Fig. 1. Schematic of the graded-index MMF optical tweezers probe structure. a, image of the MMF profile light field in the core when Δλr=0; b, image of the MMF profile light field in the core when Δλr=10  μm; c, the lateral view image of the focused output light field from the MMF when Δλr=0, here we employ the dye Eosin Y in the solution. We use the green light source of 532 nm to illuminate and a red light filter to observe. d, the lateral view image of the focused output light field from the MMF when Δλr=10  μm. The images are all taken by CCD.

Fig. 2. Relationship between Δλr and the intensity Iλr of the outgoing beam and the relationship between the Δλr and the spot size ω0 of the outgoing beam. The range of the Δλr is from 0 to 16.5 μm, the range of the Iλr is from 0 to 1, and the range of ω0 is from 6.18 to 20.20 μm.

Fig. 3. Schematic of the fiber probes with different shapes fabricated by different methods. a, the awl shape fiber probe tip fabricated by using the heating-drawing method; b, the axial force produced by the awl shape fiber tip; c, the ellipsoid shape fiber probe tip fabricated by using the two-step method; d, the axial force produced by the ellipsoid shape fiber tip; e, the tapered shape fiber probe tip fabricated by using the grinding–polishing method; f, the axial force produced by tapered shape fiber tip.

Fig. 4. a, simulated results of the axial optical trapping force introduced by the graded-index MMF probes with the grinding angles of θ1=20°, θ2=30°, and θ3=56° and different Δλr. b, the schematic diagram of the grinding angles. c, the schematic diagram to define zd.

Fig. 5. Experimental setup structure diagram of the graded-index MMF optical tweezers system. a, the schematic showing the fiber grinding and polishing configuration.

Fig. 6. Visualization 1. a, relationship between dz and Δλr when the laser power is 15.92 mW. b, images of the graded-index MMF probe with the Ω of 56° trapping and changing the position of the yeast cell.