An Integrated Core-Pumped 4-Core Erbium-Doped Fiber Amplifier with Low Differential Core Gain

Abstract

We demonstrate an integrated core-pumped 4-core erbium-doped fiber amplifier (4C-EDFA) that achieves a record-low differential core gain of 0.5 dB across the whole C-band. This is enabled by utilizing a 4C-EDF with a minimal core-dependent absorption coefficient and passive devices with low core-dependent loss. The 4C-EDFA also exhibits an average gain of 15.50 dB, an average output power of 22.5 dBm, and a maximum noise figure of 4.91 dB. Furthermore, simulations on a 4-core fiber (4CF) transmission link confirm that the proposed 4C-EDFA can support transmission exceeding 10,000 km with a minimal inter-core Q² difference of only 0.5 dB. Here, Q² is defined as the ratio of the mean received signal levels to the corresponding noise variances. It is a critical metric in optical systems to quantify the signal quality, which highlights its potential for high-capacity and long-haul uncoupled 4CF systems.

1. Introduction

The exponential growth in global data traffic is driving an urgent need for new technologies to overcome the nonlinear Shannon limit of standard single-mode fibers [1]. Space-division multiplexing (SDM) based on few-mode fibers (FMFs) or multi-core fibers (MCFs) has emerged as a promising solution to increase system capacity by orders of magnitude [2]. Among these technologies, uncoupled MCFs are particularly attractive as they do not require complex multi-input multi-output (MIMO) digital signal processing at the receiver, which makes them the SDM technologies with the highest potential for next-generation submarine optical cable systems [3]. In recent years, uncoupled MCFs with a standard 125 μm cladding diameter have attracted great attention due to their compatibility with existing standard single-mode fiber infrastructure [4,5,6,7]. It has been verified that under the constraint of the standard 125 μm cladding diameter, homogeneous uncoupled MCFs can accommodate up to four cores while maintaining acceptably low inter-core crosstalk (XT) and effective mode area [3,5]. High-capacity and long-haul transmission using uncoupled MCFs has already been experimentally demonstrated [8,9,10,11]. As one of the key devices for long-haul MCF links, multi-core fiber amplifiers should simultaneously provide high gain, low differential core gain (DCG), and low noise figure (NF). Minimizing DCG is particularly critical, as a large DCG causes signal-to-noise ratio differences among cores, ultimately limiting both the achievable transmission capacity and distance [12,13]. Therefore, reducing DCG has become a focus in the development of high-performance multi-core fiber amplifiers.

Many studies have been conducted on uncoupled 4-core erbium-doped fiber amplifiers (4C-EDFAs) [14,15,16,17,18,19]. The primary reason for a large DCG is discrepancies among the cores in multi-core erbium-doped fibers and integrated passive components, which originate from fabrication imperfections [20]. Core-pumping schemes can partially mitigate DCG by independently adjusting the pump power for each core [15,16], with the smallest value achieved to date being 0.7 dB. In contrast, uniformly pumped schemes report higher DCGs of <1.6 dB and ~2 dB, respectively [17,18]. However, even with these adjustments, the lowest reported DCG for integrated 4C-EDFAs remains above 0.5 dB.

In this work, we demonstrate an integrated 4C-EDFA that achieves a low DCG of <0.5 dB across the whole C-band, with a spectrally averaged DCG of 0.31 dB. This improvement is realized by using a 4C-EDF with a minimal core-dependent absorption coefficient and optimized 4-core passive devices with minimal core-dependent loss (CDL).

