Optical resonators: Photonic nanojet and whispering gallery mode

When a dielectric micro-sphere or micro-cylinder is illuminated by an incident plane wave, a strongly focused beam at the shadow side is formed and such phenomenon is known as photonic nanojet. In this thesis, the spectral element method (SEM) is adopted to investigate the behaviour of photonic jets resulting from different structures and excitations. The general formulation of SEM is presented for the sake of numerical modelling of two-dimensional, frequency-domain electromagnetic scattering problems. For the purpose of accuracy demonstration, one- and two-dimensional examples were chosen to show that SEM dominates the finite difference method and finite element method in terms of accuracy. Then, in addition to the successful modelling of photonic jets by SEM, several resonance modes that result in planewave-excited dielectric cylinders are also captured by SEM. Three different scenarios are also considered in the current study in order to verify the strong field confinement; one is under Bessel beam illumination, the second is the introduction of non-homogeneity in the material forming the cylinder, and the third is that the cylinders are excited by a point source. Moreover, nanojets and resonance resulting from hemicylindrical and corrugated cylinders under normally incident plane-wave illumination are studied. Finally, homogenous and isotropic magneto-dielectric micro-cylinders embedded in air background when illuminated by a unit-intensity plane wave are also investigated.