Nonlinear Light-matter Interaction : From 2D to Nonperturbative Materials

Abstract

In this thesis, we start by defining the theoretical framework for studying the light-matter interaction and describe ways to calculate the optical properties of the materials. We present two different approaches to constructing such theory, one semiclassical, where matter is represented as a quantum system and the external field included in Schrödinger equation with the use of minimal coupling. The other approach is based on path integral formulation of quantum mechanics, where we construct a Lagrangian for our system and use the principle of minimal action to evaluate the evolution of the interaction of the electromagnetic field with the system.

The semiclassical theory is used to study the nonlinear optical response of several systems. First, we focus our attention on Dirac materials and their nonlinear interaction with light. In particular, we investigate high-harmonic generation in the case of graphene with impinging structured light using an effective semiclassical model and analyze the orbital angular momentum (OAM) charge of the generated harmonics. We discovered that the nonlinear components of the response carry the OAM charge which is a multiple of the fundamental response. Next, we use another type of 2D material, Weyl materials, and see how the difference between graphene and Weyl materials is observed through their nonlinear optical response and show through calculations that the observed nonlinear optical response is polarization dependent. Contextually, we study the nonlinear response of Weyl material in the presence of a magnetic field, where Landau levels emerge as a consequence of the magnetic field, and point out how the construction of Weyl material with particular band structure configuration allows to tune nonlinear optical response.

Lastly, we investigate Kerr-like effects in the epsilon-near-zero (ENZ) materials and construct a model, based on path integrals, to derive a fully nonperturbative expression of the permittivity of such media, thus going beyond the standard nonlinear optics models for ENZ media.