论文标题

均匀波导阵列中离散孤子的碰撞动力学

Collision dynamics of discrete soliton in uniform waveguide arrays

论文作者

Lara, Anuj P., Roy, Samudra

论文摘要

我们在\ textit {衍射谐振辐射}(difrr)的上下文中研究了现实的半无线性波导阵列(WA)中离散孤子(DS)对的碰撞动力学。根据初始振幅($ a_0 $)和wavenumber($ k_0 $),这是一对相同的同一DSS对碰撞或合并以形成离散的\ textit {breather}。对于大幅度和小的波数,DSS形成一个结合状态,不相互作用。 我们通过迭代模拟映射交互的域,并在($ a_0 $ - $ k_0 $)参数空间中呈现一个相位图。 在将相互作用项视为扰动的情况下,开发了一种变分技术。适当的拉格朗日密度和\ textit {ansätz}函数之后,ritz优化使我们进入了描述碰撞机制的一组普通微分方程。分析结果用数值数据很好地证实了。 我们进一步研究了两个相同DS之间初始阶段失呼的作用,并在相互作用过程中观察到周期性的能量交换。 当两个具有不同波数的Ds碰撞时,能量交换的程度不同,从而导致三种不同的输出状态伴随着DIFRR的产生。 通过服用不同的DS对振幅和波数将我们的调查扩展到更广泛的条件,我们在$ k $ - 空间中发现了独特的二次辐射,这是由于孤子碰撞而起源的。 发现这种碰撞介导的次级辐射的性质与通常的difr不同。 我们的结果阐明了非线性WA中DS对碰撞动力学的有趣方面,并有助于理解复杂机制。

We investigate the collision dynamics of discrete soliton (DS) pair in a realistic semi-infinite nonlinear waveguide array (WA) in the context of \textit{diffractive resonant radiation} (DifRR). Depending on the initial amplitude ($A_0$) and wavenumber ($k_0$), a co-moving pair of identical DSs either collide elastically or merge to form a discrete \textit{breather}. For large amplitude and small wavenumber, DSs form a bound state and do not interact . We map the domain of interaction by iterative simulation and present a phase plot in ($A_0$-$k_0$) parameter space. A variational technique is developed where the interaction term is considered as perturbation. A proper choice of Lagrangian density and the \textit{ansätz} function followed by the Ritz optimization leads us to a set of ordinary differential equations that describe the collision mechanism. The analytical result corroborate well with numerical data. We further investigate the role of initial phase detuning between two identical DS and observe a periodic energy exchange during their interaction. Varied degree of energy exchange occurs when two DS with different wavenumbers collide which results in three distinct output states accompanied by DifRR generation. Extending our investigation to a more generalized condition by taking different amplitudes and wavenumber of DS pair, we find an unique secondary radiation in $k$-space which is originated due to the collision of solitons. The nature of this collision mediated secondary radiation is found to be different from usual DifRR. Our results shed light on the interesting aspects of the collision dynamics of DS pair in nonlinear WA and useful in understanding the complex mechanism.

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