Multimodal Semiconductor Ring Lasers: An Analytical Study

Abstract

Semiconductor ring lasers (SRLs) are lasers with a cavity consisting of a circular waveguide. Due to their rotational symmetry, every mode propagating in the cavity has a counterpart propagating in the opposite direction. Because of nonlinear interaction, while one directional mode is lasing, the mode in the other direction can be largely suppressed. This regime shows a bistability between the directional modes and is therefore of great interest due to its potential use in optical information storage. This, combined with the planar structure of the device, renders SRLs very suitable for implementation in optical integrated circuits.
Here we pursue an analytical study of SRLs with two longitudinal modes, each consisting of two directional modes. First, we derive a set of rate equations from first principles, governing the dynamical behaviour. This model yields good results, but is very involved, making the interpretation not straightforward. We have solved this by reducing the original set of nine real equations to a new set of five expressions, using asymptotic methods. This reduction is based on the different time scales present in the laser system and eliminates the relatively fast relaxation oscillations. We compare numerical solutions of the reduced model to those of the full model and in this way we validate the performed transformations and approximations. Subsequently, we determine analytically the steady-state solutions of the reduced model. These solutions describe which of the two longitudinal modes is lasing and whether these modes lase in one or both directions of propagation.
Since there are many stationary solutions, their stability determines the features of the output power as a function of the current. By performing a linear stability analysis, we calculate the bifurcation currents of the steady-state solutions. For simpler steady states, we are able to perform the stability analysis in an analytical way and we give the bifurcation currents as a function of the geometrical and dynamical parameters of the laser. The stability of the general solution is too involved to determine, but can be found numerically. By applying a parameter sweep we obtain a visual representation.
The approach followed in this master thesis provides a solid tool to explain and predict the dynamical behaviour of SRLs given their operating conditions.

Date of Award	27 Jun 2008
Original language	English
Supervisor	Jan Danckaert (Promotor), Ronald Van Loon (Jury), Lendert Gelens (Jury), Joannes Schoukens (Jury), Philippe Tassin (Jury), Philippe Tassin (Advisor) & Geert Morthier (Jury)