Optical

Design and contruction of a motorized compact laser tweezers
M.C. Gonzaleza,1, Y. Pérez Moretb, M. Arrontea, L. Poncea, E. Rodrigueza, E. de Posadaa
a

Centro de Investigación en Ciencia Aplicada y Tecnología Avanzada del Instituto Politécnico Nacional, Unidad Altamira, México b Instituto de Ciencia y Tecnología de Materiales, Universidad de La Habana, Cuba 1 mcgs@prodigy.net.mx

AbstractThe design and construction of an installation of optical tweezers is presented.The system is low cost and includes a motion control card designed on the basis of a programmable microcontroller comanded through a personal computer using the serial protocol RS-232. The optical setup is simple; a continuous wave Nd: YAG laser opereating at 532 nm, a telescope, and webcam to obtain digital images andvideo from the microscope. Using Labview virtual instruments acquisition, image processing and motion control can be achived. Laser beam quality, intensity and shape are also characterized. The feasibility of constructing a compact installation of optical tweezers, simplified, portable and low cost is demonstrated.

of the space, being used a Nd: YAG laser that emits in the wavelength of 532 nmwith a power of 40 mW; commercial optical components and a motion control card is presented. The installation is characterized by its simplicity, low cost and facility of implementation. On the other hand, the design of virtual instruments in LabVIEW increases the system potentialities, since digital images can be obtained at the same time is controlling the sample of automated form

2. Basisof optical trapping
The physical principle of optical trapping can be explained by the momentum transference associate with the redirection of light at a dielectric interface which is proportional to the intensity of light in the direction of propagation, the reflection and the refraction of light in the interface it is translated in a change of the moment of the light, this is the essence of thesecond Newton´s law. The force on the sphere due to the redirection of an incoming ray, rm , can be calculated by subtracting the total momentum of the exiting rays, {rm1 ,rm2 ,...}, from the momentum of rm , as shown in Fig. 1. The total force due to a light beam can be calculated by representing the light beam as a collection of rays, and summing the force (s) due to each of the rays. Stabletrapping requires that there be some position r rtrap where the net force on the sphere is zero and any small displacement results in a restoring force toward r rtrap .

1. Introduction
After the laser creation, Arthur Ashkin working in the Bell laboratories demonstrated in 1970 that the radiation pressure of focused beams can be used to affect the micrometric particles path. Not only it wasdemonstrated that the particle dynamics could be modified by means of the dispersion force, was observed that a unknown force existed that caused that the particles moved towards the zone of greater intensity of the beam. This force was denominated gradient force, since it comes from the intensity gradient of the light. With the passage of the years, the technique of trapping and manipulation grew upfor an ample range of type and size of particles, including as diverse materials as: dielectric spheres, viruses, bacteria, living Cells, organelles, colloidal gold, and even DNA. In this work an optical tweezers installation which is able to trap micrometric particles in the three directions

force and a stable trap will exist. Otherwise, the reflection force will dominate and the sphere willsimply be accelerated along the z axis. Notice that the net force associated with the refraction of the two rays increases with u, whereas the net force associated with reflection of the two rays decreases with increasing θ. Thus the restoring force will be stronger for incoming rays at larger θ, and there is a minimum θ that is required for stable trapping. A similar analysis will show that a...