The ability to manipulate small particles with light has opened new avenues

for synthesis and experimentation. Building upon expansive previous work in

the theoretical study of light scattering, the forces which make optical manip-

ulation of matter possible have been extensively studied both analytically and

computationally. In this dissertation we will examine the forces on complex

particle geometries, in the presence of a focused beam of light, using a two

dimensional geometric optics simulation. We begin with a brief overview on

the background of optical trapping as well as the theoretical approaches avail-

able to model optical trapping forces both analytically and numerically. The

results of our numerical geometric optics simulation are shown to be in exact

agreement with a previously published, closed form, analytic solution for the

optical forces on a solid homogeneous sphere in the geometric optics regime.¹

The trapping behavior of two dimensional circles with an inner cavity of varying size is then investigated. Generalized Lorenz-Mie theory is employed to

calculate the force on the particle interacting with an unfocused beam. An

infinite cylinder with an inner cavity size on the order of the wavelength of

incident light and an unfocused beam, incident normal to the cylinder axis,

are used. This result is compared to that found with our geometric optics simulation. We find that, for an inner cavity diameter an order of magnitude

or smaller than the wavelength of the incident light, the geometric optics simulation underestimates this force. The same holds true for very large inner

cavities, where the dielectric wall thickness is less than half the wavelength.

For cavity sizes between these two extremes we find the geometric optics simulation overestimates the force in the direction of beam incidence, by as much

as a factor of two. Finally the effect of breaking axial symmetry on the trapping behavior of a two dimensional planar shape is studied qualitatively using

an analytic approach and quantitatively using the geometric optics simulation.

Beginning with an axially symmetric rectangular shape, a small leg is added

and the trapping behavior as well as the torques examined. We find stable

trapping and balanced torques, with the long axis of the shape both parallel

and perpendicular to the direction of beam incidence, for an axially symmetric

rectangle. Once axial symmetry is broken all trapping is found to occur with

the long axis perpendicular to the direction of beam incidence and the lowest

plane of the shape above the focal point of the beam.

1. Ashkin, A. Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime. Methods Cell Biol 1998, 55, 1-27.