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We present a comprehensive optical study of the excitonic Zeeman effects in transition metal dichalcogenide monolayers, which are discussed comparatively for selected materials: MoSe$_2$, WSe$_2$ and WS$_2$. We introduce a simple semi-phenomenological description of the magnetic field evolution of individual electronic states in fundamental sub-bands by considering three additive components: valley, spin and orbital terms. We corroborate the validity of the proposed description by inspecting the Zeeman-like splitting of neutral and charged excitonic resonances in absorption-type spectra. The values of all three terms are estimated based on the experimental data, demonstrating the significance of the valley term for a consistent description of magnetic field evolution of optical resonances, particularly those corresponding to charged states. The established model is further exploited for discussion of magneto-luminescence data. We propose an interpretation of the observed large g-factor values of low energy emission lines, due to so-called bound/localized excitons in tungsten based compounds, based on the brightening mechanisms of dark excitonic states.

Single molecule trajectories of 1,1'-dioctadecyl-3,3,3'3'-tetramethylindocarbo -cyanine perchlorate (DiI) fluorophores diffusing on planar supported 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) lipid bilayers imaged through total internal reflection fluorescence (TIRF) microscopy at different temperatures are investigated. The spatial resolution limit for detecting molecular motion is evaluated by characterizing the apparent motion which arises from the limited signal-to-noise ratio (S/N) of imaged and simulated stationary DiI molecules. Statistical criteria for reliably distinguishing molecular motion from stationary molecules using F-test statistics, including the computation of local signal-to-noise ratios are then established and used for reliably detecting subdiffraction motion of DiI molecules on DMPC. The same single molecule tracking concept is used in investigating the temperature dependence of subdiffraction diffusional confinement of single Rhodamine 6G molecules in polymer brushes of poly (N-isopropylacrylamide), pNIPAAm, above and below its lower critical solution temperature (LCST) of 32 °C. Reliably distinguishing subdiffraction molecular motion from stationary events is crucial in validating the application of single molecule tracking experiment in probing nanometer-sized hydrophobic environments of polymer structure. A versatile and rapid sol-gel technique for the fabrication of high quality one-dimensional photonic bandgap materials was developed. Silica/titania multilayer materials are fabricated by a sol-gel chemistry route combined with dip-coating onto planar or curved substrate. A shock-cooling step immediately following the thin film heat-treatment process is introduced. The versatility of this sol-gel method is demonstrated by the fabrication of various Bragg stack-type materials with fine-tuned optical properties. Measured optical properties show good agreement with theoretical simulations confirming the high quality of these sol-gel fabricated optical materials. Finally, magnetic functionalization studies of sol-gel derived Co-ion doped titania thin films using superconducting quantum interference device (SQUID) magnetometry and an attempt to measure their magneto-optical properties using a home-built Faraday rotation setup are discussed. The experimental limitations in reliably measuring magnetization responses of these thin films are introduced and discussed in detail. The summary and outlook chapters summarize the scientific significance of each research project and briefly introduce ongoing research based on the work and the results presented in this dissertation.