Majorel Clément, Patoux Adelin, Estrada-Real Ana, Urbaszek Bernhard, Girard Christian, Arbouet Arnaud, Wiecha Peter R
CEMES-CNRS, Université de Toulouse, CNRS, UPS, 31000 Toulouse, France.
LAAS-CNRS, Université de Toulouse, 31000 Toulouse, France.
Nanophotonics. 2022 Jul 14;11(16):3663-3678. doi: 10.1515/nanoph-2022-0308. eCollection 2022 Sep.
The multipole expansion of a nano-photonic structure's electromagnetic response is a versatile tool to interpret optical effects in nano-optics, but it only gives access to the modes that are excited by a specific illumination. In particular the study of various illuminations requires multiple, costly numerical simulations. Here we present a formalism we call "generalized polarizabilities", in which we combine the recently developed exact multipole decomposition [Alaee et al., Opt. Comms. 407, 17-21 (2018)] with the concept of a generalized field propagator. After an initial computation step, our approach allows to instantaneously obtain the exact multipole decomposition for any illumination. Most importantly, since all possible illuminations are included in the generalized polarizabilities, our formalism allows to calculate the total density of multipole modes, regardless of a specific illumination, which is not possible with the conventional multipole expansion. Finally, our approach directly provides the optimum illumination field distributions that maximally couple to specific multipole modes. The formalism will be very useful for various applications in nano-optics like illumination-field engineering, or meta-atom design e.g. for Huygens metasurfaces. We provide a numerical open source implementation compatible with the python package.
纳米光子结构电磁响应的多极展开是解释纳米光学中光学效应的一种通用工具，但它只能获取由特定照明激发的模式。特别是对各种照明的研究需要进行多次昂贵的数值模拟。在此，我们提出一种我们称之为“广义极化率”的形式体系，其中我们将最近开发的精确多极分解[Alaee等人，《光学通讯》407，17 - 21(2018)]与广义场传播子的概念相结合。经过初始计算步骤后，我们的方法能够即时获得任何照明下的精确多极分解。最重要的是，由于广义极化率中包含了所有可能的照明情况，我们的形式体系能够计算多极模式的总密度，而无需考虑特定照明，这是传统多极展开无法做到的。最后，我们的方法直接提供了与特定多极模式最大耦合的最佳照明场分布。这种形式体系对于纳米光学中的各种应用，如照明场工程或元原子设计（例如用于惠更斯超表面）将非常有用。我们提供了一个与python包兼容的数值开源实现。
