Fibers based on propagating bound states in the continuum

We show that a circular periodic array of silicon dielectric cylinders supports nearly bound states in the continuum (BICs) propagating along the cylinders. These propagating nearly BICs with extremely large-$Q$ factors are surrounded by resonant modes weakly leaking into the radiation continuum. We present leaky zones in the form of dispersion curves for complex eigenfrequencies dependent on propagation constant $k_z$, with the wave vector directed along the cylinders in the vicinity of different types of BICs. Symmetry-protected nearly BICs have the resonant width proportional to squared propagation constant $\Gamma \sim k_z^2$; the widths of non-symmetry-protected nearly BICs behave as $\Gamma \sim {(k_z-k_c)}^2$, where $k_c$ and non-symmetry-protected nearly BICs have the resonant width proportional to $k_z^4$. The latter propagating nearly BICs can serve for the transmission of a electromagnetic signal paving a way to a different type of optical fiber. We also demonstrate weakly leaking resonant modes which carry orbital angular momentum.