Optical momentum transfer to macroscopic media

Abstract

Persistent conflicts over the momentum of light in media has led researchers to apply an alternate approach to predicting the electromagnetic force on material. Direct application of the Lorentz force to media allows for the computation of electromagnetic forces while avoiding a priori assumptions for the form of optical momentum. In this view, the forces exist everywhere in matter once the field is present. Because of this, the approach can be computationally daunting, particularly when multiple particles are surrounded by a medium with a dielectric or magnetic response to the fields. The theory presented in this thesis represents a self-consistent formulation for efficiently modeling optical momentum transfer to macroscopic media. The Maxwell stress tensor and the distributed Lorentz force are first applied to calculate forces on lossless media and are shown to be in excellent agreement. It is shown that a normally incident plane wave pushes a slab in the wave propagation direction, while it pulls a half-space toward the incoming wave. The Lorentz force density is applied to the slab in a direct way, while the half-space is dealt with by introducing a finite amount of loss. The losses have to be properly accounted for, otherwise differing results are obtained.

(cont.) The momentum transfer to lossy dielectric and magnetic media is derived from the Lorentz force density without prior assumption of the momentum of light in media. A view of momentum conservation is developed which is rooted in the stress tensor formalism and is based on the separation of momentum contributions to bound and free currents and charges consistent with the Lorentz force density. The formulation is shown to be in agreement with known observations of momentum transfer to media. The electromagnetic wave momentum is derived for a Lorentz medium and applied to study the momentum transfer to stationary, isotropic left-handed material. The model includes material dispersion and losses, which are necessary for a causal medium with negative index of refraction. The results provide a rigorous proof for the force on free currents in a lossy medium. The resulting electromagnetic wave momentum conservation theorem proves that the momentum flux of a monochromatic wave in an isotropic left-handed material is opposite to the power flow direction. However, the momentum density in a lossy medium with negative index of refraction may be parallel or antiparallel to the power flow.

(cont.) The results are applied to predict the reversal of radiation pressure on free currents in a material with negative index of refraction. Furthermore, conservation of momentum at a material boundary states that the tangential component of the wave momentum is conserved. The theory is applied to predict new experiments such a decrease in optical momentum transfer to Mie particles due to absorption, which contrasts the common intuition based on the scattering and absorption by Rayleigh particles. Lossless dielectric particles incident by multiple plane waves and a Gaussian beam are also studied using Mie theory to model existing experiments of optical manipulation using lasers. The modeling of single particles is achieved by applying analytical field calculations to infinite cylinders used to represent particles in two dimensions and to spheres used to more closely model three dimensional experiments. The application of electromagnetic wave momentum conservation via the stress tensor formalism allows us to compute the experimentally observed dynamics of particles in solution while reducing the computation by one dimension. For example, the force on a dielectric sphere can be computed by either applying a volume integration of the Lorentz force or by computing the surface integration of the Maxwell stress tensor.

(cont.) The Mie theory and the FoldyLax multiple-scattering equations are applied to compute the scattered field of an arbitrary number of infinite dielectric cylinders of arbitrary size, subject to in-plane incidences. Binding forces are studied as a function of particle size and separation. The formulation is applied to a system of 20 particles, and extends the capabilities of modeling particle interaction and optical matter beyond the simple cases of the Rayleigh regime and two-particle systems. Based on this approach, a new trapping regime is proposed, which is based on the equilibrium between a scattering force and optical binding forces only. The trap is realized from the interaction between a single plane wave and a series of fixed small particles, and is efficient at trapping multiple free particles. The possibility of serially guiding and sorting nanometer-sized particles without the use of any external control is also demonstrated. The working principle is based on an equilibrium between scattering and binding forces, the latter depending on the properties of the particles. A configuration is proposed that utilizes this property and is shown to efficiently sort small particles as function of their size. In order to understand the complex interactions between dielectric particles, a simplified geometry consisting of identical slabs subjected to normally incident plane waves is also studied.