The optical tweezers truly became a revolutionary biological tool when it was enhanced with several biological and optical innovations. Techniques were developed which allowed the force exerted by the trap on a bead as well as the displacement of the bead from the center of the trap to be measured with high accuracy. At the same time, biologists had developed methods of coating latex spheres with antibodies that bind to a specific epitope. Such activated beads could be used as a purification tool to pull a specific protein out of solution. It was soon realized that if such a bead were captured in an optical trap, force could be applied to an individual protein molecule. In one of the pivotal experiments such a bead was attached to a kinesin molecule that was 'walking' on a microtubule. This allowed researchers to determine that kinesin moves in discrete 8 nm steps on a microtubule and to and measure its force-velocity curve. Subsequent developments have dramatically increased the accuracy and flexibility of optical tweezers.
If a particle is much smaller than the wavelength of light the electric field experienced by the particle is approximately uniform in space but oscillating in time. The finite dielectric constant of the particle causes it to develop a uniform volume polarization in response to the external electric field which partially cancels the electric field in its interior (see J.D. Jackson, Classical Electrodynamics, Second edition, p. 149). This reduction of the electric field lowers the total electromatnetic energy of the system, which is given by the integral of the electric and magnetic fields over all space. It is therefore energetically favorable for the particle to go the the position of maximum field where the energy reduction is greatest.
The center of the trapping beam therefore becomes a potential well into which the particle is drawn. If the particle is at the peripheral part of the trap beam, as illustrated in the figure above at left, it will be drawn towards the center, where it causes a greater depletion of the electric field. This is closely related to the elementary problem is electro-statics, where a dielectric slab is drawn into the gap of a parallel plate capacitor held at constant charge. As in the case of the optical trap, a uniform volume polarization of the dielectric generates a surface charge that partially cancels the external field.
The work required to pull the slab out of the capacitor corresponds to the increase in increase in energy stored in the capacitor, whose capacitance is increased by the removal of the dielectric.
Another way of understanding the optical trap is to treat the trapped particle
as a lens which deflects the trapping beam as it passes through. In the
limit that the bead is large compared with the wavelength (the opposite
of the limit considered above) we can estimate the effect of the particle
on the trapping beam by determining how the bundle of light rays
representing the beam is affected by the particle. If the particle
system is totally symmetric, with the particle at the center of
the trap each ray will pass through the particle in a symmetrical
manner and there will be no pertubation to the beam. This results
in an output beam which is identical
to the input beam, as illustrated below.
The same is true if the particle moves up or down from the center of
the trap, as illustrated below.
This second way of describing the action of an optical trap is
particularly useful in understanding how force and position
detection are done in an optical trap. If we can detect this
change in momentum in the trap beam we could measure the instantaneous
force on the particle, as well as its displacement from the
center of the trap. This is done as illustrated below.
Remarkably, this technique allows forces to be measured with picoNewton accuraccy and displacements to be measured with Angstrom accuracy. The classic paper describing Optical Tweezers technology is Svoboda and Block .
The basic physical idea behind the OTW is the same as for the optical trap,
a particle will go to the position where the energy is lowest. To trap
the particle in a specific orientation as well as in a specific position
we make use of a particle which has an anisotropic polarizability. For
instance, we can use quartz, whose z axis is easier to polarize
than its x or y axes. The polarizability as a function
of direction takes the form of an elipsoid, as illustrated below.
However, for the optical torque wrench be truely analogous to the optical tweezers we need a way of measuring the torque being applied to the particle by the optical trap. This can be done in a manner entirely analogous force detection. The conservation of angular momentum requires that the torque exerted on the particle by the trapping beam is equal and opposite to the torque exerted on the trapping beam by the particle. If we can measure the change in angular momentum of the trapping beam as it leaves the sample chamber we will know the instantaneous torque exerted on the particle, as illustrated below.
Since in this case the torque is generated by an interaction between the polarization of the laser and the anisotropic polarizability of the particle, the change in angular momentum manifests itself as a change in the polarization state of the trapping beam. The linear polarization of the input trapping beam consists of equal parts right circular and left circular polarized light, and the polarization of the output beam is eliptical, for which the left and right circular components are out of balance. A polarization analyzer on the output trap beam detects this imbalance of right and left circular polarization components, which is a direct measure of the torque.
Since we can measure the instantaneous torque, it is a relatively simple
matter to use this information to actively stabilize the torque exerted
on the particle. The measured value of the torque is used to correct
to polarization angle to clamp the torque at a constant value. The plot
below shows the torque on a trapped particle, initially fluctuating due to
Brownian rotation motion.