2. Key Components of the 4C-EDFA

Figure 1 shows the schematic of the proposed 4C-EDFA in a forward 976 nm core-pumped scheme. The 4C-EDFA consists of a 4-core hybrid isolator and wavelength-division multiplexer (4C-IWDM), four single-mode 976 nm pump laser diodes (Pump-LDs), 4C-EDF, and a 4-core isolator (4C-ISO). To ensure low splice loss across all cores, we keep the core pitch of all 4-core fibers (4CFs) within the amplifier at 43 μm with a tolerance of ±0.35 μm. An image processing algorithm has been employed to automatically extract the core boundaries from end-face images of the 4CF. In this way, the core pitches of various 4CFs are measured under a uniform standard, which avoids the additional error that could be induced by manual extraction. Furthermore, a 4-core passive fiber with a mode field diameter (MFD) of 6.3 μm at 1060 nm is used to mitigate the MFD mismatch between the 4-core transmission fiber (MFD of 9.9 μm at 1550 nm) and the 4C-EDF (MFD of 5.9 μm at 1550 nm), which ensures that all splice losses remain <0.3 dB.

First, we characterize the key components, i.e., the 4C-EDF and the 4-core passive devices, to demonstrate their low inter-core difference. Figure 1 shows the cross-section of the 4C-EDF, and its key parameters are listed in

Table 1. Key parameters of the fabricated 4C-EDF.

Parameter	Value
NA	0.21
Core pitch (μm)	43.00, 42.75, 43.04, 43.03
MFD@1550 nm (μm)	5.9
Absorption coefficient@1529 nm (dB/m)	6.10, 6.12, 6.26, 6.31
Cladding diameter (μm)	125

. The measured core pitches for the four cores are 43.00 μm, 42.75 μm, 43.04 μm, and 43.03 μm, respectively, with a maximum variation of 0.29 μm and a standard deviation (SD) of 0.138 μm. To measure the absorption coefficients of the 4C-EDF, the cutback method is employed [21]. A pair of 4-core fan-in/fan-out (4C-FIFO) fabricated by the fused taper process is used in the measurement [22]. The 4CF used in the 4C-FIFO has the same MFD and core pitch as the 4C-EDF, and the inter-core XT is <−60 dB. In this way, the influence of splice loss and device XT on the measurement results is negligible. Through six sets of repeated tests, the peak absorption coefficients for the four cores are 6.10 dB/m, 6.12 dB/m, 6.26 dB/m, and 6.31 dB/m, respectively. Importantly, the core-dependent absorption coefficient remains <0.21 dB/m, with an SD of 0.103 dB/m across the four cores, which ensures a low DCG in the amplifier.

The 4C-IWDM is implemented based on free-space optics and integrates collimating lenses, a Faraday rotator, and a beam combiner, which provides both optical isolation and 976/1550 nm wavelength-division multiplexing. As shown in Figure 2a, the 4C-IWDM contains one signal input port, four pump input ports, and one common output port. The signals from the input 4CF and the pump lights emitted from four single-mode 976 nm LDs are first collimated and then directed into the WDM. After multiplexing, both the signal and pump beams are focused onto the facet of the output 4-core passive fiber by a common collimator. The isolator, placed between the input port and the WDM, can suppress backward amplified spontaneous emission (ASE) noise. During fabrication, the output 4-core passive fiber is continuously rotated to find a low CDL. For the insertion loss (IL) measurement, the input and output power of each core are measured using a 4C-FIFO assembly to guide light. The measured IL across the C-band is shown in Figure 2b, the average IL of the 4C-IWDM for the four cores are 0.63 dB, 0.65 dB, 0.65 dB, and 0.58 dB, and the maximum IL values for the four cores are <0.7 dB, with a maximum CDL of 0.12 dB observed at 1550 nm, a minimal CDL of 0.06 dB observed at 1535 nm, and an SD of 0.006 dB. Note that the wavelength-dependent loss (WDL) for each core is also very low, i.e., 0.11 dB, 0.10 dB, 0.08 dB, and 0.05 dB, respectively. The average IL for the pump lights is 1.75 dB. Furthermore, the inter-core XT of these key passive devices is measured by injecting light into one core and detecting the output power from all others. This measurement is conducted using a tunable laser source (TSL) and an optical power meter, with the device under test connected via a pair of low-XT (<−54 dB) 4C-FIFO. The 4C-IWDM exhibits a minimum isolation of 56 dB and a maximum inter-core XT of −57 dB.

