We present a rigorous design of few-mode erbium doping fiber (FM-EDF) with an oversized two-layer erbium ion distribution at the central region with effective differential modal gain (DMG) mitigation over the C-band. The proposed erbium doping distribution allows for a similar overlapping integral value among the guided modes, leading to a signal gain equalization over the C-band. When the length of the proposed FM-EDF is 8 m under the cladding pumping power of 2.5 W, our calculated results reveal that four linearly polarized (LP)-modes can achieve an average gain per mode of 24.8 dB and a typical DMG of less than 0.64 dB over the C-band. Meanwhile, we carry out numerical simulations to explore the fabrication tolerance of the oversized two-layer erbium doping distribution with respect to the DMG, indicating stable DMG mitigation over the C-band. We believe that such new manipulation of erbium doping distribution is helpful for the multiple-dimensional multiplexing of fiber optical transmission.

中文翻译：

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严格的 FM-EDF 设计，具有超大的两层铒离子分布，用于 C 波段 DMG 缓解

我们提出了一种严格设计的少模掺铒光纤 (FM-EDF)，在中心区域具有超大的两层铒离子分布，在 C 波段上具有有效的差分模态增益 (DMG) 缓解。所提出的铒掺杂分布允许导模之间具有相似的重叠积分值，从而导致 C 波段上的信号增益均衡。当在 2.5 W 的包层泵浦功率下，所提出的 FM-EDF 的长度为 8 m 时，我们的计算结果表明，四个线性极化 (LP) 模式可以实现每个模式的平均增益为 24.8 dB，典型的 DMG 小于在 C 波段上小于 0.64 dB。同时，我们进行数值模拟以探索超大的两层铒掺杂分布相对于 DMG 的制造公差，表明在 C 波段上稳定的 DMG 缓解。