Bound States in the Continuum on Periodic Structures: Theory, Computation and Applications

A bound state in the continuum (BIC) is a localized or trapped mode with a frequency inthe frequency interval where outgoing radiation modes exist. Mathematically, a BICcorresponds to a discrete eigenvalue in the continuous spectrum. For periodic structuressurrounded by homogeneous media, the BICs are guided modes above the lightline, andthey can be either standing waves or propagating Bloch modes. Recently, BICs forelectromagnetic and light waves have attracted much attention since they have veryinteresting properties, can be used to enhance nonlinear and quantum optical effects,and have potentially significant applications in lasing, sensing, optical switching, lightstorage, etc. However, there are limitations in the current theoretical understanding ofthe BICs, and their applications have not been fully explored. In this project, we studyBICs on periodic structures from three different aspects: theory, numerical computation,and applications. We intend to develop a perturbation theory to understand therobustness of BICs with respect to their underlying symmetries. We also plan to developan accurate and reliable numerical method for computing the BICs. Applications of theBICs will be explored based on the discontinuities of transmission and reflectioncoefficients and the total transmission/reflection phenomena, the arbitrarily strong fieldenhancement by resonances near BICs, and the nonuniqueness of related diffractionproblems.