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

Bulgakov, Evgeny N.; Sadreev, Almas F. PHYSICAL REVIEW A, 96 (1): Doi: 10.1103/PhysRevA.96.013841 JUL 20 2017

We report bound states in the radiation continuum (BICs) in a single infinitely long dielectric rod with periodically stepwise modulated permittivity alternating from ε1 to ε2. For ε2=1 in air the rod is equivalent to a stack of dielectric disks with permittivity ε1. Because of rotational and translational symmetries the BICs 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 BICs have definite polarization and occur in a wide range of the radius of the rod and the dielectric permittivities. More involved BICs with m0,β=0 exist only for a selected radius of the rod at a fixed dielectric constant. The existence of robust Bloch BICs with β0,m=0 is demonstrated. Asymptotic limits to a homogeneous rod and to very thin disks are also considered.