Imaging and Manipulation of Biomolecules - Bionanoelectronics: Bioinquiring and Bioinspired Devices - page 122

Fig. 3.10 The optical
tweezer and trapping
principle

laser light

high NA objective

liquid

where I 0 is the light intensity, n m is the index of refraction of the medium, and is
the scattering cross section of the sphere, given by

m 2

2

128 5 R 6
3 4

1

D : (3.35)

m 2

C 2

In ( 3.35 ), m D n p =n m ,wheren p is the index of refraction of the particle. For the
same spherical particle, the gradient force is

2˛
cn 2 m r I 0 ;

F grad D (3.36)

where ˛ is the sphere polarizability, expressed as
˛ D n 2 m R 3 m 2

:

1

(3.37)

m 2

C 2

In the case when R is comparable to , the above approach based on ray optics
and a point-like dipole is no longer valid, and more complicated electromagnetic
theories are needed to explain the trapping mechanism. The majority of objects to be
trapped are in the range of 0:1-10, and the minimum dimensions of trapped objects
are around 30 nm. The reviews in Neuman and Block ( 2004 )and Le Grimellec
et al. ( 2010 ) explain in detail the optical systems necessary to implement the optical
tweezers/traps and provide also a good description of the commercial systems for
optical trapping.
In the optical trapping setups, the particles can be trapped, manipulated from
a place to another, or rotated. There are numerous applications in biology where
optical tweezers are used. For example, a single rod-shaped E. coli bacterial cell
was trapped and rotated to allow its study from different perspectives ( Carmon
and Feingold 2011 ). In addition, using optical tweezers, the shear modulus of
the human erythrocyte membrane was determined to be D 2:5 ˙ 0:4Nm 1 .
Micromanipulation of plant cytoplasm and organelles using optical tweezers were
recently reported in the review in Hawes et al. ( 2010 ). Moreover, DNA nanome-
chanical properties are currently investigated with optical tweezers. The stretching
of the DNA molecule with a length less than 1m was achieved by fixing one