Nonlinear Response of Monolayer Graphene to THz Frequency Radiation
Graphene, as a zero-bandgap two-dimensional semiconductor with a linear electron band dispersion near the Dirac points, has potential to exhibit very interesting nonlinear optical properties. In particular, third harmonic generation of terahertz (THz) radiation should occur both due to the nonlinear relationship between the crystal momentum and the current density, and due to the interaction between interband and intraband parts of the current densities due to the vanishing bandgap. This thesis examines the nonlinear response of graphene to THz radiation. The THz response of graphene is investigated by developing density matrix equations employing the length gauge. It is possible to produce higher-frequency THz radiation through the generation of harmonics. Several experimental works have examined the harmonic generation in graphene with the radiation normally incident upon the graphene sheet. In this thesis, a configuration is considered where the graphene sheet is located inside a parallel-plate waveguide and the THz radiation is incident parallel to the sheet. This new configuration is found to increase the power efficiency by more than a factor of 100 relative to the normal-incidence configuration. The pump depletion, self-phase, and cross-phase modulation are also included in modelling the response of this system. In addition, an optimized waveguide system is designed with two dielectric layers with different indices of refraction to overcome the phase mismatch between the pump field and third-harmonic field at high input fields. Because typical scattering times in graphene are only a few tens of femtoseconds and the period of THz light is on the order of a picosecond, scattering cannot be ignored in modelling the THz response of graphene. Later in the thesis, the linear and nonlinear THz response of graphene is investigated using the velocity gauge to explore the differences between the results obtained in the length and velocity gauges when phenomenological scattering is included. Finally, the nonlinear THz response of graphene is calculated in the length gauge with microscopic scattering. Different scattering mechanisms including neutral impurity scattering and optical phonon scattering are included in our microscopic model. We find that the nonlinear response is much more sensitive to the strength and type of scattering than is the linear response, indicating that any accurate model of harmonic generation in graphene should include microscopic scattering.