How can light hold a tiny particle in optical tweezers?

Optical tweezers can hold a microscopic particle without solid jaws touching it. A tightly focused laser beam interacts with a suitable transparent particle in a surrounding fluid. Light carries momentum, so changing the direction of light changes the momentum transferred to the particle.

When the particle refracts and scatters the light, the combined momentum changes produce optical forces. For a suitable particle with a higher refractive index than its surroundings, the intensity gradient can provide a restoring effect toward the bright region. A tightly focused arrangement can make that effect strong enough to oppose forward scattering and form a stable three-dimensional trap.

The equilibrium need not coincide exactly with the beam’s geometric focus. Near that equilibrium, a small sideways displacement can be approximated by F = −κx. Here x is displacement from the trap center and κ is a supplied trap stiffness; the minus sign means that the force points back toward equilibrium.

The local example uses κ = 0.05 piconewton per nanometre and x = +20 nanometres, giving F = −1 piconewton. A nanometre is a billionth of a meter; a piconewton is a trillionth of a newton. Doubling the stipulated stiffness doubles this restoring force at the same displacement.

The particle is confined, not perfectly frozen. Thermal motion continually jostles it, and a finite trap can lose a particle. The linear relation describes only small transverse displacements in an already stable trap; it does not calculate stiffness from laser power or establish that every material can be trapped.