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We conduct a theoretical study of the nonlinear optical response of a two-dimensional semiconductor quantum dot supercrystal subjected to a quasi-resonant continuous wave excitation. A constituent quantum dot is modeled as a three-level ladder-like system (comprising the ground, the one-exciton, and the bi-exction states). To study the stationary response of the supercrystal, we propose an exact linear parametric method of solving the nonlinear steady-state problem, while to address the supercrystal optical dynamics qualitatively, we put forward a novel method to calculate the bifurcation diagram of the system. Analyzing the dynamics, we demonstrate that the supercrystal can exhibit multistability, periodic and aperiodic self-oscillations, and chaotic behavior, depending on parameters of the supercrystal and excitation conditions. The effects originate from the interplay of the intrinsic nonlinearity of quantum dots and the retarded inter-dot dipole-dipole interaction. The latter provides a positive feedback which results in the exotic supercrystal optical dynamics. These peculiarities of the supercrystal optical response open up a possibility for all-optical applications and devices. In particular, an all-optical switch, a tunable generator of THz pulses (in self-oscillating regime), a noise generator (in chaotic regime), and a tunable bistable mirror can be designed. a b c FIG. 1. PbSe rocksalt 2D nanostructures with (a) honeycomb and (b) square lattice symmetry, (c) -CdSe nanostructure with a compressed zincblende and slightly distorted square lattices (scale bars, 50 nm). Insets show the electrodiffractograms in the [111] (a) and [100] (b,c) projections. The figure is from Ref. [7].linearity of the layer is ensured by the fact that two-level emitters are nonlinear systems. The positive feedback originates from the secondary field, which is generated by the emitters themselves; this is the so-called intrinsic feedback, i.e., here a cavity (external feedback) is not required.A two-dimensional (2D) semiconductor quantum dot (SQD) supercrystal represents a limiting case of a thin layer. In this paper, we conduct a theoretical study of the nonlinear optical response of such a system. A single SQD is considered as a point-like system with three consecutive levels of the ground, one-exciton, and bi-arXiv:1910.02553v1 [physics.optics]

We present results of numerical simulations of the kinetics of excitonexciton annihilation of weakly localized one-dimensional Frenkel excitons at low temperatures. We find that the kinetics is represented by two welldistinguished components: a fast short-time decay and a very slow long-time tail. The former arises from excitons that initially reside in states belonging to the same localization segment of the chain, while the slow component is caused by excitons created on different localization segments. We show that the usual bi-molecular theory fails in the description of the behavior found.We also present a qualitative analytical explanation of the non-exponential behavior observed in both the short-and the long-time decay components.

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