Fig. 1. (a) The schematic of the trapped SSN nanoparticle, which is made of Si (magenta) and Si3N4 (blue), with its long axis aligned to the optical axis (z-axis) of the trapping beam (red). The cross section in the x−y plane is a square of width W, and the aspect ratio AR is the ratio of height H to width W. (b) The effective refractive indices and birefringence of the SSN nanoparticles as a function of ρ. (c) Top-view and (d) side-view of SEM images of SSN nanoparticles with ρ=0.2, W=450  nm, and AR=2.

Fig. 2. The relationship between the axial stiffness kz of SSN nanoparticles and the width W, aspect ratio AR under different ρ values. (a) ρ=0.1, (b) ρ=0.2, (c) ρ=0.3, (d) ρ=0.4, (e) ρ=0.5, (f) ρ=0.6, (g) ρ=0.7, (h) ρ=0.8, (i) ρ=0.9. The black pixels in the maps indicate the nanoparticle sizes that cannot be trapped in 3D due to excessive scattering forces.

Fig. 3. Architecture of the DL network based on the NN-PSO algorithm, where the input is the size parameters and the output is the kz.

Fig. 4. The kz optimization process for ρ=0.2 (a) and 0.3 (b), respectively. The arrow indicates the route to find the optimal solution. The circle numbers indicate the number of the grid to be calculated in that route, and the blue dot indicates the optimal solution.

Fig. 5. The x- (a), y- (b), and z- (c) axis power spectral density curves for two types of particles (SSN and TiO2) measured in water.

Fig. 6. The fabrication process of SSN nanoparticles. (The legend is the color coding for different materials.)

Fig. 7. Characterization of SSN nanoparticles. (a) and (b) SEM images of the sample shown In step (8). (d) Height of the unit cell as measured by AFM.

Fig. 8. To determine the exact dissolution time of the Cr sacrificial layer. (a) 47 s, (b) 80 s, (c) 120 s, (d) 180 s, (e) 7 min. (f) A small drop of DI water is dropped on the surface of the samples.

Fig. 9. The trapping efficiency as a function of the radius of the amorphous TiO2 microsphere. The blue and red curves are the axial (Qz) and lateral (Qx) trapping efficiency, respectively.

Fig. 10. The relationship between torques and the angular displacement for two shapes of SSN nanoparticles. ρ=0.2, τx (a), τy (b), τz (c); ρ=0.3, τx (d), τy (e), and τz (f). The blue and red curves represent cylindrical and rectangular SSN nanoparticles, respectively.

Fig. 11. Relationship between rotation angle γ and kz when ρ is 0.2 and 0.3, respectively.