Surface plasmons are collective oscillations of free electrons excited at a metal-dielectric interface by incident light. They possess a broad set of interesting properties including a high degree of tunability, the generation of strong field enhancements close to the metal's surface and high sensitivity to their adjacent dielectric environment. It is possible to enhance the sensitivity of plasmonic systems by using narrow plasmon resonances. In this thesis two approaches to narrowing surface plasmon resonances have been studied: diffraction coupling of localised surface plasmon resonances in gold nanoarrays and the use of graphene-protected copper thin films. Applications of these approaches in hybrid systems have been considered for modulation, waveguiding, biosensing and field enhancements. Arrays of gold nanostripes fabricated on a gold sublayer have been used to create extremely narrow plasmon resonances using diffraction coupling of localised plasmon resonances with quality factors up to a value of $Q \sim 300$, among the highest reported in the literature. The nanostructures were designed to give the narrowest resonance at the telecommunication wavelength of 1.5 Âµm, allowing for this array geometry to be used in hybrid systems for proof-of-concept optoelectronic devices. The gold nanostripe array was used in a hybrid nanomechanical electro-optical modulator along with hexagonal boron nitride (hBN) and graphene. The modulator was fabricated with an air gap between the nanoarray and the hexagonal boron nitride/graphene. Applying a gate voltage across the device moves the hBN towards the nanoarray, resulting in broadband modulation effects from the ultraviolet through to the mid-infrared dependant on the motion of the hBN instead of graphene gating. The deposition of a 400 nm hafnium(IV) oxide film on top of the gold nanoarray created a structure capable of guiding modes at 1.5 Âµm. The hybrid air-dielectric-stripe waveguide is capable of guiding modes over a distance of 250 Âµm. Copper thin films have stronger plasmon resonances and higher phase sensitivity than gold thin films. Transferring a graphene sheet on the copper prevents oxidation of the copper. A feasibility study of this hybrid system has shown that phase-sensitive graphene-protected copper biosensing can detect HT-2 mycotoxin with over four orders of magnitude greater sensitivity than commercially-available gold-based surface plasmon resonance biosensing systems. In summary, two methods of attaining narrow plasmon resonances have been demonstrated and their promise in modulation, waveguiding and biosensing have been demonstrated.