Abstract

This project looks to examine nonlinear spectra of interfaces using correlations in transverse electric fields. This experimental technique is used to study the properties of surfaces, and has been conventionally been described in terms of second order susceptibility. The representation in terms of correlations of propagating photons (transverse electric fields) is useful as a link to the physical mechanism of nonlinear optics.

This work represents the first steps of this project. This starts with an overview of the classical method used to obtain electric fields and their frequencies given a model for the dielectric constant. Then, it is noted that in the final simulations, a point dipole approximation will be used, and the induced polarisation is expected to be a Bloch wave, rather than being periodic over the lattice. It is therefore noted that standard Ewald sums for computing the electrostatic energy of this system, and dipole-dipole interaction tensors, required for dynamic optimisation of the dipoles must be modified to account for this. The second strand of this work presents the mathematical theory behind these ``Bloch Sums’’ as well as some potential applications thereof. The final section gives an outline of future work to follow, in particular an overview of the discrete dipole approximation to be used, as well as how to obtain a dielectric constant from a system of polarisable point scatterers.