Quasi-energies, parametric resonances, and stability limits in ac-driven PT-symmetric systems.
Quasi-energies, parametric resonances, and stability limits in ac-driven PT-symmetric systems.
复制标题
DOI：
10.1063/1.4883715
复制
发表时间：
2013-08
期刊：
影响因子：
2.9
通讯作者：
J. D’Ambroise;B. Malomed;P. Kevrekidis
中科院分区：
文献类型：
--
作者：
J. D’Ambroise;B. Malomed;P. Kevrekidis
我们介绍了一种在PT对称性系统中实现准能量和参数共振概念的简单模型，即一对相互平衡的耦合增益和损耗元件。通过周期性地调制考虑两个自由度耦合的系数来施加参数(AC)力。该系统可以在光学上实现为双芯波导，其增益和损耗施加到不同的芯上，并且它们之间的间隙的厚度受周期调制。本文用解析形式研究了小强迫振幅(V1)下参数不稳定性的发生和发展。通过系统仿真生成了系统的完整动态图。当强迫频率ω足够大时，参数不稳定性的舌头随着V1的增大而产生，正如分析所预测的那样。然而，随着V1的进一步增加，舌头具有与通常的(非PT)参数驱动系统截然不同的模式：它们不是弯曲到更大的DC耦合常数V0的值，而是保持平行于V1轴的方向。随着ω的减小，平行语言系统变得密集，合并成稳定和不稳定区域交替的复杂的小尺度结构。分别用绝热近似和平均近似对ω-->；0和ω-->；∞的情况进行了解析研究。立方非线性，如果添加到系统中，改变了图景，破坏了许多原本稳健的动力制度，并稳定了一些不稳定的制度。
We introduce a simple model for implementing the concepts of quasi-energy and parametric resonances (PRs) in systems with the PT symmetry, i.e., a pair of coupled and mutually balanced gain and loss elements. The parametric (ac) forcing is applied through periodic modulation of the coefficient accounting for the coupling of the two degrees of freedom. The system may be realized in optics as a dual-core waveguide with the gain and loss applied to different cores, and the thickness of the gap between them subject to a periodic modulation. The onset and development of the parametric instability for a small forcing amplitude (V1) is studied in an analytical form. The full dynamical chart of the system is generated by systematic simulations. At sufficiently large values of the forcing frequency, ω, tongues of the parametric instability originate, with the increase of V1, as predicted by the analysis. However, the tongues following further increase of V1 feature a pattern drastically different from that in usual (non-PT) parametrically driven systems: instead of bending down to larger values of the dc coupling constant, V0, they maintain a direction parallel to the V1 axis. The system of the parallel tongues gets dense with the decrease of ω, merging into a complex small-scale structure of alternating regions of stability and instability. The cases of ω-->0 and ω-->∞ are studied analytically by means of the adiabatic and averaging approximation, respectively. The cubic nonlinearity, if added to the system, alters the picture, destabilizing many originally robust dynamical regimes, and stabilizing some which were unstable.