Photonic nanojet-induced modes (NIMs) have emerged as a new paradigm for understanding the optical properties of chains of dielectric microspheres with wavelength-scale diameters (D≤10λ). Here we show that light focusing and transport properties of chains of submillimeter spheres (D>100λ) are dominated by periodically focused modes (PFMs) which can be considered a geometrical optics analog of NIMs. We review recent geometrical optics results on this subject showing that Brewster angle conditions for TM polarized rays can be periodically reproduced in chains of spheres with index n= √3 =1.73205... giving rise to lossless PFMs with the 2D period. In this work we studied the phase properties of PFMs using a novel method based on Fourier analysis of the high resolution transmission spectra of chains of submillimeter ruby spheres with n∼1.75 at λ=1.2 μm. We demonstrated that PFMs are the best surviving modes in long chains of spheres. Finally, we considered applications of PFMs for focusing multimodal beams in ultra-precise laser surgery.