## 3 Surface Plasmons in Photonic Integrated Circuits
### Plasmonic Antennas
This device enables the trapping and displacement of the biological object along the plasmonic chain axis [100]. Figure 12: Vivaldi antenna integrated on an SOI waveguide as part of an on-chip optical interconnection system (inspired by [115]). radiated signal) in the axe of the \"director\" chain. When the Yagi-Uda plasmonic antenna is integrated on a substrate or a waveguide, as shown in Figure 13, the emission is slightly deviated from the axis of the antenna elements in the case of surrounding optical index asymmetry. The typical radiation diagram thus shows emission towards the higher index medium, usually the substrate. The angle depends mainly on the index difference. Recently, it has been demonstrated that specific engineered arrangements of elementary nanoantennas, strategically positioned on the surface of a silicon waveguide, can couple the two orthogonal polarizations of incident light into different directions and modes of the underlying waveguide, thus achieving a demultiplexing function [117]. A periodic chain made of identical MNPs can also realize controlled directivity of an \"LSP\" antenna, which is evanescently coupled to a dielectric waveguide. In order to obtain collective and radiative resonance, the chain is designed as a diffraction grating while keeping a sufficiently short period to enable dipole coupling along the chain [118; 119]. The latter property enables efficient interfacing of the antenna with the dielectric waveguide (Figure 14). The diffraction grating controls the emission direction (period) and directivity (chain length). For symmetry reasons, as soon as the grating order is higher than 1, the light is diffracted simultaneously in two directions: toward the substrate and the superstrate. The emission angle is defined with respect to the guided propagation axis as follows: in the case of homogeneous surrounding index n\({}_{\text{s}}\), \(\theta=arcsin\left(\frac{n_{eff}}{n_{\text{s}}}-\frac{m,\lambda}{d,n_{\text{s} }}\right)\) where d is the grating period, m is the grating order, and \(n_{\text{eff}}\) is the effective index of the guided mode. With respect to the usual dielectric or metallic gratings, this resonant chain grating offers additional degrees of freedom:  
* The chain resonance modifies the coupling efficiency independently of the emission angle and directivity control; the MNP size is chosen to have a resonant or resonant-shifted chain. * The chain can be positioned freely around the waveguide, without diffraction efficiency modification as long as the chain and waveguide mode overlap remains similar. * The chain period determines the emission angle independently of the coupling efficiency. * Several chains can be simultaneously excited, for example, to shape the radiation diagram: two chains on both sides of the waveguide generate radiation similar to [PERSON]'s slit interferences. Figure 13: **(a,b)** Yagi–Uda antenna integrated into a waveguide. (**a**) 3D sketch of the structure. (**b**) Side view of the structure, red arrows represent the direction of light flow. The radiation is preferentially directed towards the highest optical index (substrate). Inspired by [116]. In Figure 14, a double 8 ellipsoidal MNP chain with d = 300 nm is positioned at D = 50 nm from a silicon nitride waveguide. The minima of optical transmission through the waveguide indicate the chain resonances for three values of ellipses with a long axis radius of a\({}_{y}\). The radiation diagrams are calculated for two different wavelengths: they show the independence of the emission angle and the coupling efficiency (proportional to the radiative power). This control of the coupling efficiency was verified experimentally [120]. It can vary from 10 to 50% by changing only the major axis of the nanocylinders a\({}_{y}\), offering control of the radiated power without changing the radiation diagram.