Periodical focusing mode achieved through a chain of mesoscale dielectric particles with a refractive index near unity

At present three main mechanisms of optical propagation with periodically focused modes in the chains of dielectric spherical particles with a refractive index near n = 1.59 are considered in the literature: evanescent whispering gallery mode coupling, photonic nanojet-induced modes, and the propagation of transverse magnetic modes under conditions close to Brewster angle geometry. In this paper we show that quasi-periodical focusing modes exist in a range of near unity refractive indices for chains of dielectric particles in both spherical and cubic forms. We also show that such a medium can be considered a gradient index waveguide with a parabolic law of refractive index variation.