Nanoscale stratification of optical excitation in self-interacting one-dimensional arrays

摘要

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