The study of supercrystals made of periodically arranged semiconductor quantum dots is essential for the advancement of emerging nanophotonics technologies. By combining the strong spatial confinement of elementary excitations inside quantum dots and exceptional design flexibility, quantum-dot supercrystals provide broad opportunities for engineering desired optical responses and developing superior light manipulation techniques on the nanoscale. Here we suggest tailoring the energy spectrum and wave functions of the supercrystals' collective excitations through the variation of different structural and material parameters. In particular, by calculating the excitonic spectra of quantum dots assembled in two-dimensional Bravais lattices we demonstrate a wide variety of spectrum transformation scenarios upon alterations in the quantum dot arrangement. This feature offers unprecedented control over the supercrystal's electromagnetic properties and enables the development of new nanophotonics materials and devices.

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Optical methods, which allow the determination of the dominant channels of energy and phase relaxation, are the most universal techniques for the investigation of semiconductor quantum dots. In this paper, we employ the kinetic Pauli equation to develop the first generalized model of the pulse-induced photoluminescence from the lowest-energy eigenstates of a semiconductor quantum dot. Without specifying the shape of the excitation pulse and by assuming that the energy and phase relaxation in the quantum dot may be characterized by a set of phenomenological rates, we derive an expression for the observable photoluminescence cross section, valid for an arbitrary number of the quantum dot's states decaying with the emission of secondary photons. Our treatment allows for thermal transitions occurring with both decrease and increase in energy between all the relevant eigenstates at room or higher temperature. We show that in the general case of N states coupled to each other through a bath, the photoluminescence kinetics from any of them is determined by the sum of N exponential functions, whose exponents are proportional to the respective decay rates. We illustrate the application of the developed model by considering the processes of resonant luminescence and thermalized luminescence from the quantum dot with two radiating eigenstates, and by assuming that the secondary emission is excited with either a Gaussian or exponential pulse. Analytic expressions describing the signals of secondary emission are analyzed, in order to elucidate experimental situations in which the relaxation constants may be reliably extracted from the photoluminescence spectra.

The size dependence of the quantized energies of elementary excitations is an essential feature of quantum nanostructures, underlying most of their applications in science and technology. Here we report on a fundamental property of impurity states in semiconductor nanocrystals that appears to have been overlooked—the anticrossing of energy levels exhibiting different size dependencies. We show that this property is inherent to the energy spectra of charge carriers whose spatial motion is simultaneously affected by the Coulomb potential of the impurity ion and the confining potential of the nanocrystal. The coupling of impurity states, which leads to the anticrossing, can be induced by interactions with elementary excitations residing inside the nanocrystal or an external electromagnetic field. We formulate physical conditions that allow a straightforward interpretation of level anticrossings in the nanocrystal energy spectrum and an accurate estimation of the states' coupling strength.

Nonspherical semiconductor nanocrystals (NCs) may exhibit strongly anisotropic photoluminescence due to the intraband transitions, whose matrix elements depend critically on the envelope wave functions of the confined electrons and holes. We demonstrate that this anisotropy may be used as the basis for a new type of polarization spectroscopy, enabling one to reliably determine the shape and spatial orientation of individual NCs, as well as providing important information on the symmetry of quantum states involved in optical transitions.

The coherent coupling of quantum dots is a sensitive indicator of the energy and phase relaxation processes taking place in the nanostructure components. We formulate a theory of low-temperature, stationary photoluminescence from a quantum-dot molecule composed of two spherical quantum dots whose electronic subsystems are resonantly coupled via the Coulomb interaction. We show that the coupling leads to the hybridization of the first excited states of the quantum dots, manifesting itself as a pair of photoluminescence peaks with intensities and spectral positions strongly dependent on the geometric, material, and relaxation parameters of the quantum-dot molecule. These parameters are explicitly contained in the analytical expression for the photoluminescence differential cross section derived in the paper. The developed theory and expression obtained are essential in interpreting and analyzing spectroscopic data on the secondary emission of coherently coupled quantum systems. V C 2015 AIP Publishing LLC. [http://dx

In recent years there have been active developments of spectroscopic methods for analysis of light absorption by individual nanocrystals. Here we provide a solid theoretical background for one of these methods via developing a uniform theory of anisotropic intraband absorption by a nonspherical semiconductor nanocrystal. The nanocrystal is assumed to be simultaneously excited by the linearly polarized pump and probe fields that are, respectively, resonant to the interband and intraband transitions of the nanocrystal’s electronic subsystem. Three relative arrangements of the excited electron–hole pair states are considered, covering all possible types of transition schemes that can occur in experiment. The developed theory is then used to calculate the angular absorption spectra for the most common shapes of the nanocrystals, which essentially lays the foundation of stationary pump–probe polarization spectroscopy based on the shape-induced anisotropy of intraband absorption by a semiconductor nanocrystal. This spectroscopy may serve modern nanotechnology by facilitating characterization of anisotropic nanostructures as it allows one to reliably determine the shapes and orientations of individual nanocrystals and find the symmetry of quantum states involved in the electronic transitions induced by the probe.

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