## 3 Surface Plasmons in Photonic Integrated Circuits
### Plasmonic Nano-Tweezers and Nano-Manipulators
#### 3.2.2 Plasmonic Tweezers  
Plasmonic (nano-)tweezers have been extensively studied, mainly in non-integrated configurations. Integrated localized plasmonics may enable extremely high gradient forces thanks to the powerful combination of \"high optical density\" and \"high excitation efficiency\" of integrated resonant structures. Numerical and experimental demonstrations aimed at trapping polystyrene beads of different diameters in the three published examples are shown in Figure 8. In the first case (Figure 8a), the dimensions of the metal nanostructures only enable the use of propagative plasmons. The 5 \(\upmu\)m diameter disks are positioned along a 15 \(\upmu\)m grid on the top of a multimode waveguide; 1 \(\upmu\)m diameter PS beads are trapped with an injected power of 20 mW, leading to a trap stiffness of -17 fN/\(\upmu\)m. The second structure (Figure 8b) was designed to trap 20 nm diameter beads, concentrating the light in the narrow gap of the butterfly structure; the theoretically achievable force reached more than 650 pN/W in the case of a 5 nm gap. Comparable results were obtained by  
Figure 7: Sketch of optical tweezing in a Gaussian beam. The total force \(\mathbf{F}_{\mathrm{tot}}\) represents the sum of the gradient force \(\mathbf{F}_{\mathrm{g}}\) and scattering force \(\mathbf{F}_{\mathrm{s}}\).  
varying the dimer geometry within the integration plane, as illustrated in [97]. The third example corresponds to an integrated MNP chain which maximizes the LSP excitation. In the case of a 4 MNP chain with a 150 nm period, the exerted force on a 500 nm diameter PS bead reached -40 pN/W with a stiffness of \(-\)2408 fN/nm/W. The considered power refers to the power injected into the waveguide.  
In this kind of chain, the plasmonic modes generate a high spot at the ellipsoidal nanocylinder edges, separated by a distance of around 200 nm (see Figure 9a). To trap nano-objects, the trap must be compact. The gap between MNPs can be smaller to create a resonant nano-gap, like in the longitudinal dimer represented in Figure 9b. As simulated in Figure 9 (bottom, right), a gap smaller than 40 nm is required to trap a 50 nm radius PS bead with an injected power of 10 mW [99]. Experimentally, 500 nm diameter PS beads have been trapped by injecting 6 mW (at 1550 nm) into a waveguide functionalized by a 20 gold NP chain, with a measured stiffness of \(-\)5.1 \(\times\) 10\({}^{-1}\) fN\(\cdot\)nm\({}^{-1}\) in the propagation direction (x). Considering the fibered optical injection losses in the waveguide, the stiffness was estimated at \(-\)10\({}^{2}\) fN\(\cdot\)nm\({}^{-1}\)W\({}^{-1}\).  
Chains of metallic nanostructures can be realized for any shape of resonant nanoparticles (disks, ellipsoidal cylinders, butterflies, etc.), and thus can be adapted to trap different objects, as shown in Figure 10 for a transverse dimer chain.  
Moreover, the spectral and spatial dependence of the MNP chain excitation allows all-optical trapped object manipulation. Figure 11 shows the stable trapping positions (pale pink lines) versus the excitation wavelength in the case of a 4 MNP chain and 10 mW injected power [100]. In this case, the integrated nanotweezers was designed to manipulate a biological object modeled as a spherical bead with a radius of 250 nm and with a refractive index as low as 1.38. By adjusting the source wavelength to regulate the phase mismatch of the supermodes housed by the structure, it is possible to manipulate the trapped object along the plasmonic chain. Other configurations of an integrated plasmonic \"conveyor belt\" have been proposed, based on the MNP size diversity [101]. Such structures are also able to trap and self-assemble groups of nano-objects [102].