Conditions For Fano Resonance Excitation In2D Arrays Of Metallic Nanoparticles

Interference between a discrete excited state of an atom and a continuum sharing the same energy level gives rise to an asymmetric line-shape, which is termed as Fano resonance. Recently, because of their important applications in nonlinear optics, enhanced optical transmission, and optical switching and modulating, Fano resonances in metallic micro/nano-structures have attracted wide attention. To fulfill the fundamental criterion for a Fano resonance, metallic micro/nano-structures have been designed to support spectrally overlapping sub-radiant and super-radiant modes that could be analogous to a narrow discrete state and a broad spectral line or continuum in atom systems, respectively. It is the purpose of the work presented in this thesis to investigate the optical properties of metallic nanoparticle arrays embedded in homogenous medium or placed on a dielectric planar waveguide, and demonstrate that in addition to the spectral overlapping the two modes with different line-widths should have the same electric field component to excite Fano resonances, which could help a better understanding of the physics of Fano resonances, and may be valuable to the design of metallic micro/nano-devices based on Fano resonances.The work presented is divided into three main sections. The initial section is concerned with the localized surface plasmons (LSPs) supported by individual metallic nanoparticles. To obtain the extinction spectra contributed from the absorption and scattering of individual metallic particles, a commercial finite-element method based software package (COMSOL Multiphysics) is used to solve the scattered fields with normal incident plane waves, in which the peak in the extinction spectrum corresponds to the excitation of LSPs modes. The LSPs resonance wavelengths are found to be dependent on the particle size and the refractive index of surrounding medium.In the second section the guided modes of asymmetric planar dielectric waveguides are explored. The dispersion curves of transverse electric (TE) and transverse magnetic (TM) guided modes are obtained by solving Helmholtz equations. The relation between the resonance wavelength and the guiding layer thickness could be further calculated by applying the cutoff condition to the specified guided mode. With grating coupling, the momentum conversation could be fulfilled, and therefore the incident free-space plane wave could excite the guided modes. The resonance wavelength of the guided modes propagating in the planar dielectric waveguides could effectively tuned by changing the grating periodicity.In the third section the Fano resonances of metallic nanoparticle arrays embedded in homogenous medium or placed on a dielectric planar waveguide are investigated. To fulfill the fundamental criterion for a Fano resonance, the narrow-band diffracted surface wave and guided modes are tuned to spectrally overlap with the wide-band LSPs of metallic nanoparticles by changing the periodicity of particle arrays. It is found that only when they share the same energy and the same electric field component, the two modes with different line-widths could interfere with each other and results in Fano resonances.