New approaches to modeling the dynamics of misaligned beams in nonlinear gradient waveguides

A. I. Bychenkov, V. Derbov, V. V. Serov
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Abstract

The propagation of a misaligned paraxial beam through a nonlinear waveguide medium can be presented as a nonlinear dynamical problem, where the longitudinal coordinate z plays the role of time, while the transverse pattern of the field is the dynamical system evolving with z. The reduction to a finite-dimensional system is possible within the framework of the approximate method using Gaussian probe functions whose parameters are determined by Galerkin's criterion in the basis of a small number of flexible Gaussian modes. This method is referred as the modified generalized method of moments (MGMM). Using the MGMM we studied the dynamics of an off-axis initially Gaussian beam propagating through a Kerr nonlinear parabolic waveguide and revealed stationary, periodic and quasiperiodic regimes, as well as nontrivial phenomena, such as phase locking, cycle generation, etc. In particular, the behavior of the beam variables in the vicinity of the stationary states was analyzed. However, direct numerical modeling shows significant non-Gaussian distortions of the beam caused by Kerr nonlinearity, so MGMM is expected to describe correctly the dynamics of the beam moments rather than the field transverse pattern itself. To check this idea alternative approaches are desirable. The method proposed here involves the exact numerical calculation of nonlinear modes followed by the linear analysis of small nonstationary perturbations of these modes based on Bogoliubov's equations.
非线性梯度波导中失调光束动力学建模的新方法
准直光束在非线性波导介质中的传播可以表示为非线性动力学问题,其中纵坐标z扮演时间的角色;而场的横向模式是随z演化的动力系统。在近似方法的框架内,利用高斯探测函数的参数由伽辽金准则在少量柔性高斯模的基础上确定,可以将其还原为有限维系统。这种方法被称为修正广义矩量法(MGMM)。使用MGMM,我们研究了离轴初始高斯光束通过克尔非线性抛物波导传播的动力学,揭示了平稳、周期和准周期状态,以及非平凡现象,如锁相、周期产生等。特别地,分析了梁变量在稳态附近的行为。然而,直接数值模拟显示了Kerr非线性引起的光束的显著非高斯畸变,因此MGMM有望正确描述光束矩的动力学而不是场横向图本身。为了验证这一观点,我们需要其他方法。本文提出的方法包括非线性模态的精确数值计算,然后根据Bogoliubov方程对这些模态的小的非平稳扰动进行线性分析。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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