Tutorials - Optical Tweezers

Physics of optical trapping

The actual physical description of optical trapping depends on the size of the trapped object. As the particles that are usually used in PFM are in the dimension of several tens of nanometers to several micrometers, two different regimes need to be consulted to satisfy the range. For very small particles (d«l), the Rayleigh regime applies to describe the particles' interaction with light. Here, the particles can be treated as point dipoles. For objects with dimensions much larger than the wavelength (d»l), ray optics applies. In this case, diffraction effects can be neglected and the trapping forces of the light can be understood in terms of ray optics.

In an optical trap, two types of optical forces have to be balanced to trap a particle: scattering and gradient forces. In each beam, a particle will be propelled away along the direction of propagation of light due to the forward radiation pressure caused by light scattering.

By focusing a laser beam using a high numerical aperture lens, an intensity gradient is generated that exerts a force against the gradient. When the gradient force exceeds the scattering force, the object of interest will be attracted to the point of highest intensity. In a Gaussian laser beam, the particle is thus trapped in the center of the beam. Axially, it is slightly shifted in the direction of the light propagation due to the forward radiation pressure.

Graphically, it is most convenient to describe trapping in the ray-optics regime, where the trapping can be understood in terms of refraction of light rays between different indices of refraction. If the particle is laterally off-center in a Gaussian beam, rays of differing intensity will refract at both sides of the particle, resulting in differing momentum changes and thus causing a net force on the refracting medium towards the highest intensity. In a focused laser beam, the intensity gradient in the axial direction and the herein associated gradient force tends to counteract the forward scattering force. By tightly focusing the laser beam with a high numerical aperture objective, the gradient force will be strong enough to hold the particle in the focus. The maximum forces that can be exerted on the particle by the trap can be enhanced by increasing the laser power, the extent of the refraction on the particle (refractive index change) and by optimizing the particle size, which should be around the wavelength of the trapping laser in an aqueous medium.

Manipulation

Technically, the manipulation of the probe is performed in a similar fashion to confocal fluorescence microscopes. The laser focus is scanned over the specimen while maintaining illumination across the full back aperture of the objective. Moderately fast solutions for trap steering include a moveable lens in the laser beam or a moveable optical fiber mount.

Ultra fast steering can be achieved using galvanometric mirrors (several kHz) and acousto-optic deflectors (AODs) (up to MHz).

Because of their speed and their capability to jump to different positions without any intermediate step, AODs are particularly applicable for time-sharing experiments.

In this type of setup, multiple traps can be formed by rapidly scanning the laser position across several locations. The drawback of this technique is that this renders the force detection highly challenging, because the trap is only physically present for a fraction of the time. In addition, AODs are expensive and have relatively low light transmission. Another approach to create multiple optical traps is to use spatial light modulators (SLMs). Such holographic optical tweezers offer an almost unlimited number of traps and shapes. Unfortunately, detecting displacements or forces exerted on the trapped particles using SLMs is even more challenging. For by far most applications and experiments, the use of galvanometric mirrors for scanning the laser yields the best price/quality ratio.

The magnitude of optical forces is well suited to trap transparent micron- and submicron-sized particles. Due to their modifiability, polystyrene and silica beads have proved successful in the application field of optical tweezers. Biological macromolecules can be chemically and biochemically linked to microparticles to perform single-molecule experiments on biological systems. Here, beads serve as handles to manipulate or track those biomolecules as they undergo physico-chemical transitions. This leads to applications such as the study of unfolding of macromolecules, interaction and kinetics between single molecules.

Due to their high optical density, trapping of cells and in particular organelles like the nucleus or vesicles is also applicable. Position tracking of such irregularly shaped objects is feasible, but precise position and force calibration are currently only practical with spherical (sub-)micrometer-sized particles.