We numerically study supercontinuum (SC) generation (SCG) in a rare-earth-doped highly nonlinear photonic crystal fiber (HNL-PCF) with anomalous dispersion (AD) in the sub-picosecond pulse regime. We develop a semi-classical numerical model based on the generalized Ginzburg-Landau equation in order to take account of ultrafast interactions between gain ions and ultra-broadband SC radiation encompassing sub-100-femtosecond solitons. Based on the numerical model, we analyze SCG characteristics of an active HNL-PCF in comparison with a passive-type counterpart, unveiling novel optical gain effects in a highly nonlinear optical fiber with AD. We rigorously investigate gain-induced soliton dynamics, such as soliton-cascade-like behaviors, soliton-quasi-soliton collisions, and phase-matched dispersive wave generation, which eventually contributes to enhancement of energy scaling of SC radiation without incurring considerable degradation of its spectral flatness. We also verify that such superior performance characteristics of an active HNL-PCF make it suitable for the use as a boost amplifier for SC radiation. We think that the findings from this study will incite other subsequent studies on unveiling detailed nonlinear pulse dynamics in various gain-embedded nonlinear optical media.

中文翻译：

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反常色散有源高非线性光子晶体光纤中超连续谱产生的数值研究

我们数值研究了在亚皮秒脉冲范围内具有异常色散 (AD) 的稀土掺杂的高度非线性光子晶体光纤 (HNL-PCF) 中的超连续谱 (SC) 生成 (SCG)。我们开发了一个基于广义 Ginzburg-Landau 方程的半经典数值模型，以考虑增益离子和超宽带 SC 辐射之间的超快相互作用，包括亚 100 飞秒孤子。基于数值模型，我们分析了有源 HNL-PCF 与无源型对应物的 SCG 特性，揭示了具有 AD 的高度非线性光纤中的新型光学增益效应。我们严格研究了增益引起的孤子动力学，例如孤子级联行为、孤子准孤子碰撞和相位匹配色散波生成，这最终有助于增强 SC 辐射的能量缩放，而不会导致其光谱平坦度的显着降低。我们还验证了有源 HNL-PCF 的这种卓越性能特性使其适合用作 SC 辐射的升压放大器。我们认为，这项研究的发现将激发其他后续研究，以揭示各种增益嵌入式非线性光学介质中详细的非线性脉冲动力学。