Research On Bound States In The Continuum In Photonic-crystal Waveguides

Optical resonances in waveguides are classified into guided modes,radiation modes and bound states in the continuum(BICs).Resonances arise from the transverse Fabry-Perot condition.Those with radiation are caused by coupling between inner resonances and radiation channels of the background.BICs are singularities in the radiation continuum,of which the energy is localized despite the ability of coupling with radiation channels.Due to its counter-intuitive properties,BIC is the most interesting type of all the resonances.It has found applications in the design of resonators,lasers and filters.In this thesis a semi-analytical model is developed to describe the eigenstates and bandstructure of photonic crystal waveguides.The method is based on the mode expansion theory.It provides both analytical insights and a numerical approach to the formation mechanisms of optical resonances.BICs in photonic crystal slabs are demonstrated with this method.The divergence of the resonance lifetimes at the BICs is explained by the destructive interference of radiation from different propagating components inside the slab.This thesis shows BICs at the center and on the edge of the Brillouin zone protected by symmetry,BICs at generic wave vectors not protected by symmetry(Friedrech-Wintgen BICs),and the annihilation of BICs at low-symmetry wave vectors.The relation between structural symmetry and formation of BIC is also discussed.BICs and lasing modes in a parity-time(PT)symmetric system are revealed.BICs as well as guided modes are revealed in fiber gratings.This thesis paves a way to improve the performance of lasers,sensors and optical filters.