Super-bound States in the Continuum: Theory and Computation

In the last a few years, the so-called super-bound states in the continuum (super-BICs)have attracted significant research interest in the photonics community. A BIC is aspecial eigenmode of a wave system with the eigenvalue in the continuous spectrum.Around the wavevector of a BIC, there are resonant modes with a complex frequencyand satisfying outgoing radiation conditions. Near a super-BIC, the resonant modes havean ultrahigh quality factor which causes extraordinary resonant effects and hasimportant applications in lasing, sensing, nonlinear optics, etc. Existing examples ofsuper-BICs are mostly found by tuning parameters of the structure. We propose todevelop a comprehensive theory for super-BICs governed by the Maxwell's equations.The proposed theory will include a mathematical characterization that clarifies theconcept of super-BICs and is useful for finding super-BICs numerically. The theory willalso reveal how a super-BIC may be preserved under structural perturbations and mayturn to regular BICs through different types of bifurcations. Our study on super-BICswill enhance understanding on resonant wave phenomena and help realizing theirapplications in photonics and other wave systems.