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

Abstract

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. 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. This paper is now published, with very minor changes, in Phys. Rev. A 79, 053834 (2009).

Condition for resonant optical bistability

“…However, OB and optical hysteresis remain of considerable interest from the fundamental standpoint as a clear manifestation of a nonlinear light-matter interaction. Some new types of bistability mechanisms have been discussed recently [16][17][18][19]. Besides, the question of OB and hysteresis has received renewed attention in connection with novel hybrid zero-dimensional (0D) nanoscopic systems, e.g., artificial molecules comprising a semiconductor quantum dot (SQD) and metal nanoparticles (see Refs.…”

Local-field excitations in two-dimensional lattices of resonant atoms

“…This effect is best manifested in small-scale ordered arrays and lattices of atoms at near-resonance conditions, which allow to attain high interaction strength between neighboring atoms and to easily control it by tuning the laser frequency. We have shown [1,2] that when the interaction with neighboring atoms becomes comparable to that with the external field, so that the interaction strength exceeds some critical value, the system will support LF excitations, which we call locsitons. In finite-size arrays and lattices, standing waves of locsitons may form nanoscale strata and complex patterns in the LF (and hence, in the induced atomic dipoles).…”

“…As we have shown in [1,2], this assumption of the LF uniformity is not universally applicable; moreover, it completely falls apart when the uniformity of the atomic lattice is disturbed by impurities, boundaries, etc. Indeed, when the interatomic interactions are sufficiently strong and the system is not very large, highly nonuniform LF distributions emerge, resulting in a strong stratification of the LF and atomic excitations.…”

“…In [1,2] we suggested a few promising methods of locsiton detection. In particular, locsitons could be observed via size-related resonances in a scattering of laser radiation or via x-ray or electron-energy-loss spectroscopy.…”

“…By their nature, locsitons may be classified as Frenkel excitons [7], because there is no charge transfer between atoms and the dipole interaction is due to bound electrons. Some of the locsiton effects, first of all, wave resonances, may be viewed as analogues of other types of oscillations and waves in condensed matter, like plasmons and phonons [7], as well as low-dimensional effects, like surface plasmons [8,9], size-related resonances in thin metal films [10] or long organic molecules [11], "quantum carpets" [12], arrays of pendulums or electronic circuits [2], etc. Approaching from another perspective, one can view the formation of a locsiton band as a Rabi broadening of the atomic resonance due to strong interatomic interactions, which is essentially similar to the band formation in solid-state theory.…”