Ivan S. Nikolaev

Statistical analysis of time-resolved emission from ensembles of semiconductor quantum dots: Interpretation of exponential decay models

We present a statistical analysis of time-resolved spontaneous emission decay curves from ensembles of emitters, such as semiconductor quantum dots, with the aim of interpreting ubiquitous non-single-exponential decay. Contrary to what is widely assumed, the density of excited emitters and the intensity in an emission decay curve are not proportional, but the density is a time integral of the intensity. The integral relation is crucial to correctly interpret non-single-exponential decay. We derive the proper normalization for both a discrete and a continuous distribution of rates, where every decay component is multiplied by its radiative decay rate. A central result of our paper is the derivation of the emission decay curve when both radiative and nonradiative decays are independently distributed. In this case, the well-known emission quantum efficiency can no longer be expressed by a single number, but is also distributed. We derive a practical description of non-single-exponential emission decay curves in terms of a single distribution of decay rates; the resulting distribution is identified as the distribution of total decay rates weighted with the radiative rates. We apply our analysis to recent examples of colloidal quantum dot emission in suspensions and in photonic crystals, and we find that this important class of emitters is well described by a log-normal distribution of decay rates with a narrow and a broad distribution, respectively. Finally, we briefly discuss the Kohlrausch stretched-exponential model, and find that its normalization is ill defined for emitters with a realistic quantum efficiency of less than 100%.

Size dependence of the wavefunction of self-assembled InAs quantum dots from time-resolved optical measurements

Jeppe Johansen, Søren Stobbe, Ivan S. Nikolaev, Toke Lund-Hansen, Philip T. Kristensen, Jørn M. Hvam, Willem L. Vos, and Peter Lodahl COM · DTU, Department of Communications, Optics, and Materials, Nano · DTU, Technical University of Denmark, DTU Building 345V, DK-2800 Kgs. Lyngby, Denmark Center for Nanophotonics, FOM Institute for Atomic and Molecular Physics (AMOLF), Amsterdam, The Netherlands Complex Photonics Systems, MESA+ Institute for Nanotechnology, University of Twente, The Netherlands

Strongly nonexponential time-resolved fluorescence of quantum-dot ensembles in three-dimensional photonic crystals

We observe experimentally that ensembles of quantum dots in three-dimensional (3D) photonic crystals reveal strongly nonexponential time-resolved emission. These complex emission decay curves are analyzed with a continuous distribution of decay rates. The log-normal distribution describes the decays well for all studied lattice parameters. The distribution width is identified with variations of the radiative emission rates of quantum dots with various positions and dipole orientations in the unit cell. We find a striking sixfold change of the width of the distribution by varying the lattice parameter. This interpretation qualitatively agrees with the calculations of the 3D projected local density of states. We therefore conclude that fluorescence decay of ensembles of quantum dots is highly nonexponential to an extent that is controlled by photonic crystals.

Quantitative analysis of directional spontaneous emission spectra from light sources in photonic crystals

We have performed angle-resolved measurements of spontaneous-emission spectra from laser dyes and quantum dots in opal and inverse opal photonic crystals. Pronounced directional dependencies of the emission spectra are observed: angular ranges of strongly reduced emission adjoin with angular ranges of enhanced emission. It appears that emission from embedded light sources is affected both by the periodicity and by the structural imperfections of the crystals: the photons are Bragg diffracted by lattice planes and scattered by unavoidable structural disorder. Using a model comprising diffuse light transport and photonic band structure, we quantitatively explain the directional emission spectra. This work provides detailed understanding of the transport of spontaneously emitted light in real photonic crystals, which is essential in the interpretation of quantum optics in photonic-band-gap crystals and for applications wherein directional emission and total emission power are controlled.

Orientation-dependent spontaneous emission rates of a two-level quantum emitter in any nanophotonic environment

We study theoretically the spontaneous emission rate of a two-level quantum emitter in any nanophotonic system. We derive a general representation of the rate on the orientation of the transition dipole by only invoking symmetry of the Green function. The rate depends quadratically on orientation and is determined by rates along three principal axes, which greatly simplifies visualization: emission rate surfaces provide insight on how preferred orientations for enhancement (or inhibition) depend on emission frequency and location, as shown for a mirror, a plasmonic sphere, and a photonic band-gap crystal. Moreover, insight is provided on means to “switch” the emission rates by actively controlling the orientation of the emitters’ transition dipole.

“On Donuts and Peanuts”: Strongly orientation-dependent spontaneous emission rates in any nanophotonic environment

According to quantum electrodynamics, the emission rate of a two-level quantum emitter is described by Fermis golden rule. Currently, there are many efforts to control the emission rate of quantum emitters by optimizing the nanoscale environment via the local density of optical states (LDOS) by, e.g., reflecting interfaces, microcavities, photonic crystals, or plasmonic nanoantennae [1]. Control of spontaneous emission is notably relevant to solid-state applications, including miniature lasers and light-emitting diodes, single-photon sources for quantum information, and solar energy harvesting.

Quantum efficiency of self-assembled quantum dots determined by a modified optical local density of states

We have measured time-resolved spontaneous emission from quantum dots near a dielectric interface with known photonic local density of states. We thus experimentally determine the quantum efficiency and the dipole moment, important for quantum optics.

Accurate Measurement of the Transition Dipole Moment of Self-Assembled Quantum Dots

Here we present quantitative measurements of the dipole moment of an ensemble of self-assembled quantum dots employing a modified optical local density of states (LDOS). The LDOS is controlled by varying the distance from the QDs to a semiconductor/air interface.

Dynamics of spontaneous emission controlled by local density of states in photonic crystals

We have measured time-resolved spontaneous emission from quantum dots in 3D photonic crystals. Due to the spatially dependent local density of states, the distribution of decay rates varies strongly with the photonic crystal lattice parameter.