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Computational Models of Optical Traps Casey Cannon, Tom Donnelly, and Roland Smith

Motivation Our research group is interested in studying stochastic heating, a heating process with applications to laser-driven nuclear fusion. We expect this heating mechanism to produce hot electrons when a high-intensity laser pulse interacts with the electrons in a spherical target. The interaction between the spherical target and the laser pulse must happen in vacuum and the sphere cannot be in contact with any support structure. One strategy is to use an optical trap to hold the target sphere in place.

Harvey Mudd College Physics Department

Air" Vacuum"

Trapping"Beam"

Trapping"Beam"

High"Intensity"Pulse"

Goals •  Model the trapping of reflective spheres. Traditionally, optical

traps have been used with transparent spheres. We are interested in trapping metal/reflective spheres because they have a large electron density. We want to be able to explore this regime.

•  Measure the radius of trapped spheres. We expect the heating mechanism to be significantly different for different size spheres, so it is important to accurately know the size of the spheres.

•  Have the sphere trapped at least ~10 cm away from the expensive optic used to focus the laser, so that no optics are damaged by the high-intensity pulse.

Figure'1:'An aerosol of spheres is sprayed in the vicinity of a continuous-wave trapping laser. At least one of these spheres is caught. The chamber is brought to vacuum and a high-intensity pulse is fired at the trapped sphere.

Casey"Cannon ccannon@hmc.edu (805) 302-7179

Optical Trapping Mechanism In Figure 2 we have a continuous-wave laser oriented vertically in air, and a spherical target is a certain distance away from the z-axis, the beam’s central axis. In Figure 2a, the spherical target is transparent, and in Figure 2b, it is reflective. The transparent sphere lenses photons inwards while the reflective sphere deflects them outwards. The change in the photons’ momentum pushes the sphere up, counteracting gravity. Depending on if there are more photons incident on the inner half of the sphere versus the outer half, the sphere will be pushed either towards or away from the beam axis. The curve at the bottom of the figures indicates the laser intensity distribution that will impart a restoring force on the sphere to trap it.

Figure"2"(a) " " " " ""(b)"A transparent (a) and reflective (b) sphere are being trapped by lasers with intensity profiles given by the curves at the bottom of the figures.

Results/Future Work I have successfully created a computational model for trapping reflective spheres. I have performed various tests to make sure my model is working properly. I have found reasonable parameters for trapping spheres using a donut mode beam and the Bessel beam. I have also studied responses of trapped spheres to temporal changes in power. Since the responses depend on sphere size, this can be used to measure sphere radius. Future work includes characterizing the stability of the traps and modeling of thin spherical shells.

Acknowledgements Ashkin, Arthur. “Acceleration and trapping of particles by radiation pressure.” Physical review letters 24.4 (1970): 156 "Green laser pointer TEM00 profile" by Zaereth - Own work. Licensed under CC0 via Wikimedia Commons - https://commons.wikimedia.org/wiki/File: Green_laser_ pointer_TEM00_profile.JPG#/media/File:Green_laser_pointer_TEM00_profile.JPG McGloin, D., and K. Dholakia. “Bessel beams: diffraction in a new light.” Contemporary Physics 46.1 (2005): 15-28

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Figure"3"(a) " " """"(b)" " " "(c)"The intensity profiles of different laser modes have advantages and disadvantages for trapping spheres. A Gaussian beam (a) can trap transparent spheres as in Figure 2a while a donut (b) or Bessel (c) beam can trap reflective spheres as in Figure 2b. The donut beam spreads out as it propagates but can propagate indefinitely in a vacuum. The Bessel beam does not spread out, but its intensity eventually dies off.