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Optical trapping
It was known from physics and the early history of optics that light had linear
and angular momentum, and therefore could exert radiation pressure and torques
on physical objects. However, its strength was not recognized until recently to
be large enough for practical uses. With the advent of laser radiation, Ashkin
showed, in 1970, that one could use the forces or radiation pressure from
focused laser beams to significantly affect the dynamics of small transparent
micro and nanometer sized neutral particles. In 1986, Ashkin and Chu achieved
the trapping of dielectric particles with a focused laser beam, giving rise to
the first steps in the field of optical nanomanipulation.
Starting from Maxwell equations,
which are the laws governing light propagation, it is possible to calculate the
force exerted on small particles in an analytically easy fashion. We can
think of a laser as a light cannon, shooting photons in rectilinear
trayectories. These light bullets go through the physical objects and, in doing
so, they cause a whole of events which we pretend to analyse. The total effect
of these photons when they interact with an object is the so-called
radiation pressure, and it can be splitted into two force components: the
scattering force, which represents the photons hitting the
object, and the gradient force, which is the force responsible for
the trapping. To levitate particles, for instance, only the scattering force is
needed; we can think of a laser as a Geyser, pointing vertically against the
gravitational force and levitating particles by opposing their weight with the
upward photon flow.
Origin of the scattering, Fscat, and gradient, Fgrad,
force components on a dielectric particle with its refractive index higher than
the surrounding medium, under the action of a laser beam (mode TEM00).
Fig.
(a) shows that both
force components arise from radiation pressure. Consider a
typical pair of rays "a" and "b" striking the
particle symmetrically about its center. Neglecting relatively minor surface
reflections, most of the rays refract through the particle, giving rise to
forces Fa
and Fb in the direction of the momentum change. Since the intensity of ray "b"
is higher than ray "a", the force
Fb
is larger than Fa.
Adding all such symmetrical pairs of rays striking the object, one sees that the
net force can be resolved into two components,
Fscat,
called the scattering force component pointing in the direction of the incident
light, and Fgrad,
a gradient component arising from the gradient in light intensity and pointing
transversely toward the high intensity region of the beam. For a particle on
axis, Fa=Fb
and there is no net gradient force component. As a result of the forces acting
on the particle, in theory, it can be eventually trapped on axis and moving in
the direction of light propagation.
Gradient force in
the direction of a light beam propagation which has been focused by a lens.
If we want to trap a particle in three
dimensions, we need to take advantage of the gradient force. For this purpose,
we produce the ray convergence towards a common center by using a lens, as shown
in Fig. (b). In these conditions, the focal point becomes the maximum of light
intensity. If the gradient is high enough, the gradient force, thus, will be
strong enough to overcome the radiation pressure exerted by the scattering force,
and the particle will also end up trapped in the direction of propagation.
Force transducer
The optical tweezers system is both
a force transducer and a nanomanipulation device. It is a force transducer because it allows
force measuring, and it is a manipulator because it makes possible both
moving a sample in space and applying a force on it. The AFM (Atomic
Force Microscope)
can perform these operations but its force range is much higher (by thousands,
tipically), and so it is not very sensible for experiments with biomolecules.
Our
optical tweezers setup measures the force from first principles, that is, by
measuring the light momentum change (Smith, S. B., Cui, Y &
Bustamante, C. Methods Enzymol. 361, 134-162, 2003).
The accessible force range is 0.1-200 pN.
An optical-trap
force transducer that operates by direct measurement of light momentum.
As shown, the effect of an external force on a
trapped particle is a change in the light intensity angular distribution, I(θ,φ),
that impinges the particle. This intensity pattern is registered by a
position-sensitive photodetector which is placed at the exit of the optical
trap. The force is inferred by using this signal, as described in next equation:
Experimental setup
To set a device for trapping particles, we need a
laser and a configuration of lenses capable of producing a high focusing or high
numerical aperture, NA, which can be achieved with a microscope objective. To
measure the displacements of the trapped particle and the force exerted on it,
we need to collect the scattered light. For this purpose, a second
objective is used.
The infrared radiation does not damage biological
samples, but can alter its normal operation. Then, it is desirable to decrease
the amount of energy reaching the optical trap. This fact can be
facilitated by using a dual-beam system, in which two counter-propagating lasers
converge to the same foci. This dual trap has two additional advantages: it
provides a very high trapping efficiency in the axial direction (the scattering
force of the opposing laser paths is canceled out), and it avoids the loss of most of
the marginal scattered rays (i.e., it is possible to use low-NA beams inside high-NA
objectives)
Optical
components and light trajectories in the dual optical trap.
The lenses and mirrors steer the IR lasers
towards the objectives' foci, where the trapping is achieved.
Each objective focuses one beam while collecting the other, which ends up on a
photodetector plane. To perform in vitro experiments, a fluidic
chamber is placed in the gap between the objectives. This chamber contains a buffer with
biomolecules. Besides the particle in the optical trap, a second sphere is held
by suction on a micropipette whose aperture is ~0.5 μm
in diameter. Both particles are used as handles to attach a molecule. In
principle, their position is measured with subnanometer resolution.
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