Terahertz Response of Excitons in Nanorod Heterostructures

Quantum-confined systems are one of the most promising ways to enable us to control a material's interactions with light. Nanorods in particular offer the right dimensions for exploring and manipulating the terahertz region of the spectrum. In this thesis, we model excitons confined inside a nanorod using the envelope function approximation. A region-matching transfer matrix method allows us to simulate excitonic states inside arbitrary heterostructures grown along the length of the rod. We apply the method to colloidal CdSe rods 70 nm in length and under 10 nm in diameter, capped with ligands of DDPA and pyridine. We extend past studies on these types of rods by taking into account their dielectric permittivity mismatch. Compared to previous calculations and experimentally measured terahertz absorption, we predict a higher energy main 1S$z$ to 2P$z$ transition peak. This indicates that the rods are likely larger in diameter than previously thought. We also investigate a nanorod with GaAs/Al$_{0.3}$Ga$_{0.7}$As coupled double dots. The excitonic transitions were found to be manipulable by varying the strength of an applied electric field. We employ quasi-static state population distributions to simulate the effects of exciton relaxation from optically active states to dim ground states. A critical value of the applied field, corresponding to the exciton binding energy of ~18 meV, was found to dramatically alter the terahertz absorption due to state mixing. Above this critical field, more nuanced shifts in transition energies were observed, and gain from radiative relaxation to the ground state is predicted.

Tight-Binding Approximations in 1D and 2D Coupled-Cavity Photonic Crystal Structures

Light confinement and controlling an optical field has numerous applications in the field of telecommunications for optical signals processing. When the wavelength of the electromagnetic field is on the order of the period of a photonic microstructure, the field undergoes reflection, refraction, and coherent scattering. This produces photonic bandgaps, forbidden frequency regions or spectral stop bands where light cannot exist. Dielectric perturbations that break the perfect periodicity of these structures produce what is analogous to an impurity state in the bandgap of a semiconductor. The defect modes that exist at discrete frequencies within the photonic bandgap are spatially localized about the cavity-defects in the photonic crystal. In this thesis the properties of two tight-binding approximations (TBAs) are investigated in one-dimensional and two-dimensional coupled-cavity photonic crystal structures We require an efficient and simple approach that ensures the continuity of the electromagnetic field across dielectric interfaces in complex structures. In this thesis we develop \textrm{E} -- and \textrm{D} --TBAs to calculate the modes in finite 1D and 2D two-defect coupled-cavity photonic crystal structures. In the \textrm{E} -- and \textrm{D} --TBAs we expand the coupled-cavity \overrightarrow{E} --modes in terms of the individual \overrightarrow{E} -- and \overrightarrow{D} --modes, respectively. We investigate the dependence of the defect modes, their frequencies and quality factors on the relative placement of the defects in the photonic crystal structures. We then elucidate the differences between the two TBA formulations, and describe the conditions under which these formulations may be more robust when encountering a dielectric perturbation. Our 1D analysis showed that the 1D modes were sensitive to the structure geometry. The antisymmetric \textrm{D} mode amplitudes show that the \textrm{D} --TBA did not capture the correct (tangential \overrightarrow{E} --field) boundary conditions. However, the \textrm{D} --TBA did not yield significantly poorer results compared to the \textrm{E} --TBA. Our 2D analysis reveals that the \textrm{E} -- and \textrm{D} --TBAs produced nearly identical mode profiles for every structure. Plots of the relative difference between the \textrm{E} and \textrm{D} mode amplitudes show that the \textrm{D} --TBA did capture the correct (normal \overrightarrow{E} --field) boundary conditions. We found that the 2D TBA CC mode calculations were 125-150 times faster than an FDTD calculation for the same two-defect PCS. Notwithstanding this efficiency, the appropriateness of either TBA was found to depend on the geometry of the structure and the mode(s), i.e. whether or not the mode has a large normal or tangential component.