1 Nanophotonics Theory and Signal Processing, Department of Photonics Engineering, Technical University of Denmark2 Department of Photonics Engineering, Technical University of Denmark3 Quantum Photonics, Department of Photonics Engineering, Technical University of Denmark4 Risø National Laboratory for Sustainable Energy, Technical University of Denmark
Light-matter interaction in nanostructured materials is studied theoretically with emphasis on spontaneous emission dynamics of quantum dots in photonic crystals. The main topics of the work are electromagnetic scattering calculations, decay dynamics of single quantum dots and multiple quantum dot dynamics. The electromagnetic Green's tensor enters naturally in calculations of light-matter interaction in multiple scattering media such as photonic crystals. We present a novel solution method to the Lippmann-Schwinger equation for use in electric field scattering calculations and Green's tensor calculations. The method is well suited for multiple scattering problems such as photonic crystals and may be applied to problems with scatterers of arbitrary shape and non-homogeneous background materials. By the introduction of a measure for the degree of fractional decay we quantify to which extent the effect is observable in a given material. We focus on the case of inverse opal photonic crystals and locate the position in the crystal where the effect is most pronounced. Furthermore, we quantify the influence of absorptive loss and give example calculations with experimental parameters for PbSe quantum dots in Si inverse opals showing that absorption has a limiting but not prohibitive effect. In addition, we discuss how the resonant nature of the phenomenon puts rather severe restrictions on the stabilization of the system in possible experiments. Last, we examine the influence on the decay dynamics from other quantum dots. Using a self-consistent Dyson equation approach we describe how scattering from other quantum dots can be included in the Green's tensor for a passive material system. We numerically calculate both local and non-local elements of the Green's tensor for a photonic crystallite slab and apply the method for an example calculation with two quantum dots at specific locations in the unit cell. In this way it is explicitly shown how the decay dynamics of one quantum dot is qualitatively changed by the scattering properties of another.