In this thesis, I study the localized surface plasmon resonance phenomenon in dielectrically coated, closely-spaced gold nanoparticles. I examine the effect of a dielectric coating (that models the sensing of a biomolecular analyte layer) on the optical absorption of these particles. The extinction spectra and the electric field around the particles are calculated. The particles are chosen to be either spheres or hemispheres to be representative of solution phase (3D) or surface (2D) experiments. Calculations are based on the Discrete Dipole Approximation method. In particular, I study the effect of a dielectric coating on the localized surface plasmon spectra around clusters of coated gold nanohemispheres. Based on this study, I propose a new sensing mechanism for detecting biomolecules attached onto a linear array of closely-spaced gold nanohemispheres immobilized on a waveguide surface
