward pumping for both LP02 and LP21 modes are implemented, the gain values of LP01, LP11 and LP02 signal modes gradually increase with the growing LP02 pump powers, while the gain value of LP21 gradually decreases. Due to the gain priority of LP01 signal mode, the LP01 signal gain speeds up, leading to an DMG enhancement from 3.48 dB to 4.48 dB. Similarly, when the backward pumping for both LP02 and LP21 modes are implemented, as shown in Fig. 8(b), the DMG is still more than 2.3 dB. However, for the case iii), when the LP02 mode at the forward pumping with a power of 91 mW and the LP21 mode at the backward pumping with a power of 179 mW are implemented, the minimum DMG of ∼0.43 dB and the average gain of four modes is ∼21.16 dB, as shown in Fig. 8(c).
Fig. 8. Variations of gains and DMGs with respect to pump power ratio, when the pump directions are (a) forward, (b) backward, and (c) LP02 forward and LP21 backward, respectively, and (d) variations of gains and DMGs with respect to the operation wavelength.
Meanwhile, NFs for different pump power ratios are also measured. As shown in Fig. 9(a), with the growing pump power ratio, the NF values are decreased accordingly. In addition, when the power of forward LP02 mode is 91 mW, the NF values of LP01, LP11, LP21, and LP02 modes are 5.53 dB, 6.45 dB, 7.97 dB, and 8.50 dB, respectively.
Fig. 9. (a) variations of NF with respect to pump power ratio when the pump combination is both forward LP02 and backward LP21 modes. And variations of (b) average gain and (c) DMGs with respect to the input signal power at 1550 nm, when the LP02 pump powers are 51 mW, 71 mW, 91 mW, 111 mW and 131 mW, respectively.
Moreover, we vary the operation wavelength of TLS over the C-band from 1530 nm to 1565 nm with a resolution of 5 nm, in order to examine both the gain value and DMG over the C-band, when both LP02 forward pumping and LP21 backward pumping powers are set as 91 mW and 179 mW, respectively. As shown in Fig. 8(d), the gain values of the proposed 4M-EDFA are higher than 18.6 dB over the C-band. We do observe a gain peak at around 1530 nm and a gain dip at 1540 nm, while the gain profile of all four-mode is flat within the wavelength range from 1550 nm to 1565 nm. Overall, both an average gain of 20.64 dB and a DMG of less than 1.6 dB can be achieved over the C-band. Furthermore, the gain variation of the proposed 4M-EDFA with respect to the variable input signal power is examined. Here, we fix the total pumping power to be 270 mW, increasing the input signal power from -20 dBm to -8 dBm with an increment of 2 dB, when the LP02 pump power is 51 mW, 71 mW, 91 mW, 111 mW, and 131 mW, respectively, and the experiment results of the variation of the average gain and DMGs are shown in Fig. 9. It can be observed from Fig. 9 that, as the input signal power increases, the gains decrease and the DMGs are gradually reduced. In addition, the DMG is maintained below 2 dB, when the input signal power is higher than -15 dBm. Since various signal modes have different saturation output powers, the DMG under the region of small signal input is different from the case under the condition of gain saturation. Thus, the DMG of a specific FM-EDFA is not a constant. Therefore, the proposed bidirectional hybrid-mode pumped 4M-EDFA can maintain good gain characteristics, when the signal power is within the range of -15 dBm to -10 dBm.
5. Conclusion
We have numerically investigated the impact of forward, backward and bidirectional pumping on both gain and DMG of 4M-EDFA, together with the experimental verification. After determining LP21 and LP02 as the optimal pump modes and the corresponding power ratio of 70%:30%, we find that, the bidirectional hybrid mode pumping scheme can not only achieve more than 20 dB gain but also suppress the DMG to less than 1 dB, when both the total pump power and the FM-EDF length are fixed. Experimental studies have shown that, under 91 mW LP02 mode forward pumping and 179 mW LP21 mode backward pumping, an average gain of up to 21.16 dB and a low DMG of 0.43 dB can be achieved at 1550 nm. Meanwhile, an average gain of up to 20.64 dB and a DMG of less than 1.6 dB can be realized over the C-band. In addition, the 4M-EDFA under the bidirectional hybrid-mode pumping can keep gains higher than 20 dB and DMG less than 2 dB, when the input power varies from -15 dBm to -10 dBm. The proposed bidirectional hybrid-mode pumping scheme is ideally desired to solve the trade-off between gain and DMG arising in the FM-EDFA.
Funding
National Natural Science Foundation of China (62305071, U22A2087); China Postdoctoral Science Foundation (2023M740747); Guangdong Introducing Innovative and Entrepreneurial Teams of “The Pearl River Talent Recruitment Program” (2019ZT08X340, 2021ZT09X044).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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.
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