Fibers based on propagating bound states in the continuum

We show that a circular periodic array of $N$ dielectric cylinders supports nearly bound states in the continuum (BICs) propagating along the cylinders. These propagating nearly BICs with extremely large $Q$ factors of order $exp(\lambda N)$ are surrounded by resonant modes weakly leaking into the radiation continuum. We present leaky zones in the vicinity of different types of BICs: symmetry protected nearly BICs with the resonant width proportional to the squared propagation constant $\Gamma \sim k_z^2$, non-symmetry protected nearly BICs with finite propagation constant $k_c$ with $\Gamma\sim (k_z-k_c)^2$ and non-symmetry protected nearly BICs with $\Gamma\sim k_z^4$. The latter propagating nearly BICs can serve for transmission of electromagnetic signal paving a way to novel type of optical fibers. We also demonstrate weakly leaking resonant modes which carry orbital angular momentum.