Fig. 1. Generation of customized dark traps. (a) Schematic illustration of generating customized dark traps using the free lens modulation (FLM) method. Customized dark traps’ profiles correspond to free lens models with different colors. (b) Light path diagram. Subfigure: experimental setup. HWP: half-wave plate; PBS: polarizing beam splitter; SLM: spatial light modulator; QWP: quarter-wave plate. (c) Simulated (first row, scale bar=10  mm) and experimental (second row, scale bar=10  μm) annular dark traps, with radius ratio σ=0.05 and 1. (d) Simulated (first row, scale bar=10  mm) and experimental (second row, scale bar=10  μm) annular dark traps, with amplitude weight ratio ε=1 and 2. (e) Gap width dgap against σ plot, with σ from 0.05 to 1. (f) Normalized intensity of inner and outer POVs against ε, with ε from 1 to 2.

Fig. 2. Simulated dynamic analysis of LRI particles in annular dark traps. (a) Simulated transverse force distribution on a hollow glass sphere with l=25. (b) Simulated transverse force distribution and line plot of the radial force along the y-axis on a hollow glass sphere with l=−25 in the focal plane. (c) Azimuthal force (Fθ) against the gap width dgap for LRI particles with rp=2.5, 3, and 3.5 μm at the corresponding equilibrium positions with l=15. (d) Azimuthal force (Fθ) with ideal gap width dgap against topological charge for LRI particles with rp=2.5, 3, and 3.5 μm trapped at the corresponding equilibrium positions.

Fig. 3. Rotation performance of customized dark traps. (a) Screenshots (left) and time-lapse images (right) of an LRI particle with rp=5.3  μm in annular dark traps with l=24, dgap=7  μm. Scale bar=10  μm. (b) Screenshots and (c) rotation rate against the gap width of LRI particles with rp=5.3, 4.7, and 3.1 μm in annular dark traps with l=24 (see Visualization 1). Scale bar=10  μm. (d) Rotation rate against the topological charge of the LRI particle with rp=5.3  μm in annular dark traps with dgap=7  μm (see Visualization 2). (e) Free lens models, simulated light field models, phase maps, and experimentally generated light fields with l=10 for oval, triangular, square, and pentagonal dark traps, respectively. Scale bar: 10 μm. (f) Screenshots (left) and time-lapse images (right) of an LRI particle with rp=4.8  μm in customized dark traps corresponding to (e) with l=28 (see Visualization 3). Scale bar: 10 μm.

Fig. 4. Generation of dark traps for sorting and sorting experiments by size of LRI particles. (a) Free lens models, light field models, and intensity profiles of the dark traps for sorting. (b) Schematic structure for the homemade microfluidic chip (see Appendix B for details). Screenshot of sorting of LRI particles by size when setting the gap width dgap to (c) 8.9 μm, (d) 6.6 μm, and (e) 4.2 μm (see Visualization 4). Scale bar: 10 μm.

Fig. 5. Generation of dark trap arrays for parallel manipulation of multiple LRI particles. (a) Generation of dark trap array. Free lens models and intensity profiles of 4 dark traps, 9 dark traps, 9 intensity modified dark traps, 9 triangular dark traps, and hybrid dark traps. Scale bar: 10 μm. (b) Multiparticle trapping procedure with adjustable intensity array. L: left ring; R: right ring. Scale bar: 10 μm. (c) Array trapping and aggregation process of LRI particles (see Visualization 5). Scale bar: 10 μm.

Fig. 6. Dynamic analysis of LRI particles in annular dark traps. (a) Electromagnetic scattering model. (b) Simulated radiation exerted on an LRI microparticle in the transverse plane. (c) Radial force (Fρ) of the LRI particle with rp=3  μm and the gap width between the inner and outer rings dgap=3.6−6.6  μm. (d) Azimuthal force (Fθ) of the LRI particle with rp=3  μm and the gap width between the inner and outer rings dgap=3.6−6.6  μm.

Fig. 7. Schematic structure for the homemade microfluidic chip. (a) Frontal view of the microfluidic chip. (b) Structure of the microfluidic system. (c) Lateral view of the microfluidic chip.