Biomedical Engineering Reference
In-Depth Information
Fig. 14.5.
(
a
) The EM model of optical trapping of a dielectric microsphere in a
Gaussian beam in terms of the minimum potential energy analogous to (
b
) the force
that pulls a dielectric block partially filling a parallel plate capacitor connected to
a constant voltage source
14.2.2 Electromagnetic (EM) Model
In the EM model [35, 36, 39], stable trapping of a dielectric microparticle in
one or more laser beams can be understood in terms of the potential energy
minimum of the dielectric particle in the electric field associated with the opti-
cal beam. The physical mechanism that a dielectric microparticle is attracted
towards the region with high optical intensity is analogous to the electrostatic
force on a dielectric block partially filling a parallel plate capacitor connected
to a constant voltage source (Fig. 14.5). In cases where the dielectric constant
of the particle (or the block in the example of the capacitor) is smaller than
that of the surrounding medium, the direction of the force is reversed, i.e., the
particle is repelled away from the region of high optical intensity and attracted
towards the region of lower optical intensity. For detailed mathematics of the
EM model, please consult the references cited above.
14.3 Experimental Measurements of Optical Forces
Optical forces on microparticles can be measured by several methods. In gen-
eral, under identical experimental condition, optical forces scale linearly with
optical power. For a particle in the vicinity of the trap center of a stable
three-dimensional optical trap, the net optical force along the direction of
each orthogonal axis can be approximated by a Hookean optical spring; a set
of optical force constants (or spring constants,
k
x
,
k
y
,and
k
z
) can thus be
used as a convenient set of parameters that specifies the three-dimensional
optical force field within a small volume surrounding each stable equilibrium
position of the particle in the trap. Techniques to measure the optical forces
and optical force constants are described below in this section.
14.3.1 Axial Optical Force as a Function of Position along
the Optical Axis
One way to measure the axial optical force on a particle in a counter-
propagating dual-beam trap as a function of position along the optical axis
