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ABSTRACT: The terahertz frequency range is a relatively unstudied region of the electromagnetic spectrum. However with the emergence of numerous applications for terahertz light in diverse areas such as security scanning, biological imaging, gas spectroscopy and astrophysics there has been considerable recent growth in the volume of research activity in this area. The studies presented in this thesis aim to introduce the physics of surface plasmons to the terahertz frequency range, and on the way to use some of the unique capabilities of terahertz spectroscopy to try and find new information about fundamental surface-plasmon based electromagnetic structures. Four distinct experiments are described in this work, all of them underpinned by the technique of terahertz time-domain spectroscopy (Chapter 2). This is a very powerful and adaptable spectroscopic method which allows us to measure the electric field of pulsed terahertz radiation as a function of time. This in turn allows us to directly extract both phase and amplitude of the terahertz light as a function of frequency, over a broad frequency range. Furthermore, this method of terahertz spectroscopy can be combined with photoexcitation pulses of visible/NIR light which can be used to make dynamic changes to the properties of materials in the terahertz beam. The first experiment reported (Chapter 3) measures the propagation of coupled surface plasmons in a resonant slit cavity. We use terahertz time-domain spec- troscopy to determine the characteristics of the cavity resonances in a semiconductor slit near the surface plasma frequency of the material, where we are able to mea- sure very large red-shifts in the frequency of the cavity resonance. By considering the phase information which can be extracted directly from time-resolved terahertz measurements we are able to link the behaviour of the resonances to the propagation characteristics of the surface plasmon modes inside the slits. The second experiment (Chapter 4) is a more direct measurement of surface plasmons, propagated over the surface of a semiconductor wafer. We show that the electric field of the surface plasmon is confined to a subwavelength region around the surface, and that the confined field is useful for spectroscopy of very thin layers above the surface. We are able to measure films with thickness less than 1/600th of the wavelength of the terahertz light. After these two experiments with confined semiconductor surface plasmons we move on to a pair of experiments looking at terahertz surface modes mediating the transmission of light through holes in metal films. In the initial experiment (Chapter 5) we use the time-domain data from terahertz spectroscopy to determine the role that surface mode lifetime plays in modifying the amplitude and width of Extraor- dinary Optical Transmission (EOT) resonances, which arise from the periodicity of a hole-array lattice. By changing the temperature of the lossy dielectric semicon- ductor substrate we are able to modify the surface mode lifetime, and link this to the resonant transmission characteristics. In Chapter 6 we extend the hole array EOT experiment by making dynamic changes to the propagation of the surface mode which mediates the transmission. This is achieved by photo-exciting the semiconductor substrate inside the holes and forming a thin layer of material with high charge carrier density on the surface. Interaction of the surface mode with the photoexcited region quenches the resonant transmission. We show that by changing the hole size so that the surface-mode mediated transmission pathway predominates in the spectrum it is possible to use optical pulses to modulate the transmission of terahertz radiation with very high efficiency. In the conclusions (Chapter 7) we link together some of the insights and infer- ences which can be drawn from the above results, as well as evaluating the efficacy of the experimental and simulation methodology.