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Spatial, temporal, and spatio-temporal modulational instabilities in a planar dual-core waveguide

机译：平面双芯波导中的空间，时间和时空调制不稳定性

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摘要

We investigate modulational instability (MI) in a planar dual-core waveguide (DWG), with a Kerr and non-Kerr polarizations based on coupled nonlinear Schrodinger equations in the presence of linear coupling term, coupling coefficient dispersion (CCD) and other higher order effects such as third order dispersion (TOD), fourth order dispersion (FOD), and self-steepening (ss). By employing a standard linear stability analysis, we obtain analytically, an explicit expression for the MI growth rate as a function of spatial and temporal frequencies of the perturbation and the material response time. Pertinently, we explicate three different types of MI-spatial, temporal, and spatio-temporal MI for symmetric/antisymmetric continuous wave (cw), and spatial MI for asymmetric cw, and emphasize that the earlier studies on MI in DWG do not account for this physics. Essentially, we discuss two cases: (i) the case for which the two waveguides are linearly coupled and the CCD term plays no role and (ii) the case for which the linear coupling term is zero and the CCD term is nonzero. In the former case, we find that the MI growth rate in the three different types of MI, seriously depends on the coupling term, quintic nonlinearity, FOD, and ss. In the later case, the presence of quintic nonlinearity, CCD, FOD, and ss seriously enhances the formation of MI sidebands, both in normal as well as anomalous dispersion regimes. For asymmetric cw, spatial MI is dependent on linear coupling term and quintic nonlinearity. (C) 2015 Elsevier Inc. All rights reserved.
机译：我们在线性耦合项，耦合系数色散（CCD）和其他更高阶存在的情况下，基于耦合非线性Schrodinger方程研究具有Kerr和非Kerr极化的平面双芯波导（DWG）中的调制不稳定性（MI）诸如三阶色散（TOD），四阶色散（FOD）和自增强（ss）之类的效果。通过采用标准的线性稳定性分析，我们得到了MI增长率作​​为扰动的时空频率和物质响应时间的函数的显式表达式。相应地，我们针对对称/反对称连续波（cw）解释了三种不同类型的MI空间，时间和时空MI，对于非对称cw则阐述了空间MI，并强调了DWG中关于MI的较早研究并未解释这个物理学。从本质上讲，我们讨论了两种情况：（i）两个波导线性耦合且CCD项不起作用的情况；（ii）线性耦合项为零而CCD项为非零的情况。在前一种情况下，我们发现三种不同类型的MI的MI增长率严重取决于耦合项，五次非线性，FOD和ss。在后一种情况下，无论是在正常色散还是异常色散状态下，五次非线性，CCD，FOD和ss的存在都会严重增强MI边带的形成。对于不对称的连续波，空间MI取决于线性耦合项和五次非线性。 （C）2015 Elsevier Inc.保留所有权利。

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