Bound states in the continuum with high orbital angular momentum in a dielectric rod with periodically modulated permittivity

Abstract

We report bound states in the radiation continuum (BSCs) in a single infinitely long dielectric rod with periodically stepwise modulated permittivity alternating from $ε_1$ to $ε_2$. For $ε_2=1$ in air the rod is equivalent to a stack of dielectric discs with permittivity $ε_1$. Because of rotational and translational symmetries the BSCs are classified by orbital angular momentum $m$ and the Bloch wave vector $β$ directed along the rod. For $m=0$ and $β=0$ the symmetry protected BSCs have definite polarization and occur in a wide range of the radius of the rod and the dielectric permittivities. More involved BSCs with $m\neq 0, β=0$ exist only for a selected radius of the rod at a fixed dielectric constant. The existence of robust Bloch BSCs with $β\neq 0, m=0$ is demonstrated. Asymptotic limits to a homogeneous rod and to very thin discs are also considered.