Effects of constant and spatially varying higher-order dispersions on spatial solitons in $$\mathcal{P}\mathcal{T}$$ -symmetric optical media under the alternative complex potentials
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Abstract
We investigated analytically and numerically the nonlinear Schrödinger (NLS) equation with constant and spatially varying third-order dispersion (TOD) in the alternative type of complex parity-time \((\mathcal{P}\mathcal{T})\)-symmetric potentials. This equation describes the propagation of ultra-short pulses through the optical media, where the real part of the potential models the index guiding and the imaginary part the loss/gain distribution of light within optical material. For the constant TOD, the regions of stability/instability linear \(\mathcal{P}\mathcal{T}\)-symmetric phases are numerically carried out. By means of the linear stability analysis and direct numerical simulation, the effects of interplay between constant TOD and \(\mathcal{P}\mathcal{T}\)-symmetric potential on the stability of these solutions are also tested. It is found that the constant TOD can be used to control the stability of these solutions. For the spatially varying TOD, the additive terms of the \(\mathcal{P}\mathcal{T}\)-symmetric potential are considered for the nonlinear model and the robustness of these solutions against noise is tested by means of the split-step Fourier beam technic. Moreover, the elastic interactions of the two spatial solitons are generated under the \(\mathcal{P}\mathcal{T}\)-symmetric potential for the spatially varying TOD. The power and the transverse power-flow density are further examined. Results indicate that the spatially varying TOD does not yield any instability in the self-focusing nonlinear medium with the chosen parameters values.
摘要 我们分析和数值研究了在另一种类型的复平分时间（(\mathcal{P}\mathcal{T})\）对称势中具有恒定和空间变化三阶色散（TOD）的非线性薛定谔（NLS）方程。该方程描述了超短脉冲在光学介质中的传播，其中电势的实部模拟了光学材料内部的折射率导向，虚部模拟了光的损耗/增益分布。对于恒定的 TOD，用数值方法计算了线性（\mathcal{P}\mathcal{T}\）对称相的稳定/不稳定区域。通过线性稳定性分析和直接数值模拟，还检验了恒定TOD和（\mathcal{P}\mathcal{T}）-对称势之间的相互作用对这些解的稳定性的影响。结果发现，恒定的 TOD 可以用来控制这些解的稳定性。对于空间变化的 TOD，考虑了非线性模型的 \(\mathcal{P}\mathcal{T}) - 对称势的加法项，并通过分步傅里叶波束技术测试了这些解对噪声的鲁棒性。此外，在空间变化的 TOD 的（\mathcal{P}\cal{T}\）-对称势下产生了两个空间孤子的弹性相互作用。进一步研究了功率和横向功率流密度。结果表明，在所选参数值下，空间变化 TOD 在自聚焦非线性介质中不会产生任何不稳定性。
期刊介绍：
Indian Journal of Physics is a monthly research journal in English published by the Indian Association for the Cultivation of Sciences in collaboration with the Indian Physical Society. The journal publishes refereed papers covering current research in Physics in the following category: Astrophysics, Atmospheric and Space physics; Atomic & Molecular Physics; Biophysics; Condensed Matter & Materials Physics; General & Interdisciplinary Physics; Nonlinear dynamics & Complex Systems; Nuclear Physics; Optics and Spectroscopy; Particle Physics; Plasma Physics; Relativity & Cosmology; Statistical Physics.
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