As a promising technique to overcome the capacity crunch of a standard single-mode fiber (SSMF), mode division multiplexing (MDM) has attracted worldwide research interests, as it can carry different data information over individual spatial modes^[1]. The few-mode erbium-doped fiber amplifier (FM-EDFA), as a crucial component in compensating for the loss of long-haul MDM transmission, has been actively explored during the past few years^[2–6]. The FM-EDFA employs one pump laser to simultaneously amplify multiple guided modes arising in the few-mode fiber (FMF). One of the main challenges for the FM-EDFA is realizing the low differential modal gain (DMG) among all guided modes with a sufficient small-signal gain (SSG). It has been identified that the DMG is determined by the overlap integral between the intensity profiles of both the specific guided mode and the pump mode within the erbium-ion-doped region^[7]. Thus, all existing schemes of DMG mitigation can be generally divided into three categories.

First, researchers start to optimize the DMG performance with respect to the intensity profile of the guided modes^[8–12]. Using a ring refractive index (RI) structure, both a DMG of 0.8 dB between LP01 and LP11 modes and an average gain of about 17 dB can be secured, when the input signal power at 1550 nm is −10dBm per mode^[13]. Second, researchers have proposed several FM-EDFs with novel erbium doping distributions. Using annular doping, researchers realized the maximum gain of the LP11 and the LP21 signal modes close to 20 dB and a DMG of less than 1 dB when the input signal power is −10dBm per mode at 1550 nm^[14]. Then, using ‘Batman’ doping, the researchers achieved an average gain of 15 dB and 2.5 dB DMG for the 6 LP modes when the input signal power is −13dBm per mode at 1550 nm^[15]. Since realizing either the RI distribution or the erbium doping profile needs a sophisticated fiber fabrication process, a performance penalty always exists between the experimental verification and the theoretical prediction. Moreover, the mode-field matching between the EDF and the commercial FMF needs to be further considered. Third, the FM-EDFA with a small DMG can be achieved by manipulating the intensity profile of the pump laser^[16]. By converting the pump laser from the LP01 to the LP21 mode through a photonic lantern (PL), both a DMG of about 0.5 dB among the 6 LP modes and a gain of about 16 dB can be secured when the input signal power at 1550 nm is −10dBm per mode^[17].

In addition, once the pumping mode varies, the dynamic gain of the FM-EDFA will also be affected. In fact, the signal saturation input power is a key indicator of the dynamic gain for the EDFA. It is known that the operation of a traditional single-mode EDFA (SM-EDFA) above the input saturation power will lead to gain compression^[17]. In particular, when the input signal power is higher than the input saturation power, the gain decreases faster with the growing input signal power^[18]. When the FM-EDFA is operated at the saturated region, the fluctuation of the input power will cause severe gain fluctuation, leading to the DMG variation of the FM-EDFA. Thus, the linear amplification range determined by the input saturation power is particularly critical for the reconfigurable optical network, where large input power variations of all guided modes occur. It is highly desired that the optical amplifier has a wider range of linear amplification. However, current FM-EDFA investigations are mainly focused on the statistic gain and the DMG performances under a specific input signal power without considering its dynamic gain. Therefore, the input saturation power of the FM-EDFA needs to be clarified under the intensity profile manipulation of the pump laser together with the DMG mitigation.

In this work, an all-fiber FM-EDFA supporting three modes under various manipulations of the pump mode is comprehensively investigated. We numerically identify that higher-order pumping is helpful for mitigating the DMG. However, in terms of the input saturation power, it leads to a reduction of the linear amplification range. When a mode selective coupler (MSC) is used to convert the LP01 mode to the LP11 mode for a 976-nm pump laser, in comparison with the fundamental mode pumping, the DMG can be mitigated from 2 dB to 1 dB under the condition of the LP11 mode pumping. However, the input saturation powers of the LP01 and the LP11 signals are reduced by 0.3 dB and 1.6 dB, respectively. Therefore, there occurs a trade-off between the DMG mitigation and an extension of linear amplification range.

We start to numerically investigate the impact of different pumping schemes on the FM-EDFA performance in terms of the DMG and the input saturation power. As shown in Fig. 1, the experimentally used FM-EDF has a core radius of about 7 µm and a cladding radius of 62.5 µm with a numerical aperture (NA) of around 0.19. By calculating the normalized depth (ND)^[19], we can find that the ND is lower than 0.3, and the width of the RI drop is lower than 15% of the core diameter. Thus, there exists almost no impact on the mode profile of the pump and signal. It can be reasonably approximated as the RI structure shown in Fig. 1(b), leading to a guidance of the LP01, LP11a, and LP11b modes over the C-band. Erbium ions are uniformly doped at the core region with a doping concentration of about 4 × 10²⁴ m⁻³. Based on the above parameters, according to Ref. [20], we maintain that the difference values of the overlapping factors are 2.6×109 and 5.4×107 when the pump modes are LP01 and LP11, respectively. We can see that the difference of the overlapping factor is smaller than the condition of the LP11 pumping, leading to a lower DMG. For this EDF, we have performed the modeling of the FM-EDFA as a three-level system^[20,21].

