| In recent decades, surface plasmons have attracted tremendous attentions in Nanophotonics. Localized surface plasmon resonances (LSPRs) play the key role in the optical properties of metallic nanoparticles. At the resonance frequency, the electric fields around the nanoparticles can be greatly enhanced, which significantly improves the efficiencies of many linear or nonlinear optical processes. In this thesis, we mainly investigated the LSPRs supported by the periodic arrays of split ring resonators (SRRs) and metallic nanoshells, and discussed the possibility of applying the metallic nanoshells as a bio-sensor. The work presented is divided into four main sections.1. In the initial section, we give a general background of SPs, and review the current achievements and potential applications of localized surface plasmons and Fano resonances.2. In the second section, the magnetic plasmon resonances and enhancement of optical magnetic fields are explored in the periodic array of SRRs. It is found that with decreasing the gap width between two arms, the linewidth of the magnetic plasmon resonances decreases. In particular, at the resonant wavelength of magnetic plasmon λ= 1340 nm, the maximum magnetic field is enhanced to be about 3790 times of the incident field. In addition to the gap width, the effect of the corner roundness, the refractive index of substrate and the periodicity on the enhancement of magnetic fields is also investigated.3. In the third section, the optical properties of individual metallic nanoshells are investigated. The localized surface plasmon modes supported on the metallic shells are analyzed by using Mie theory and numerical simulations based on the finite element method. It is found that both magnetic and electric-based cavity plasmon modes are supported by the metallic shells. In addition to the cavity plasmons with electric fields confined within the spherical cavity, metallic shells also exhibit sphere plasmon modes associated with the outer surfaces of the shell.4. In the fourth section, we report on the observation of Fano resonances in the periodic array of metallic shells. These Fano resonances are demonstrated to originate from the interference between the cavity and sphere plasmon modes of the same angular momentum index, and to be dominated by the characteristics of the cavity plasmons. Therefore, it is expected that these Fano resonances are sensitive to the refractive index of dielectric cores. Furthermore, it is shown that the observed Fano resonances are independent of the incident angles and the polarization configurations. Finally, we also discuss the performance such as sensitivity, quality factor and contrast ratio of bio-sensors based on the observed Fano resonances. |