Accurate modelling of VCSEL distributed Bragg reflectors by Floquet-Bloch theory

Abstract

Nowadays, vertical cavity surface emitting lasers (VCSELs) provide a very exciting area of research. The unique geometry of VCSELs results in several significant advantages over their edge-emitting counterparts, including low threshold current, single-longitudinal-mode operation, circular output-beam profile. The optimization of the DBR structure is of fundamental importance to increase the performance of optical systems based on the VCSEL technology. To this aim, sophisticated modelling techniques are needed, where only negligible or no approximations are included in the calculations. Therefore, we have used the Floquet-Bloch theory (FBT) formalism to simulate the DBR performance of VCSEL structures. In this paper we explain the general VCSEL theory and propose a number of simulations to individuate the optimal configuration of DBR mirrors with the aim to maximise the output power laser and reduce the threshold current density. The VCSEL optimization is carried out by considering the best trade off among various parameters, including period number, materials, and doping concentration and profile. It is clearly shown the superiority of the FBT approach in the prediction of the best DBR performance and VCSEL properties by comparing results (reflectivity, spectrum, peak wavelength, gain) with other well-known methods, such as the transfer matrix method (TMM) and coupled-mode theory (CMT).