Page 122 -

112 3 Optical Tweezers
optical springconstant) equals the thermal energy kT/2 (Brownian motion
2
energy) [3.11], Therefore, K = kT/z .
At the moment of escape, z =d/2 because the maximum trappingeffi-
ciency is close to the surface of the sphere. In this case, the equivalent force
of the Brownian motion is
kT 2kT
F = Kz = z = .
z 2 d

3.4 Applications of Optical Tweezers

Ashkin et al. [3.19] demonstrated the optical trappingof a transparent mi-
crosphere by a strongly focused laser beam. A single-beam gradient-force
optical trappingtechnique has been proved to be useful in the study of
biological processes because of its noninvasive nature [3.20]. Recently, op-
tical tweezers have been applied in various scientific and engineering fields
listed in Table 3.8. Inexpensive fiber manipulation is expected for easy
implementation.
Not only a solid laser but also an LD can be used as a light source for
trapping. The optical pressure force is very weak, nearly pN/mW, but can
manipulate particles on the micrometer scale. Since the gravitational force in-
creases proportional to the third power of the particle radius and the Brownian
effect increases inversely proportional to the radius, there exists an adequate
objective size in trapping. It corresponds to several micrometers, facilitating
the manipulation of livingcells in its early developingstage. 3-D trappingis
possible for various particles ranging from 20 nm to tens of micrometers in-
cludingbiological, dielectric and polymer particles which are transparent for
the laser beam, as shown in Fig. 3.38.
Recently, materials have been wideningfor further applications. For ex-
ample, the 3-D trappingof metallic objects is possible due to a gradient force
of the light intensity in the Rayleigh regime where the size is much less than
the wavelength, and also due to the diffractive effect of the light at the sur-
face of the object with a size of several wavelengths [3.21]. Gahagam et al. of
Wochester Polytechnic Institute demonstrated the 3-D trappingof low-index
particles in the size range of 2–50 µm usinga donut-shaped intensity pro-
file beam [3.22]. Higurashi et al. of NTT trapped ringlike (hollow), low-index
microobjects in a high-index liquid using upward bottom-surface radiation
pressure [3.17]. The ringlike microobject was made of fluorinated polyimide,
with a refractive index of 1.53 and a surroundingliquid refractive index of
1.61. Followingare the actual applications of the optical tweezers classified in
the field of basic research and industry.

3.4.1 Basic Research
Biology

Livingcells of several micrometers in size, which are easy to trap, leads to
optical tweezers were first used in biology [3.23]. For example, results of the