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 ${\epsilon }_1$ to ${\epsilon }_2$. For ${\epsilon }_2=1$ in air the rod is equivalent to a stack of dielectric discs with permittivity ${\epsilon }_1$. Because of rotational and translational symmetries the BSCs are classified by orbital angular momentum $m$ and the Bloch wave vector $\beta$ directed along the rod. For $m=0$ and $\beta =0$ 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 $m\ne 0,\beta =0$ exist only for a selected radius of the rod at a fixed dielectric constant. The existence of robust Bloch BSCs with $\beta \ne 0,m=0$ is demonstrated. Asymptotic limits to a homogeneous rod and to very thin discs are also considered.

arXiv comment15 pages, 15 figures

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