Polarisation and angular momentum of light in guided modes: theory and implementations of dipolar sources coupling

光具有许多自由度，其中最独特的是偏振、角动量、坡印亭矢量和螺旋度，它们在受限几何中的表现与在自由空间中的表现非常不同。在受限几何中，这些自由度可以相互作用，产生自旋到轨道的角动量转移或自旋动量锁定等现象。在本文中，我们将重点放在偶极源和导模的自由度交换上。这允许实现有趣的引导模式激发，如偏振依赖耦合，或单向激发。实现这些现象所需的偶极子是用一种非常简单的符号用解析法找到的。通过数值分析，设计和优化了平面波照射下的真实光源（通常是纳米粒子）和波导结构。我们将以前用圆极化电偶极子获得的引导模式的单向激发扩展到圆极化磁偶极子和电偶极子和磁偶极子的叠加，如惠更斯偶极子。这是使用角谱方法完成的，我们证明它提供了使用费米黄金法则获得的相同结果。我们还揭示了一个源的存在，即Janus偶极子，其与引导模式的耦合可以任意开关，只需反转其极化，我们展示了一个实验实现。此外，我们证明了电偶极子和磁偶极子的叠加足以在同一波导中分别控制多达五种不同导模的幅度，相位和方向。最后，我们对纳米纤维和纳米线的本征模的自旋、角动量和螺旋度进行了精确的数值和解析计算，显示了圆柱导向模的总角动量的量子化。

Light possesses many degrees of freedom, the most distinctive of which are polarisation, angular momenta, Poynting vector and helicity, which, in confined geometries, behave very differently than in free space. In confined geometries, these degrees of freedom can interact with one-another giving rise to phenomena such as Spin-to-Orbit angular momentum transfer or Spin-momentum locking. In my thesis, we focus our attention on the exchange between the degrees of freedom of dipolar sources, and those of guided modes. This allows to achieve interesting excitations of guided modes, such as polarisation-dependent coupling, or unidirectional excitation. The dipoles needed to achieve these phenomena are found analytically, with a very simple notation. Via numerical analysis both realistic sources, usually being nanoparticles under plane wave illumination, and waveguiding structures are designed and optimised. We extend the unidirectional excitation of guided modes, previously obtained with circularly polarised electric dipoles, to circularly polarised magnetic dipoles and superpositions of electric and magnetic dipoles, such as the Huygens dipole. This is done using the angular spectrum approach, and we prove it provides the same results that would be obtained using Fermi's golden rule. We also reveal the existence of a source, the Janus dipole, whose coupling to guided modes can be arbitrarily switched on-and-off simply inverting its polarisation, of which we show an experimental realisation. Moreover, we demonstrate that a superposition of electric and magnetic dipoles is sufficient to control amplitude, phase and direction of individually up to five different guided modes in the same waveguide. Finally, we present accurate calculations, both numerical and analytical of spin, angular momenta and helicity for the eigenmodes of nanofibers and nanowires, showing, among other properties, the quantization of the total angular momenta of cylindrical guided modes.