The 4C-ISO is also implemented based on free-space optics, as shown in Figure 2c. It is placed at the output of the 4C-EDFA to suppress backward ASE by preventing it from re-entering the 4C-EDF, which effectively reduces the NF. The measured IL of the device across the C-band is shown in Figure 2d. The maximum IL values for the four cores are as low as 0.38 dB, with a maximum CDL of 0.09 dB and an SD of 0.047dB. The WDLs for all four cores are less than 0.04 dB. Furthermore, the 4C-ISO exhibits a minimum isolation of 59 dB and a maximum inter-core XT of −48 dB. These results demonstrate that both the fabricated 4C-IWDM and 4C-ISO possess high inter-core consistency and low WDL across the whole C-band.

3. Characterization of the 4C-EDFA

Figure 3a illustrates the experimental setup used to characterize the proposed 4C-EDFA. Fifty-one tunable laser sources TLSs are used to cover the wavelength range from 1528 nm to 1569 nm with a uniform channel spacing of 0.8 nm. A variable optical attenuator (VOA) is placed after each TLS to precisely control the per-channel output power, which ensures a power flatness within ±0.1 dB across all wavelength channels. These channels are then combined to form a 51 λ light output serving as the input signal to the 4C-EDFA, and the corresponding spectrum is shown in Figure 3b. An additional VOA is placed between the combined source and the 4C-FI to adjust the total signal power launched into each core of the 4C-EDFA to 7 dBm/core, which is typical in long-haul transmission systems across the whole C-band [9,14]. A pair of 4C-FIFO is used to characterize the gain and NF of each core, and its impact has been excluded. Its 4CF has the same structural parameters as that of the 4C-EDFA, which ensures low splice loss between them. At the output of the 4C-EDFA, an optical spectrum analyzer (OSA) is used to record the amplified output spectrum.

To determine the optimal length of the 4C-EDF, we initially set the fiber length to 16 m and gradually shortened it. The output spectra are recorded and compared to evaluate the amplifier performance. According to refs. [3,9], the 4C-EDFA should provide a gain of >12 dB across the whole C-band to compensate for the loss of a fiber span as well as additional losses from passive components and splices. As shown in Figure 3c, as the length of the 4C-EDF decreases, the gain at shorter wavelengths increases gradually, whereas the gain at longer wavelengths decreases. At a length of 12.9 m, the gain exceeds 12 dB across the whole C-band. Therefore, this length is selected as the optimal 4C-EDF length for the amplifier.

Figure 4a shows the measured gain and DCG of the 4C-EDFA across the wavelength range of 1528–1569 nm. With pump powers individually optimized to 527.7 mW, 566.6 mW, 523.4 mW, and 486.5 mW for each core of the 4C-EDF, the DCG is minimized, with an average input pump power of 789.1 mW/core before the 4C-IWDM. Over this wavelength range, the maximum and minimum gains of the proposed 4C-EDFA are 17.47 dB and 12.60 dB, respectively, corresponding to a gain ripple of ~5 dB. The average gains for the four cores are 15.60 dB, 15.39 dB, 15.44 dB, and 15.70 dB, respectively, with a spectrally averaged DCG of 0.31 dB, and the average total signal output power reaches 22.5 dBm. The 4C-EDFA exhibits a maximum DCG of 0.50 dB at 1569 nm, which is attributed to the use of all key components with low inter-core differences. The total power conversion efficiency (PCE) is calculated to be 21.9%. A potential method to further improve the PCE is to reduce the loss of the 4C-IWDM for the pump light. For example, if this loss is decreased from the current 1.75 dB to 0.5 dB, the PCE can be enhanced from 21.9% to 29.9%. Figure 4b shows a maximum NF of 4.91 dB and an inter-core variation of <0.12 dB across the C-band, resulting from the low-loss 4C-IWDM combined with the forward 976 nm core-pumping. A further reduction in NF remains feasible by minimizing the signal light loss in the 4C-IWDM.

Representative studies on uncoupled 4C-EDFAs are summarized in

Table 2. Comparison of integrated 4C-EDFAs.

