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134 4 Optical Rotor
50
Torque efficiency (10 -3 mm) 30 (a) Gaussian (a)
40

(b)
20

10
(c) Donut
0 (b) Uniform (c)
-4 -3 -2 -1 0 1 2 3 4
Beam waist position (mm)
Fig. 4.16. Relationship between torque eﬃciency Q torque and beam waist position
z f for diﬀerent beam proﬁles

800
Focused beam
Rotation rate (rpm) 400 NA= 1.0 NA= 0.8
600

200
(a) (b) (c)
0
0 20 40 60 80 100
Incident laser power (mW)
Fig. 4.17. Relationship between rotation rate and incident laser power for diﬀerent
beam proﬁles

Solution. Figure 4.16 shows the relationship between Q torque and z f for the
diﬀerent beam proﬁles. Good trappingand fast rotation are possible when
the outer part of the input aperture is ﬁlled by a high intensity beam. In
addition, the dependence of the rotation rate on the incident power for two
NAs is shown in Fig. 4.17. The rotation rate increases as the intensity of the
outer part becomes high. We can improve the rotation rate by adjusting the
incident beam proﬁles.
In summary, it is conﬁrmed that a high rotation rate can be obtained
under the followingconditions:
1. high NA of the objective lens
2. large slope angle of the microobject
3. high refractive index of the microobject (Problem 4.3)
4. large number of slopes on the microobject (Problem 4.4)
5. beam proﬁle of high intensity at the outer part of the aperture.

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