| Summary: | We demonstrate bound states in the radiation continuum (BSC) in a linear periodic array of dielectric spheres in air above the light cone. We classify the BSCs by orbital angular momentum m = 0,±1,±2 according to the rotational symmetry of the array, Bloch wave vector ꞵ directed along the array according to the translational symmetry, and polarization. The most simple symmetry protectedBSCshavem = 0,ꞵ = 0 and occur in a wide range of the radius of the spheres and dielectric constant. More sophisticated BSCs with m 6= 0,ꞵ = 0 exist only for a selected radius of spheres at fixed dielectric constant. We also find robust Bloch BSCs with ꞵ 6= 0,m = 0. All BSCs reside within the first but below the other diffraction continua. We show that the BSCs can be easily detected by bright features in scattering of different plane waves by the array as dependent on type of the BSC. The symmetry protected TE/TMBSCs can be traced by collapsing Fano resonance in cross-sections of normally incident TE/TM plane waves. When plane wave with circular polarization with frequency tuned to the bound states with OAM illuminates the array the spin angular momentum of the incident wave transfers into the orbital angular momentum of the BSC.This ,inturn, gives rise to giant vortical power currents rotating around the array. Incident wave with linear polarization with frequency tuned to the Bloch bound state in the continuum induces giant laminar power currents. At last, the plane wave with linear polarization incident under tilt relative to the axis of array excites Poynting currents spiralling around the array. It is demonstrated numerically that quasi-bound leaky modes of the array can propagate both stationary waves and light pulses to a distance of 60 wavelengths at the frequencies close to the bound states in the radiation continuum. A semi-analytical estimate for decay rates of the guided waves is found to match the numerical data to a good accuracy.
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