# L-Band Erbium-Doped Fiber Optimization and Transmission Investigation +
## 1 Introduction  
The introduction of rare-earth-element-doped fiber amplifiers and wavelength division multiplexing (WDM) technology has significantly enhanced both the transmission distance and capacity of optical communication systems [1]. However, the widespread adoption of dense wavelength division multiplexing (DWDM) technology has led to the exhaustion of available optical spectrum resources in the C-band (1530-1565 nm) [2]. Consequently, new transmission bands are being explored for further capacity expansion. Due to the device compatibility and proximity in wavelength, the L-Band (1565-1625 nm) is a promising candidate for capacity expansion. Extensive research has been conducted to realize amplification in the L-band [3, 4, 5] or combined C+L band [6, 7, 8]. Additionally, the mode division multiplexing (MDM) method has been applied to increase the number of channels, thereby promoting the transmission capacity [9, 10]. When the existing single-mode optical transmission systems are not able to meet the capacity demand, constructing new transmission networks based on few-mode fibers emerges as a good choice. However, the widelyused single-mode EDFA cannot directly support effective amplification of the optical signal transmitted in few-mode fibers. This requires the use of mode-demultiplexing and mode-multiplexing devices, and doubles the number of single-mode EDFAs, significantly increasing the system complexity and cost. In contrast, a few-mode erbium-doped fiber amplifier (FM-EDFA) can supply power compensation for all the different mode channels, without requiring mode converters. Therefore, FM-EDFA is an essential component in few-mode optical transmission systems. In an FM-EDFA, the distribution of different signal modes leads to a high power difference among various mode channels. This power imbalance severely impairs the overall transmission performance. Thus, there is an urgent demand for suitable L-band FM-EDFAs to meet the requirements of few-mode transmission systems, ensuring signal power equalization among all signal modes. This is essential for realizing high-bit-rate and long-distance transmission [11; 12]. Significant efforts have been made to realize gain equalization in the L-band, including pump mode regulation and active fiber design. Pump mode regulation is an effective method to reduce the DMG among different modes. In 2015, [PERSON] et al. implemented an EDFA with a DMG of less than 1 dB in the wavelength range of 1570 nm to 1600 nm, utilizing pump mode, wavelength regulation, and fiber design [13]. In 2021, an FM-EDFA was proposed only theoretically, supporting a DMG of 0.28 dB in the wavelength range of 1570-1616 nm through a mode-hybrid pumped method [14]. As the gain medium, both the refractive and doping profiles of the rare-earth-doped fiber significantly impact the gain equalization characteristics. Thus, optimizing the fiber structure is another promising way to realize gain equalization in the L-Band. In 2022, [PERSON] et al. proposed a gain-equalized FM-EDFA, obtained by optimizing a few-mode active fiber and pumped with two LP\({}_{11}\) pump mode lasers [15]. However, the pump mode conversion induces more insertion loss and increases the system complexity. In 2021, a few-mode erbium-ytterbium co-doped fiber amplifier (FM-EYDYA) was proposed, capable of supporting a minimum modal gain of 20 dB in the whole L-band [16]. Nevertheless, the EYDFA has not yet been characterized in a transmission system. In this paper, we present the optimization and fabrication of an L-band few-mode erbium-doped fiber (FM-EDF). Utilizing this homemade FM-EDF, we develop a gain-equalized FM-EDFA operating in the wavelength range of 1575 nm to 1610 nm. The experimental results demonstrate that the maximum modal gain achieved is 22.22 dB, with a minimum DMG of 0.54 dB. Additionally, the gain flatness over all modes and wavelengths is 4.54 dB.