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]

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We conduct a theoretical study of the nonlinear optical dynamics of a 2D super-crystal comprising regularly spaced identical semiconductor quantum dots (SQDs), subjected to a resonant continuous wave excitation. A single SQD is considered as three-level ladder-like systems involving the ground, one-exciton and bi-exction states. We show that the super - crystal reveals a rich nonlinear dynamics, exhibiting multistability, self-oscillations and chaos. The behaviour is driven by the retarded SQD-SQD interactions and bi-exciton binding energy.

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Abstract. We investigate theoretically the nonlinear optical response of a two-dimensional supercrystal comprized of semiconductor quantum dots. An isolated quantum dot is modeled as a three-level ladder-like system with ground, one-exciton, and biexciton states. It is shown that the optical response of supercrystal demonstrate a rich nonlinear dynamics, including bistability, self-oscillations, and dynamical chaos. Supercrystals (SCs) comprising semiconductor quantum dots (SQDs) represent a class of new materials not existing in nature. Modern nanotechnology has in its disposal a variety of methods to design such systems [1]. Optical properties of SCs depend on the SQD's size, shape, and chemical composition, as well as on the lattice geometry and can be easily controlled [2].We conduct a theoretical study of the optical response of a two-dimensional SC. Due to a high density of SQDs in the SC, the SQD-SQD dipole-dipole interaction plays an important role in the SC's optical response, both linear and nonlinear. This interaction provides a positive feedback which, together with the SQD's nonlinearity, results in a rich optical dynamics of SC, including bistability, self-oscillations, and dynamical chaos.It is assumed that the SC undergoes an action of an external field of an amplitude Е0 and frequency ω0, which is quasiresonant with the SQD allowed transitions. A single SQD is modelled as a three-level ladder-like quantum system with the ground |1⟩, one-exciton |2⟩, and bi-exction |3⟩ states. Only the optical transitions |1⟩↔ |2⟩ and |2⟩↔|3⟩ are dipoleallowed. They are characterized by the transition dipole moments d21 and d32, transition frequencies ω21 and ω32, and the spontaneous decay constants γ21 and γ32. The frequency ω32 is down-shifted with respect to ω21 by an amount ΔB being the biexciton binding energy.The optical dynamics of an isolated SQD is governed by 3x3 density matrix. The field acting on a given SQD in the SC represents a sum of the external field and the field produced by all others SQDs in place of the given one. In this way, the total (retarded) dipole-dipole interaction is taken into account. As the mean dipole moment of an SQD depends on how strong the SQD is excited, the SQD-SQD interaction appears to depend on the current SQD's condition as well. Similar to a one-dimensional case [3], the near-zone part of the retarded SQD-SQD dipole-dipole interaction gives rise to a dynamic shift of the transition frequencies