Discrete Snaking: Multiple Cavity Solitons in Saturable Media
Discrete Snaking: Multiple Cavity Solitons in Saturable Media
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离散蛇行：饱和介质中的多腔孤子
DOI：
10.1137/080734297
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发表时间：
2010
影响因子：
2.1
通讯作者：
Yulin A
中科院分区：
文献类型：
--
作者：
Yulin A
研究了由相干光源泵浦的周期性光腔阵列组成的光学系统中光场的一维晶格方程。该模型包括线性失谐、线性和非线性耗散以及饱和非线性效应。各种各样的不同的参数区域进行了研究，其中有低功率和高功率空间均匀的稳态之间的双稳态。通过将稳态问题作为时间可逆的四维离散映射，证明了这些态的时间稳定性是空间局域模存在的必要条件。数值路径跟踪被用来找到所谓的亮孤子（其核心是在一个较高的强度比尾巴）和灰孤子（非零低强度的尾巴），其时间稳定性也计算。从聚焦非线性的情况下，在连续极限和能量守恒，耗散和空间离散的影响分别和组合进行了研究。麦克斯韦点的存在，其中异宿连接存在于不同的均匀状态，被发现导致蜿蜒的分岔图中的孤子的宽度增长通过一个过程的连续增加和减少的参数代表的泵强度。这些结构被发现导致参数区间有无限多个不同的稳定孤子，明亮和灰色。揭示了机制，蛇可以创建和销毁的第二个参数是不同的。特别是，明亮的孤子到达双稳态区域的边界处的孤子的尾巴的均匀状态进行折叠，于是蛇分裂成许多独立的环路。更复杂的机制下的灰孤子分支的形态发生，例如，由于折叠的均匀状态，形成的蛇形孤子的核心。进一步蛇形图散焦和纯耗散非线性，但进一步的机制被解开，蛇被创建或销毁的两个参数的变化。
A one-dimensional lattice equation is studied that models the light field in an optical system comprised of a periodic array of optical cavities pumped by a coherent light source. The model includes effects of linear detuning, linear and nonlinear dissipation, and saturable nonlinearity. A wide variety of different parameter regions are studied in which there is bistability between low-power and high-power spatially homogeneous steady states. By posing the steady problem as a time-reversible four-dimensional discrete map, it is shown that temporal stability of these states is a necessary condition for the existence of spatially localized modes. Numerical path-following is used to find both so-called bright solitons (whose core is at a higher intensity than the tails) and grey solitons (with nonzero lower intensity tails), whose temporal stability is also computed. Starting from the case of focusing nonlinearity in the continuum limit and with energy conservation, the effects of dissipation and spatial discreteness are studied both separately and in combination. The presence of Maxwell points, where heteroclinic connections exist between different homogeneous states, is found to lead to snaking bifurcation diagrams where the width of the soliton grows via a process of successive increase and decrease of a parameter representing the pump strength. These structures are found to cause parameter intervals where there are infinitely many distinct stable solitons, both bright and grey. Mechanisms are revealed by which the snakes can be created and destroyed as a second parameter is varied. In particular, the bright solitons reach the boundary of the bistability region where the homogeneous state in the soliton's tail undergoes a fold, whereupon the snake splits into many separate loops. More complex mechanisms underlie the morphogenesis of the grey soliton branches, for example, due to a fold of the homogeneous state that forms the core of the snaking soliton. Further snaking diagrams are found for both defocusing and purely dissipative nonlinearities, and yet further mechanisms are unraveled by which the snakes are created or destroyed as the two parameters vary.
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