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3.2 Theoretical Analysis 95
0.40
Diameter
Beam waist 40 mm
0.35
Trapping efficiency 0.25 s Ray optics 10
20
0.30
4
2
0.20
0.15
0.10
0.05
0
0 0.2 0.4 0.6 0.8 1.0
Normarized distance between microsphere center and focus point
Fig. 3.16. Transverse trapping efficiency of polystyrene microsphere by two con-
verging ray approximations

n
w 2 2 R
r(z) n 1 w 1

d 2 d 1

Fig. 3.17. Geometry for calculating trapping efficiency for microsphere along prop-
agation axis by laser beam emitted from tapered lensed optical fiber

lensed optical fiber of curvature R =10 µm, beam waist radius ω 1 =5.0 µm,
core refractive index n 1 =1.462, as shown in Fig. 3.17. The focus distance
from the tapered lensed fiber end d 2 and the beam radius r(z) with the beam
waist ω 2 are given as

2

n 2 R(n 2 − n 1 ) z

d 2 = − , r(z)= ω 2 1+ .
2 kω 2
(n 2 − n 1 ) + R 2 λ 2
2
πω 2
1
Solution. An equation of a ray going along the z-direction is expressed by
the variable parameter t(0 ≤ t ≤ 1) as

2
z 2
y = tω 2 1+ , Z 0 = kω ,
2
Z 0
where t = r/R m and
ω 1
.
ω 2 =
2
2 2
πω
1 n 2 −n 1 +1
λ n 1 R