When the length of the used FM-EDF is 5 m and the pump power is 210 mW, we can obtain the gain as a function of the input power for both the LP01 and the LP11 pumping. As shown in Fig. 2, the gain values of the three guided modes remain constant and then rapidly decrease when the input signal power gradually increases. In particular, when the pump laser is operated at the LP01 mode and the input signal power is −10dBm per mode, the gain values of the LP01 and the LP11 modes are 25.56 dB and 22.95 dB, respectively, leading to a DMG of 2.61 dB. However, when the intensity profile of the pump laser is in the LP11 mode, the corresponding gain values are 24.68 dB and 24.32 dB, respectively, leading to a DMG of 0.36 dB. Normally, the input power corresponding to a 3-dB drop of its SSG is defined as the input saturation power^[18]. For the proposed FM-EDFA, the input saturation power values of the three guided modes under different pumping schemes can be obtained, as shown in Table 1. For the same pump mode, the saturation input powers of the LP11 mode are 0.7 dB and 0.3 dB higher than that of the LP01 mode, respectively, implying a wider range of linear amplification for the higher-order signal mode, which is consistent with the findings of previous studies^[21]. This is due to the fact that the intensity profile of the LP11 signal mode is more divergent than that of the LP01 signal mode. Thus, the higher order signal modes consume the upper-level population more slowly. However, after manipulating the intensity profile of the pump laser for the purpose of DMG mitigation, the saturation input power drops by 0.2 dB for the LP01 mode and 0.6 dB for the LP11 mode, respectively. Since the intensity profile of the higher-order pump mode is less concentrated at the central region of the core, the excited populations into the upper energy level are not enough to satisfy the consumption of the signal, leading to faster amplifier saturation compared to the LP01 pumping. Thus, not only does the FM-EDFA have different saturation input power for different signal modes but also there occurs a trade-off between the pump manipulation induced by the DMG mitigation and the extension of the linear amplification range.

Next, we start to develop an all-fiber FM-EDFA, for the ease of experimental verification. As shown in Fig. 3, the signal to be amplified is generated by a C-band tunable laser source (TLS) with the SSMF pigtail. We connect the SSMF pigtail with the input port of the mode-selective photonic lantern (MSPL, Phoenix Photonics 3PL-0160153), so that either the LP11a or the LP11b mode can be separately excited and multiplexed with the LP01 mode. Polarization controllers (PCs) are used to manage the intensity profile of the higher-order modes, and 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 input power of each mode. To prevent the unwanted reflections, an isolator with a two-mode fiber (TMF) pigtail is used after the MSPL. The used commercial TMF (YOFC FM SI-2) has a core radius of about 7 µm and the core refractive index of 1.4485, respectively. Meanwhile, we experimentally implement two pumping schemes. The first one is to directly introduce the 976-nm laser with the LP01 mode into wavelength division multiplexer 1 (WDM1) as the pump source. The other pumping scheme is used to convert the LP01 mode to the LP11 mode by using an all-fiber MSC with conversion efficiency of 85.2%. Here, we place a PC after the 976-nm pump laser in order to ensure the high mode purity. With the help of WDM1, the pump laser and three-mode division multiplexing signals can be successfully introduced into a 5-m FM-EDF. The FM-EDF has the same parameters in the numerical investigation. After the FM-EDF, WDM2 is applied to filter out the residual pump, whose intensity profile can be monitored. Meanwhile, the amplified 1550-nm signal can be characterized by a charge-coupled device camera (CCD, SP928-1550-OSI), an optical spectrum analyzer (OSA, AQ6370D), and a power meter (PM100D), respectively.

In order to monitor the evolution of the signal mode, we record its intensity profile at the output port of each passive device denoted as points A, B, and C in Fig. 3, as shown in Fig. 4(a). From those results, we can conclude that the intensity profile of each guided mode is well preserved. Meanwhile, the MDL of each passive device is provided in Table 2. Here, we measure the output power P1 of the previous device and then fuse the device under test with the output pigtail of the previous device. Next, we measure the output power P2 of the device under test to obtain the insertion loss as Loss=P1−P2. Thus, the splicing loss is taken into account during the device loss measurement. According to this result, we can adjust the VOA to manage the launch power of each spatial mode at the FM-EDF input. Furthermore, the mode profile of 976-nm pump laser is also recorded by another CCD (GS3-U3-32S4C), as shown in Fig. 4(b). Before introducing the pump into the FM-EDF, denoted as point C in Fig. 3, we can observe either the LP01 or the LP11 mode profile of the pump laser. After co-propagation with the 1550-nm signal over the FM-EDF, the mode profile of the residual pump at the WDM2 output, denoted as point D in Fig. 3, is recorded as well. It can be seen that the intensity profile is well preserved for either the LP01 or the LP11 pump mode, and the MDL of WDM1 at 976 nm is summarized in Table 2 as well.

