Theoretical and experimental analysis of phase noise in semiconductor lasers biased below threshold

Abstract

We report a theoretical and experimental study of phase noise in semiconductor lasers when the bias current is below the threshold value. The theoretical study is performed by using two types of rate equations, with additive and multiplicative noise terms. We find the conditions for which the evolution in those rate equations can be described by 1-dimensional and two dimensional Brownian motions, respectively. The main statistical differences between the additive and multiplicative noise models are then illustrated by using the simplified Brownian motion models. Additive and multiplicative noise models predictions are compared with measurements of the phase noise with a coherent receiver using a 90º optical hybrid. We develop a novel method to extract the phase noise directly from our measurements, that in contrast to the usual direct method is not based on the analysis of the phase noise difference. The method permits a direct visualization of the phase noise trajectories and a calculation of the averages and the distribution that is valid in the short-time limit. Our results are in very good agreement with the results obtained with the method based on the phase noise difference. Our experimental results show that the variance of the phase noise grows linearly in time and has Gaussian statistics, supporting the modelization of the phase noise statistics with the additive noise model.