Effect of the second mode on the optical properties of quantum-dot microcavity lasers

Abstract

For several decades light-matter interaction has been an important scientific field and has led to numerous investigations and researches in various fields such as condensed matter physics, medicine and electrical engineering, and is still expected to be one of the most active areas of research over the coming years. However, there are still many open questions that necessitate further investigation. In this doctoral thesis we investigate the coherence properties of light emitted by quantum-dot microcavity lasers. To accomplish this task, we consider an open quantum-mechanical system to formulate equation of motion based on the theory of microscopic semiconductor. In this way, the cluster expansion method is employed to solve the infinite hierarchy problem. Within this theory, we can generate correlations required to calculate the quantities of interest in microcavities. Current work is concerned with the effect of the second mode on the lasing behavior of the quantum-dot microcavity lasers where the quantum dot contains two shells, a s- and a p-shell in the valence and in the conduction band. In this regard, this thesis addresses two main parts: Two-mode, and two-state quantum-dot-microcavity lasers. In the first half of this thesis, we investigate correlations between two cavity modes in a quantum-dot-microcavity laser where both modes are coupled to the quantum-dot s-shell transition. The significant differences in the lasing behavior of two modes indicate the gain competition between modes which is also confirmed by autocorrelation and cross-correlation functions. In this part we especially emphasize on the effects of the direct dissipative coupling on the gain competition. Numerical results for a semiconductor quantum-dot microcavity laser demonstrate an enhanced autocorrelation of both modes and also an enhanced anticorrelation with increasing the direct coupling between two modes. In order to describe and analyze these issues, we introduce dark and bright modes by applying the unitary transformation. It is seen that beyond a certain lasing threshold original modes are composed and as a result a bright mode is generated that is coupled to the quantum dots. In addition, a dark mode is created that has only indirect interaction with the quantum dots through the bright mode. It will be also shown that the population of the dark mode can justify an efficient transfer of photons between two original cavity modes. In the second half of the thesis, we investigate two-state lasing in quantum-dot laser, through ground-state (s-shell) and excited-state (p-shell) transitions. Based on the microscopic semiconductor theory, we show that the ground-state laser is qualitatively uninfluenced by the onset of lasing in the excited-state mode due to the delay time between carrier saturation of two states. It is influenced solely by the relaxation of the carrier into the ground state which can be affected via the Q-factor of the excited mode, however it has only quantitative effect on lasing operation of the ground-state mode.