Initially, we examine both the gain and the DMG characteristics of the FM-EDFA. Figure 5 shows the DMG as a function of the pump power for two different pumping schemes. Here, the signal power of each mode at the FM-EDF input is fixed at −10dBm. As shown in Fig. 5, the pump power, no matter the pump mode is either LP01 or LP11, ranges from 50 to 250 mW. When the pump mode is LP01, the average gain eventually reaches about 19.57 dB. However, when the pump mode is LP11, the average gain can be more than 20.34 dB. Furthermore, as for the LP01 pumping scheme, the DMG is about 1.61 dB, while for the LP11 pump scheme, the DMG can decrease to about 0.97 dB when the pump power is fixed at 210 mW. Here, the NF values of the LP01, LP11a, and LP11b signal modes are 4.9 dB, 10.1 dB, and 9.4 dB, respectively, under the condition of the LP01 pumping scheme, while the NF values become 5.2 dB, 8.8 dB, and 8.7 dB, respectively, under the LP11 pumping scheme. Moreover, the gain and the DMG of the FM-EDFA with respect to the operation wavelength of the input signal are also characterized. The operation wavelength of the input signal is tuned over the C-band from 1530 nm to 1565 nm with a resolution of 2.5 nm when the signal and pump powers are fixed at −10dBm and 210 mW, respectively. Overall, both an average gain of 19.93 dB and a DMG of less than 1 dB can be achieved from 1530 nm to 1560 nm, as shown in Fig. 6. This is in line with the simulation results.

Second, we investigate the dynamic gain under different pumping schemes. When the pump power is 210 mW, the gain variations with respect to the input signal power are shown in Fig. 7. Similar to the simulation analysis, the gain first remains constant and then gradually decreases as the signal power increases. As shown in Table 3, the saturation input powers of the LP01 and the LP11 models are −12.7dBm and −7.2dBm, respectively, when the LP01 pumping scheme is chosen. However, when the pumping scheme is converted to the LP11 mode, the saturation input powers of the two spatial modes are −13.0dBm and −8.8dBm, respectively. For each pumping scheme, the saturation input power of the LP01 mode is 5.5 dB and 4.2 dB lower than the saturation input power of the LP11 mode, respectively. A mode-dependent difference of the saturated input power among the guided modes can be clearly summarized. Moreover, although the mode selective conversion of the pump laser from the LP01 mode to the LP11 mode leads to a low DMG of 0.97 dB under an input signal power of −10dBm, it reduces the saturation input power by 0.3 dB for the LP01 signal mode and 1.6 dB for the LP11 signal mode, respectively. Thus, the high-order pumping results in a small range of linear amplification. A trade-off between the DMG mitigation and the extension of the linear amplification range for the all-fiber FM-EDFA is experimentally verified when the intensity profile of pump laser is manipulated.

We have examined the dynamic gain of an all-fiber FM-EDFA in terms of the DMG and the input saturation power when the intensity profile of the pump laser is manipulated. During the numerical simulation, we found that not only the mode-dependent difference of the saturated input power occurs for all guided modes but also the implementation of higher-order pumping. The ease of DMG mitigation results in a reduction of the saturation input power for each guided mode. In the experiment, the gain of the all-fiber FM-EDFA at 1550 nm is more than 20 dB and the DMG can be reduced to be 0.97 dB. In particular, both an average gain of 19.93 dB and a DMG of less than 1 dB can be achieved from 1530 nm to 1560 nm. However, the saturation input powers of the LP01 and the LP11 modes are −12.7dBm and −7.2dBm, respectively, when the pump laser is operated at the fundamental mode. The corresponding saturation input powers drop to −13.0dBm and −8.8dBm, respectively, under the LP11 pumping scheme. Furthermore, the saturation input power of the LP11 mode is 5.5 dB and 4.2 dB higher than that of the LP01 mode, respectively, under the fixed pumping scheme. The manipulation of the pump intensity profile results in the reduced saturation input powers by 0.3 dB and 1.6 dB, respectively. There occurs a mode-dependent dynamic gain and a trade-off between the DMG mitigation and the extension of the linear amplification range under the high-order pumping scheme.