论文标题

在非平凡时期背景中的光学标量束传播

Optical scalar beam propagation in nontrivial spacetime backgrounds

论文作者

Escobar, C. A., Martín-Ruiz, A., Mondragón, M., Jáuregui, R.

论文摘要

储层计算是预测湍流的有力工具,其简单的架构具有处理大型系统的计算效率。然而,其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间,然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用,该系统模拟了湍流的若干特征。我们表明,使用径向基函数作为非线性投影器,即使只有部分观测并且不知道控制方程,也能稳健地捕捉复杂的系统非线性。最后,我们表明,当测量稀疏、不完整且带有噪声,甚至控制方程变得不准确时,我们的网络仍然可以产生相当准确的预测,从而为实际湍流系统的无模型预测铺平了道路。

We study the propagation of structured optical scalar beams in a spacetime background parameterized by a second-rank symmetric tensor. An analytic expression for the Green's function in a cylindrical coordinate system is obtained for particular choices of such a tensor. This facilitates the numerical exploration of the propagation of apertured Gaussian beams in this nontrivial background. Unusual focusing properties are found along with a decrease in the Gouy phase compared to that in standard vacuum. In the case of apertured Bessel beams, the medium allows to overcome finite aperture effects so that the corresponding diffraction length is increased; besides, the central spot of a zero order Bessel concentrates an increased fraction of the energy of the beam. Multiple scenarios beyond an electromagnetic field in the presence of an anisotropic medium could support the results reported here. They include a bosonic field in a weak gravitational field or a nontrivial spacetime background arising from Lorentz symmetry breaking. In particular, our results could illustrate how optically transparent multiferroic materials offer unprecedented opportunities to tailor structured beam propagation, as well as to simulate nontrivial spacetime backgrounds.

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