Waveguides based on metamaterials may exhibit strongly frequency-dependent nonlinearities. In this work, we focus on the phenomenon of modulation instability in this type of waveguide, departing from a new modeling equation that ensures strict conservation of both the energy and photon number of the parametric process. In particular, we analyse the case of a waveguide with a linearly frequency-dependent nonlinear coefficient, revealing unique features such as narrowband and ultra-wideband gain spectra and the suppression of the power cutoff giving rise to an ever-growing MI gain. These markedly distinct regimes are enabled by self-steepening (SS) and manifest themselves depending upon the magnitude and sign of the SS parameter. We believe these findings to be most relevant in the context of mid-IR supercontinuum sources.

中文翻译：

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非线性超材料波导中的窄带和超宽带调制不稳定性

基于超材料的波导可能会表现出强烈的频率依赖性非线性。在这项工作中，我们关注于这种类型的波导中调制不稳定性的现象，它偏离了一个新的建模方程式，该方程式可确保严格保留参数过程的能量和光子数。尤其是，我们分析了具有线性频率相关非线性系数的波导情况，揭示了诸如窄带和超宽带增益谱之类的独特功能以及对功率截止的抑制，从而产生了不断增长的MI增益。这些明显不同的机制可以通过自增强（SS）来实现，并根据SS参数的大小和符号来体现出来。我们认为，这些发现与中红外超连续谱源最相关。