The effects of periodical focusing of light are studied in chains of spheres with diameters varying from 2 μm to 300 μm and with index of refraction varying from 1.3 to 2.5. Experimentally, we show that the coupled focused beams decrease in size along the chain of polystyrene microspheres with index n = 1.59, reaching wavelength-scale dimensions in the case of small beads with 4 < D/ λ 10, where D is the spheres diameter and is λ the wavelength of light. We show that these effects are determined by the existence of so-called photonic nanojet-induced modes with the period approximately equal to the size of two spheres. By using numerical ray tracing we show that in the limit of geometrical optics such effect of "tapering" of optical beams does not exist for spheres with n = 1.59, however it should be very pronounced in a narrow range of indices around n = 1.75. The results can be used for developing various focusing devices for photonics and biomedical optics applications.