Year and Ref.	Wavelength (nm)	Input Signal Power (dBm/core)	Average Gain (dB)	Output Power (dBm)	NF (dB)	DCG (dB)
2023 [14]	1529–1565	\	13.3	<16.3	6.3	\
2023 [15]	1525–1572	6	16.5	22.5	<6.5	<1
2023 [16]	1528–1568	0	18.8	18.8	<4.6	0.7
2024 [17]	1570–1610	0	21.4	21.4	6.8	<1.6
2025 [18]	1529–1564	0	14.7	14.7	4.9	~2
2025 [19]	1530–1566	0	12.6	12.6	7.1	2.2
This work	1528–1569	7	15.5	22.5	<4.9	<0.5

. The pump compensation method is widely used to reduce the DCG [15,16,23,24], with a reported low of 0.7 dB. However, the DCG’s further reduction is constrained by inherent core-to-core discrepancies in the 4C-EDF and passive devices. By utilizing a 4C-EDF with a minimal core-dependent absorption coefficient and optimized 4-core passive devices with minimal CDL, we have achieved a record-low DCG of <0.5 dB. Meanwhile, the proposed 4C-EDFA also exhibits high output, low NF across the whole C-band.

4. Transmission Results and Discussions

To evaluate the transmission performance of the proposed 4C-EDFA, we conduct a numerical simulation of a long-haul SDM system based on the Gaussian-noise model [25,26]. The system model, illustrated in Figure 5a, consists of multiple cascaded fiber spans. The 4CF is configured with the following parameters: a loss of 0.16 dB/km, a chromatic dispersion of 20 ps/(nm·km), an inter-core XT of −70 dB/km, and an effective mode area of 80 μm². A 34-GBaud 128 λ polarization-division multiplexed quadrature phase-shift keying (PDM-QPSK) signal is transmitted through the 4CF, amplified by the 4C-EDFA, and shaped by a gain-flattening filter (GFF). In the system model, the measured broadband gain and NF for each core of the 4C-EDFA are applied to all wavelength channels within that respective core. The Q² factors for all signals are estimated at the receiver. For a given DCG, the gains of the four cores are set to follow an arithmetic progression to emulate the DCG. Figure 5b shows the maximum transmission distance calculated based on the 25.5% overhead forward error correction (FEC) threshold, corresponding to a Q² limit of 5 dB [27]. The results show an approximately linear decrease in maximum transmission distance as DCG increases. Benefiting from the low DCG of 0.50 dB offered by the proposed 4C-EDFA, the system can achieve a maximum transmission distance exceeding 10,000 km. The inter-core Q² differences (ΔQ²s) among the four cores at a transmission distance of 10,000 km are shown in Figure 5c. The performance difference between the cores increases with DCG. Note that the ΔQ² induced by the proposed 4C-EDFA with a DCG of 0.5 dB is only 0.5 dB, which emphasizes the importance of a low DCG for achieving uniform performance across all cores.

5. Conclusions

In conclusion, we have experimentally demonstrated an integrated 4C-EDFA in a 976 nm core-pumped scheme, which achieves a record-low DCG of 0.5 dB. The low DCG is realized by minimizing the core-dependent absorption coefficient of the 4C-EDF to 0.21 dB/m, as well as reducing the CDLs of the integrated 4-core passive devices to 0.12 dB for the 4C-IWDM and 0.09 dB for the 4C-ISO. The 4C-EDFA also achieves an average gain of 15.50 dB, a maximum NF of 4.91 dB, and an average output power of 22.5 dBm across the whole C-band. Furthermore, through a 34-GBaud PDM-QPSK transmission simulation over a 4CF link, the proposed 4C-EDFA is shown to be able to support transmission distances exceeding 10,000 km, and ΔQ² is only 0.5 dB. These results confirm that the proposed 4C-EDFA exhibits low DCG, low NF, and high output power, demonstrating its potential in high-capacity and long-haul uncoupled MCF systems.