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arXiv 1408.0237physics.optics
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辐射连续谱中束缚态的拓扑性质

Topological nature of bound states in the radiation continuum

Bo Zhen, Chia Wei Hsu, Ling Lu, A. Doug Stone, Marin Soljacic

摘要:

连续介质中的束缚态(英语:Bound states in the continuum,BIC)是描述光或物质的波动方程的不寻常解:它们是离散的,空间上有界的,但与传播到无穷远的连续介质的能量相同。直到最近,BIC都是通过微调波动方程中的参数或利用波动方程由于对称性而具有的可分性来构造的。最近,已经预测并实验性地在周期性结构中实现了既鲁棒又不受保护(意外)的BIC;最简单的这种系统是周期性电介质板,其也具有受保护的BIC。在这里,我们表明,这两种类型的BIC在这样的系统中的涡流中心的偏振方向的远场辐射。这些BIC的鲁棒性是由于存在守恒和量子化的拓扑电荷,定义的偏振矢量的次数围绕涡旋中心。这种电荷只能通过系统参数的大变化产生或湮灭,然后只能根据严格的规则,我们推导和测试数值。我们的结果意味着基于这种状态的激光发射将产生矢量光束。

英文摘要:

Bound states in the continuum (BICs) are unusual solutions of wave equations describing light or matter: they are discrete and spatially bounded, but exist at the same energy as a continuum of states which propagate to infinity. Until recently, BICs were constructed through fine-tuning parameters in the wave equation or exploiting the separability of the wave equation due to symmetry. More recently, BICs that that are both robust and not symmetry-protected (accidental) have been predicted and experimentally realized in periodic structures; the simplest such system is a periodic dielectric slab, which also has symmetry-protected BICs. Here we show that both types of BICs in such systems are vortex centers in the polarization direction of far-field radiation. The robustness of these BICs is due to the existence of conserved and quantized topological charges, defined by the number of times the polarization vectors wind around the vortex centers. Such charges can only be generated or annihilated by making large changes in the system parameters, and then only according to strict rules, which we derive and test numerically. Our results imply that laser emission based on such states will generate vector beams.

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