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106 3 Optical Tweezers
that considers gravity, buoyancy and Brownian movement (theoretical trap-
ax
ax
pingpower is calculated usingthe expression P pre = F pre c/n 1 Q max ).
π
3
ax
F pre = (ρ s − ρ m ) d g +2kT/d, (3.21)
6
where ρ s and ρ m are the densities of the sample spheres and suspending
medium, respectively; d is the diameter of the spheres, g is the gravitational
acceleration, and kT is the thermal energy.
Results of comparison of traps between experimental and theoretical meth-
ods are summarized in Table 3.7 as the ratio of P ax to P ax . The measured
min pre
P ax for glass beads matches the theoretical P ax at large diameters (only
min pre
about 1.5 times difference for the diameter of 5.8 µm) because the ray op-
tics model is appropriate and the Brownian effect is relatively small for large
diameters. In parentheses, the experimental value with the upward-directed
beam for the 5.8 µm diameter becomes large because the wall force (between
the bead and the cover slip) strongly pulls the bead downward at a small
distance of about 4.2(= 10 − 5.8) µm.
A comparison is also given for the axial trapping power in both straight ray
and parabolic ray approximations. Figure 3.29 shows the minimum axial trap-
pingpower for polystyrene microspheres comparingthe experimental measure-
ments to the predicted results for a straight ray model (broken line) and a
parabolic ray model (solid line). It is seen from the figure that the minimum
axial trappingpower largely increases for the parabolic ray model and is close
to the experimental results. This is because the actual focused trappinglaser
beam has a beam waist (parabolic ray model) and the individual ray enters
almost vertically to the sphere surface leadingto a reduced trappingefficiency.

3.3.3 Transverse Trapping Power
trans
Next, the transverse trappingpower P min was measured as the minimum
power for trappinga particle movingat the constant velocity v in water, as

Table 3.7. Ratio of experimental and theoretical minimum axial trapping powers
of polystyrene sphere (a), and those of glass sphere (b)
diameter (µm)downward directed upward directed
(a) Polystyrene
3.25 7.6 4.0
5.85 3.5 1.7
7.73 2.4 1.5
(b) Glass
1.0 40 50
2.5 2.5 2.2
3.1 1.9 2.0
5.1 1.8 1.7
5.8 1.5 -