Stochastic differential equation model for spontaneous emission and carrier noise in semiconductor lasers

TL;DR

This paper introduces a stochastic differential equation model for semiconductor laser noise that accurately captures the negative correlation between spontaneous emission and carrier noise, aligning with classic theoretical results.

Contribution

The model explicitly accounts for the correlated noise processes using the same Wiener processes, improving upon previous models that neglected these correlations.

Findings

The model matches Henry's correlation coefficients.

Correlated noise influences mean laser dynamics.

Additional drift terms describe the effect of noise correlation time.

Abstract

We present a new stochastic differential equation model for the spontaneous emission noise and carrier noise in semiconductor lasers. The correlations between these two types of noise have often been neglected in recent studies of the effects of the noise on the laser dynamics. However, the classic results of Henry show that the intensity noise and the carrier noise are strongly negatively correlated. Our model demonstrates how to properly account for these correlations since the corresponding diffusion coefficients agree exactly with those derived by Henry. We show that in fact in the correct model the spontaneous emission noise and the carrier noise are driven by the same Wiener processes. Furthermore, we demonstrate that the nonzero correlation time of the physical noise affects the mean dynamics of both the electric field amplitude and the carrier number. We show that these are systematic corrections that can be described by additional drift terms in the model.