Nonlinear optical response of a two-dimensional quantum-dot supercrystal: Emerging multistability, periodic and aperiodic self-oscillations, chaos, and transient chaos

Abstract

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]

Nonlinear Optical Dynamics and High Reflectance of a Monolayer of Three-Level Quantum Emitters with a Doublet in the Excited State

“…the ladder [14][15][16] and Λ schemes of optical transitions [17]. It should be noted in this connection that in spite of the global similarity of responses of the abovementioned systems of three-level QEs, the physics of the optical response formation of a V-QE monolayer differs significantly from the other two analogs.…”

“…The Rabi amplitude Ω(t) is the sum of the Rabi amplitudes Ω 0 = d 31 E 0 / of the external field and of the field produced by other V-QEs in place of the given V-QE. In the mean-field approximation, Ω(t) is given by the following equation [16] (here and in what follows, we suppress the time dependence of all variables):…”

“…(5) The expressions for constants γ R and Δ L depend on the relationship between the lateral lattice size Na (N is the lateral number of sites and a is the lattice constant) and radiation wavelength λ = 2πc/ω 0 , c being the speed of light. For a simple square lattice with lateral size Na ≪ λ (pointlike system), the quantities γ R and Δ L are given by [16] (6) (7) where = λ/2π. In the opposite case of Na ≫ λ (extended system), we have [16] (8) (9) As follows from Eqs.…”

“…For a simple square lattice with lateral size Na ≪ λ (pointlike system), the quantities γ R and Δ L are given by [16] (6) (7) where = λ/2π. In the opposite case of Na ≫ λ (extended system), we have [16] (8) (9) As follows from Eqs. (6) L a V-QEs in the lattice, while the value of γ R for an extended system is proportional to the number of V-QEs within an area of size .…”

“…However, nonlinear optical properties of 2D SCs have been investigated to a far lesser extent. It was shown in recent publications [14][15][16][17] that the nonlinear response of a SC of quantum emitters (QEs) with a ladder scheme [14][15][16] and Λ scheme of optical transitions [17] exhibits multistability, self-oscillations, and dynamic chaos. In addition, in a certain frequency range, the SC almost totally reflects the incident field, i.e., operates as an ideal nanometer-thick mirror, which, in addition, exhibits bistability.…”