An optical trap, also known as an optical tweezer, is a scientific instrument that uses a highly focused laser beam to trap and manipulate microscopic particles, such as cells or individual molecules, in three dimensions and has many applications in various fields of science, including biology, physics, and chemistry. The optical trap works by transferring themomentum of photons to the trapped particles, creating a force that can hold the particle in place. Ashkin developed a model to predict the forces in an optical trap in theMie regime, i.e. for particles larger than the wavelength of the laser. His model is based on geometrical ray optics,whereby the rays fromthe microscope objective trace straight lines to a single focal point. These rays are refracted by the trapped particle and resultant change in direction of the ray imparts a force due to the conservation of momentum. The model takes no account of the effects of wave optics, which are highly pronounced in the focal region of a lens. The model cannot, therefore, account for the transfer orbital angular momentum from a Laguerre-Gaussian laser in a so-called optical spanner, or the effects of wavefront aberration caused by an imperfect microscope objective. In this thesis, we seek to bridge the gap between wave optics and Ashkin’smodel using the concept of the Eikonal function, which traces the flux lines through the focus. We call these flux lines non-linear rays, and these are used to replace the rays in Ashkin’s model. This augmented model can account for the spin of a particle in an optical spanner and for the deleterious effect of aberration. In the journey towards this final result several significant contributions are made. These include the extension of Ashkin’s model to account for absorption within the particle; we see a natural consequence for this is the emergence of a rotational force. Another important contribution are a set of algorithms to sample the three-dimensional diffraction in the focal region of a lens and to trace the flux lines with high accuracy.