Absorption and Spatial Dispersion in Electromagnetic Susceptibility Models

Abstract

This thesis focuses on two key aspects of light-matter interactions: absorption and spatial dispersion, both of which are described on a macroscopic scale by the electromag- netic susceptibility.

The first part of this thesis contains an investigation into the microscopic origin of absorption in dielectric models, providing a detailed calculation for a long-held assump- tion of the Hopfield model that has formed the basis of many key works on the subject. While previous work has either focused on the quantum regime or used phenomenological methods which lack a clear relationship to the underlying physics, the microscopic model and calculations presented here are purely classical in nature, matching Hopfields initial proposal. A discrete model of a dielectric is developed, containing nonlinear interaction terms between polarizable dipoles and lattice vibrations. The lattice vibrations are found to act as a pseudo-reservoir, leading to broadband absorption of electromagnetic radia- tion that naturally emerges from the model, without the need to add damping terms to the dynamics. The effective linear susceptibility is calculated using a perturbative iteration method and is found to match the form of a model that is widely used for real dielectrics.

The second half of the thesis presents a series of modifications to the Halevi-Fuchs susceptibility model, which is used to calculate the electromagnetic reflection and trans- mission coefficients of a spatially-dispersive half-infinite medium. The initial model, valid only for an idealized single-resonance scalar susceptibility with a specific wave vector dependence, is extended to include many more of the susceptibility features found in real materials, including unequal transverse and longitudinal components, multiple res- onances, anisotropy and alternate wave vector dependences. In each case, the effect of the boundary is characterized by a set of phenomenological reflection coefficients for the polarization waves in the medium, with specific values corresponding to various addi- tional boundary conditions for Maxwell’s equations. The exact expressions derived for the electromagnetic reflection and transmission coefficients can be used in the calculation of a range of physical phenomena near the boundary of the medium. This thesis consid- ers the spectral energy density of thermal and zero-point radiation outside the medium, with the key result that the inclusion of spatial dispersion naturally removes an unphysical divergence associated with the use of a spatially local susceptibility model.