## Optical trapping in evanescent standing wave

### Principle and theoretical results

TwoGaussian beams are focused to a spot of diameter tens of micrometers and directed to the top surfaces of a prism from opposite directions so that total internal reflection is achieved. Above the prism surface evanescent waves are generated and they propagate along the surface in opposite direction. The evanescent wave decays exponentially from the surface and so the trapping is obtained only very close to the surface. Since both Gaussian beams are coherent the evanescent waves interfere and interference fringes are generated above the surface.

There exists steep axial intensity gradient between the fringe maximum and minimum causing strong gradient optical force - similarly as in the Gaussian standing wave. Therefore similar properties can be expected with respect to the particle size (size effect). Based on Almaas' theoretical work we developed a method how to calculate any interference field created from several interfering evanescent waves intersecting under various angles. The only restriction is that the incident waves are plane waves. This considerably simplifies the problem, speeds up the calculations but keeps the interference to be the dominant studied effect. The following movie shows how the size of the object determines the object behaviour in the standing wave and especially where the object is localized.

MOVIE showing the size effect in evanescent standing waveExplanation: d - diameter of the polystyrene bead.

The following figure shows how the depth of the axial potential well depends on the sphere diameter d and on the incidence angle. Similarly as in the standing Gaussian wave there exist certain sphere diameters that are not influenced by the standing wave and move freely over the interference fringes (for example white numbers in the figure below).

More can be found in the following papers:

M. Siler, T. Cizmar, M. Sery, P. Zemanek:

**"Optical forces generated by evanescent standing waves and their usage for sub-micron particle delivery"**,

Appl. Phys. B 84, 157-165, 2006, ABSTRACT DOWNLOAD

M. Siler, M. Sery, T. Cizmar, and P. Zemanek:

**"Submicron particle localization using evanescent field"**,

Proceedings of SPIE 5930, 0R1-0R9, 2005, ABSTRACT DOWNLOAD

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