A single beam could hold a particle in water
In their 1986 abstract, Ashkin, Dziedzic, Bjorkholm and Chu report trapping dielectric particles in water with the gradient force of a single beam. The trap held particles stably across a wide range of sizes. The 2018 prize also recognized applying optical tweezers to biological systems.
Light passing through the particle exchanges momentum with it. With suitable dielectric contrast and focusing, the gradient force that pulls the particle back can beat the scattering force that tends to push it out of the trap. A bright focus alone does not guarantee a stable trap in every direction.
Before the objective, the laser beam is widened
A stable trap needs a very steep change in brightness, so the beam is focused as tightly as a microscope objective allows. Neuman and Block’s review of optical trapping names objectives with a numerical aperture of about 1.2 to 1.4, which gather light in a very wide cone. The rays that enter at the edge of that cone supply most of the force that pulls the bead back along the beam, while the central rays mostly push it forward. So the beam from the laser is first widened, usually with a simple two-lens telescope, until its edge, where the brightness falls to 13.5 % of the centre, matches the opening at the back of the objective or slightly overfills it. The light that spills over is absorbed around that opening and can warm the objective, enough to move the trap along the beam by around a micrometre when the laser power changes.
Two lenses whose focal points meet keep a parallel beam parallel and widen it by the ratio of their focal lengths. In the compound-optics Lab, a 25 mm lens followed 125 mm later by a 100 mm lens widens a He-Ne beam from 0.81 mm to 3.24 mm. Move the second lens a few millimetres and the beam leaves slightly converging or spreading. Neuman and Block describe the same effect in a trap’s second, steering telescope: changing the spacing of its two lenses changes how the light spreads as it enters the objective, and so how deep in the sample the trap sits.
Sources: [3]
A trapped bead keeps jiggling, and the jiggling carries the stiffness
Near its center, a stable trap often behaves like a spring. Thermal kicks from the surrounding viscous fluid keep the bead jiggling, and that motion carries information about the spring’s stiffness. To use it, the detector signal must first be converted into displacement.
For harmonic, overdamped motion in an equilibrium Newtonian fluid with frequency-independent drag, the corner frequency links stiffness to drag. The three symbols below are trap stiffness, drag coefficient and corner frequency in cycles per second. A nearby wall or a nonspherical particle requires an appropriate drag coefficient; neither automatically destroys this relation. A viscoelastic medium can require frequency-dependent drag and a different spectral model.
Sources: [2]
Two calibrations can disagree for a physical reason
The equipartition method uses the variance of the bead’s displacement and the temperature. The power-spectrum method uses where the spectrum rolls off, together with a drag model. An added sinusoidal drive can give more information about the detector conversion. The cited original experiment compares these methods side by side; it does not claim they are interchangeable in every situation.
A clean Lorentzian fit can still come with a biased force scale. Drift adds slow variance, a finite exposure time blurs the motion, sampling aliases fast fluctuations into slower ones, and local heating changes the temperature.
Sources: [2]
Displacement gives force only within the calibrated range
Within the calibrated harmonic range, the optical force opposes displacement from the trap center. Farther out, the real force-displacement relation is needed and the bead may escape. For a single harmonic coordinate in equilibrium at a known absolute temperature, the variance formula describes thermal fluctuations about the mean position. A constant external force can shift that mean away from the trap center, so the uncentered mean-square displacement is not generally the variance. The force equation still uses displacement from the optical trap center.
Measuring the force on a molecule brings more factors: how the bead is linked to the molecule, the compliance of the system, the bandwidth and the geometry. A trapped bead, or a photograph of optical tweezers, does not by itself measure any molecular force.
Sources: [2]
A magneto-optical trap works differently
The site’s atom-cooling Lab shows radiation forces on atoms, which involve internal transitions and magnetic fields. It has no bead in a fluid and no Brownian calibration. Use it to compare how light exerts force; measuring force with optical tweezers would need its own apparatus and its own analysis.