Study of multi-mode VCSEL lasers and how their performances are affected by the external optical feedback

The focus of this Master’s thesis is the analysis of multi-mode VCSEL and their dynamics. The study proposes a particular emphasis on the contribution that the optical external feedback exerts on the performances of the laser. VCSEL is the acronym for Vertical Cavity Surface Emitting Laser, they are laser diodes that can be pumped directly by an electrical current and have small dimensions (hundreds of micron). In the first part of the thesis, the behaviour of a single-mode and a multi-mode VCSEL are numerically simulated. In order to do that, the evolution of some quantities for different current injected are simulated, such as the carrier density distribution and the output power. Moreover, a time analysis has been conducted to highlight the temporal evolution of the electric field modal intensities. This analysis reveals the switching on of different modes, and after the transient phase, the system reaches a steady state. Another important feature that has been analyzed is the Relative Intensity Noise (RIN). It is a measure of the relative variation in time of an optical signal intensity, it represents the intrinsic noise of the system that can degrade the transmission. For a single mode VCSEL, the RIN exhibits a characteristic peak at low frequency due to the relaxation oscillation of the system. When more than one mode starts to turn on in the laser, some spurious peaks appear in the spectra due to the spatial overlapping of transverse modes. The main purpose of the analysis is to accurately characterize these spurious peaks to understand the variables on which they depend on and to attempt to shift them out of the receiver band, thereby minimizing their impact on transmission quality. After the characterization of the device itself, the contribution of the optical feedback has been added to the analysis. The optical feedback originates from the light reflected back into the VCSEL cavity from the optical fiber. Within the cavity, the feedback combines with the output power, introducing a modulation that is a periodic function of the phase of the back-reflected field. The effects of the feedback include variations in the emitted power and the threshold condition, as well as changes in the carrier density and the emitted wavelength. As a result there is a further increase of the noise. All these analysis are conducted using a MATLAB code that implements rate equations, which is a set of differential equations that describe the evolution of the electric field intensity and of the carrier density in time. The purpose of the second part of the thesis is to validate the code and the model used to simulate the device. In order to do that, two different approaches have been followed. The first one concerns the reproduction of the results obtained and published in the paper: "Effects of Optical Feedback on Static and Dynamic Characteristics of Vertical-Cavity Surface-Emitting Lasers" by Joanne Y. Law and Govind P. Agrawal, Fellow. The second one includes the comparison between the code used to simulate the VCSEL under the application of proper hypothesis and another MATLAB code that implements the Lang-Kobayashi equations. In the last part of the thesis, a mathematical model has been developed to derive steady-state (continuous-wave, CW) solutions for the VCSEL system and perform stability analysis on these solutions. This approach helps to identify the stability region of the CW solutions. The mathematical model is based on an existing model developed for simplified two level laser.