MC 5479
Candidate
Asbjorn (Matt) Hansen | Applied Mathematics, University of Waterloo
Title
Interaction of electromagnetic fields with two-dimensional materials at the interface between dielectric media
Abstract
This thesis investigates the interaction of electromagnetic plane waves with two-dimensional (2D) materials approximated by infinitesimal sheets positioned at interfaces between non-magnetic, isotropic, lossless dielectrics. On their own, 2D materials offer a host of useful properties, including high carrier mobility, dopant-free tuning through the application of external electromagnetic fields or stacking, as well as significant anisotropy. When combined with the excitation of plasmon modes to enhance light-matter interactions, the range of potential applications broadens greatly, including, for example, high-speed optical computation and enhanced light trapping in solar cells.
In this thesis, a new derivation of the boundary condition for out-of-plane response is presented for a 2D material immersed in an infinite homogeneous dielectric. To account for the influence of distinct dielectric surrounding media, Fresnel coefficients are derived using a vacuum gap method. This approach yields novel dispersion relations for surface plasmons that incorporate the out-of-plane response of 2D materials. In the presence of distinct surrounding dielectrics, the out-of-plane mode hybridizes with the in-plane longitudinal plasmon mode. The hybridization is destroyed when the surrounding materials are made identical. Additionally, expressions for the conservation of energy and momentum are derived in terms of the Fresnel field amplitudes for the 2D materials described by singular current sheets. The vacuum gap method is also applied to solve the conservation equations in the presence of dielectric media, as this avoids controversial notions of electromagnetic momentum in media. The electromagnetic stress tensor derived through the vacuum gap method satisfies conservation of linear momentum, thus confirming that the forces on a 2D material can be self-consistently separated from those on surrounding dielectrics.
This theoretical framework is applied to both graphene and phosphorene. For graphene, the reflectance, transmittance, and absorption characteristics are compared with and without considering the out-of-plane response. The analysis confirms that the influence of the out-of-plane component is minimal for plasmon modes at low frequencies as is often assumed, but becomes significant at high frequencies. Forces calculated around frequencies and wavenumbers defined by the plasmon dispersion relation showed significant amplification. However, the new non-monotonic dispersion profile of the hybridized plasmon mode introduces additional resonant and antiresonant behaviour in the forces. To emphasize the in-plane anisotropy of phosphorene, only in-plane response was considered, with a focus on forces in the plasmonic regime at low frequencies. Based on numerical examples, predictions are made for possible future experimental studies of both plasmon modes in the presence of the out-of-plane response and forces on 2D materials for possible optomechanical and sensing applications.