论文标题
部分可观测时空混沌系统的无模型预测
Twisted polaritonic crystals in thin van der Waals slabs
论文作者
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。
Polaritons - hybrid light-mater excitations - are very appealing for the confinement of light at the nanoscale. Recently, different kinds of polaritons have been observed in thin slabs of van der Waals (vdW) materials, with particular interest focused on phonon polaritons (PhPs) - lattice vibrations coupled to electromagnetic fields in the mid-infrared spectral range with - in biaxial crystals, such as e.g. MoO3. In particular, hyperbolic PhPs - having hyperbola-like shape of their isofrequency curves - in MoO3 can exhibit ultra-high momenta and strongly directional in-plane propagation, promising novel applications in imaging, sensing or thermal management at the nanoscale and in a planar geometry. However, the excitation and manipulation of in-plane hyperbolic PhPs have not yet been well studied and understood. Here we propose a technological platform for the effective excitation and control of in-plane hyperbolic PhPs based on polaritonic crystals (PCs) - lattices formed by elements separated by distances comparable to the PhPs wavelength -, twisted with respect to the natural vdW crystal axes. In particular, we develop a general analytical theory valid for an arbitrary PC made in a thin biaxial slab. As a practical example, we consider a twisted PC formed by rectangular hole arrays made in MoO3 slab and demonstrate the excitation of Bragg resonances tunable by the twisting angle. Our findings open novel avenues for both fundamental studies of PCs in vdW crystals and the development of mid-infrared sensing and photodetection applications