Biomedical Engineering Reference
In-Depth Information
90
90
2
2
a)
b)
120
60
120
60
1
1
150
30
150
30
180
180
z
z
0
0
210
330
210
330
240
300
300
240
270
w/ R = 1
270
w/R=2
Fig. 14.4.
Non-uniform force distribution with four distinguished peaks at the
surface of a dielectric microsphere in a pair of counter-propagating Gaussian beams
with equal optical power. Optical power
P
= 100 mW, particle radius
R
=3
.
30
ยต
m,
refractive index of surrounding medium
n
1
=1
.
334, refractive index of the particle
n
2
=1
.
378, beam radius =
w
.(
a
)
w/R
=1;(
b
)
w/R
= 2. (adapted from Bareil
et al. [38])
model [38], however, indicate several distinguished spikes in the force distri-
bution on the surface of a dielectric microsphere in a counter-propagating
dual-beam trap (Fig. 14.4). In the counter-propagating dual-beam trap, the
particle is stably trapped along the axial direction by the balanced scattering
forces from the two beams, and in the transverse direction by the co-operative
action of the transverse gradient forces from the two beams. In the single-beam
gradient-force optical trap, the particle is stably trapped axially, balanced by
the axial scattering force against the axial gradient force, and transversely by
the transverse gradient force.
To compare the e
ciency of different optical trapping configurations, the
optical force as given in (14.2) above is often written as
F
=(
Pn
1
/c
)
Q,
(14.3)
where the parameter
Q
, known as the trapping e
ciency, represents the frac-
tion of photon momentum per second associated with the trapping beam,
which is converted into the net trapping force. In most of the optical trapping
configurations that have been demonstrated to date, the transverse trap-
ping e
ciency is typically on the order of 0.1-0.001, whereas the axial trapping
e
ciency is typically a factor of 3-10 smaller than the transverse trapping
e
ciency. The exact value of the trapping e
ciency depends on many fac-
tors, including the numerical aperture (NA) of the trapping beam, the size of
the particle, the refractive index of the particle and that of the surrounding
fluid, etc.
