  The major assumption of the Lorentz-Lorenz theory about uniformity of local
fields and atomic polarization in dense material does not hold in finite groups
of atoms, as we reported earlier [A. E. Kaplan and S. N. Volkov, Phys. Rev.
Lett., v. 101, 133902 (2008)]. The uniformity is broken at sub-wavelength
scale, where the system may exhibit strong stratification of local field and
dipole polarization, with the strata period being much shorter than the
incident wavelength. In this paper, we further develop and advance that theory
for the most fundamental case of one-dimensional arrays, and study nanoscale
excitation of so called "locsitons" and their standing waves (strata) that
result in size-related resonances and related large field enhancement in finite
arrays of atoms. The locsitons may have a whole spectrum of spatial
frequencies, ranging from long waves, to an extent reminiscent of ferromagnetic
domains, -- to super-short waves, with neighboring atoms alternating their
polarizations, which are reminiscent of antiferromagnetic spin patterns. Of
great interest is the new kind of "hybrid" modes of excitation, greatly
departing from any magnetic analogies. We also study differences between
Ising-like near-neighbor approximation and the case where each atom interacts
with all other atoms in the array. We find an infinite number of "exponential
eigenmodes" in the lossless system in the latter case. At certain "magic"
numbers of atoms in the array, the system may exhibit self-induced (but linear
in the field) cancellation of resonant local-field suppression. We also studied
nonlinear modes of locsitons and found optical bistability and hysteresis in an
infinite array for the simplest modes.
