Controlling Directionality and Dimensionality of Radiation by Perturbing Separable Bound States in the Continuum

A bound state in the continuum (BIC) is an unusual localized state that is embedded in a continuum of extended states. Here, we present the general condition for BICs to arise from wave equation separability. Then we show that by exploiting perturbations of certain symmetry such BICs can be turned into resonances that radiate with a tailorable directionality and dimensionality. Using this general framework, we construct new examples of separable BICs and resonances that can exist in optical potentials for ultracold atoms, photonic systems, and systems described by tight binding. Such resonances with easily reconfigurable radiation allow for applications such as the storage and release of waves at a controllable rate and direction, as well systems that switch between different dimensions of confinement.