### Shaping optical forces for the manipulation of colloidal particles

An optical beam (equivalent to an electromagnetic beam) can be used to exert a force on a dielectric uncharged particle. This effect is known as radiation pressure, and is for example responsible for the deflection of comets' tails. The forces generated are tiny, even with highly collimated and intense beams such as those output by current lasers, so that these forces have significant effects on colloidal particles only. These forces are therefore typically used by colloidal physicists and biologists, who thus benefit of new and very powerful manipulation tools (e.g. the optical tweezer).

### From a simulation point of view, the challenges appear from various sides:

- Computation of the force itself: it has to be computationally efficient and exact (which relates to long debated controversies in the literature, although these remain on a very theoretical ground). We typically use a Maxwell stress tensor formulation which has the appeal of reducing the dimensionality of the problem compared to a direct Lorentz force approach.
- Multi-body systems: colloidal particles are scarcely alone, and the optical scattering of one particle affects the force on other particles, the whole system being self-contained. The optical scattering has therefore to be computed in a self-consistent manner, including all particles interactions. We have performed this using the Foldy-Lax multiple scattering equations for cylindrical particles, which is a valid approximation for spherical particles and in-plane incidences.
- Dynamics of particle: the dynamics of all the particles has to be predicted in order to design some applications (such as particle sorting for drug delivery, micro-fluidics, etc). The Newton equations of motion have therefore to be combined with the Maxwell's equations and the proper experimental conditions (such as the viscosity of the background fluid where the particles evolve) in order to provide meaningful predictions.

The animation below illustrates the dynamics of 20 particles in a three-beam interference pattern shown in the background. The particles start at random positions and gradually assume stable positions due to both the incident field and the self-consistent scattering between them. If submitted to a fluid flow, this system can be used for particle sorting. (need to include movie)

read more : http://web.mit.edu/~ceta/obt/index.html

#### Collaborators

- Swiss Federal Institute of Technology