Abstract

An averaged variational procedure has been developed to study the propagation of light bullets in optical fibers using the propagation of light pulses in media with Kerr and quadratic nonlinearities as examples. Criteria for the correct choice of trial solutions are discussed. The condition under which the dispersion length is much greater than the length of diffraction spreading is called the diffraction limit. It is shown that, in this limit, the temporal and spatial dynamics of a bullet are independent of each other, while finding the dynamic parameters of a soliton is reduced to finding various solutions of the nonstationary linear Schrödinger equation for an imaginary quantum particle. The efficiency of the proposed approach is demonstrated by the example of finding solutions in the form of optical vortices in a waveguide for nonlinearities of both types.

中文翻译：

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轻子弹理论的衍射极限

摘要

已经开发了平均变分程序来研究光脉冲在光纤中的传播，并以Kerr和二次非线性为例，研究了光脉冲在介质中的传播。讨论了正确选择试验解决方案的标准。色散长度远大于衍射扩展长度的条件称为衍射极限。结果表明，在此极限下，子弹的时间和空间动力学是相互独立的，而寻找孤子的动力学参数却减少了，从而找到了关于虚构量子粒子的非平稳线性薛定ding方程的各种解。