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5.3 Experimental Analysis 187
Table 5.3. Parameters for calculation of gradient force of Rayleigh particles

refractive index of medium n 1 1.33
refractive index of particle n 2 0.272 + i7.07
objective NA 1.3
laser power 20 mW
laser wavelength 1,064 nm
beam profile 100 nm
Gaussian

40
Trapping force F (pN) 30 Fgrad 20 mW

20
10

0 Fscat
-1,000 -500 0 500 1,000
Distance from focus (nm)

Fig. 5.23. Calculated gradient force F grad in transverse direction and in axial di-
rection for gold particle with refractive index n 2 =0.272 + i7.07, diameter 100 nm,
medium refractive index n 1 =1.33, objective lens NA = 1.3, and Gaussian laser
power 20 mW

F grad in the transverse direction and in the axial direction were calculated
for the gold particle refractive index n 2 =0.272 + i7.07, the gold particle
diameter 2r = 100 nm, the medium refractive index n 1 =1.33, the objective
lens NA = 1.3, and the Gaussian laser power is 20 mW as listed in Table 5.3.
We found from Fig. 5.23 that the gradient force along the transverse direction
is eight times greater than that along the axial direction. This result shows
that the trapped particle is very stable alongthe transverse direction but
unstable alongthe optical axis, which leads to the particle beingtrapped and
pushed onto the sample surface by the upward-directed beam.
Here, we estimate the forces [5.26] between the optically trapped particle
and the sample surface for reference. See the problems at the end of this
chapter.

Dependence on Scanning Velocity
The theoretical transverse trappingpower P trans can be expressed in (5.22)
pre
by takinginto consideration the maximum trappingefficiency Q max

& '
1
3πµdvc 1+ 9d T 1 − H−T
32
trans
P pre = , (5.22)
n 1 Q max