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102 3 Optical Tweezers

Sphere 8 10 0.5
Optical trapping efficiency -20 6 7 -10 -0.1 0 0.2 10 3 2 20
radius
9
0.4
(mm)
0.3
0.1

-0.2
-0.3
-0.4 5 4
-0.5
Off-axial distance (mm)

Fig. 3.22. Variation in transverse trapping efficiency at beam waist as function of
off-axial distance, with microspore radius as a parameter

Y
Beam axis

Incident F
angle F gz sz
Z
F s

F g

Fig. 3.23. Balancing between scattering force F s and gradient force F g at fiber
incident angle of θ [3.15]

Followingare the analyses for the incident angle of θ that satisfies F gz =
F sz for polystyrene radii ranging from 2 to 10 µm. Figure 3.24 shows the fiber
incident angle for different sphere radii at the maximum gradient force on
off-axial position. It is seen from the figure that as axial distance increases
the fiber incident angle illuminating the sphere first decreases, then increases
◦
a little and becomes constant (about 40 ) at the axial distance of 10 µm.
Figure 3.25 also shows the numerical results, showing that incident angle
decreases at radius intervals of 0–3 µm; after that it remains almost constant
◦
at 35 . From the results stated earlier, we may trap a microsphere two di-
mensionally by a solitary fiber illuminatingat an angle of about 40 .Bythe
◦
way, the experimental results for glass and polystyrene microspheres of 5 µm
diameter show that the minimum trappingpower linearly increases with stage
velocity (Fig. 3.37).