New Model for Mode Partition Noise in VCSEL-MMF Links Based on Langevin-Driven Spatio-Temporal Rate Equations

Abstract

We develop a new model to describe the Mode Partition Noise (MPN) in VCSEL-Based Multi-Mode Fiber (MMF) links starting from the well-known Langevin noise-driven laser rate equations. Using the spatio-temporal representation of the rate equations for the VCSEL transverse modes, we develop a comprehensive physical model for VCSEL noise properties using covariance (COV) matrix approach. Neglecting second-order effects, we then reduce the COV matrix elements to three VCSEL-specific parameters ${{\alpha }}$ , ${k_n}$ and ${{\Gamma} _{\boldsymbol p}}$ , which completely characterizes the VCSEL noise. We further illustrate that the VCSEL Relative Intensity Noise (RIN) influences the MPN penalty and thus cannot be treated independently. The model also describes the dependence of the VCSEL mode correlation properties on the relative time-delays which can be measured as fiber-enhanced RIN. Lastly, we verify experimentally the new model assumptions about the cross-correlation properties of the VCSEL modes through direct experimental measurements on 900 nm VCSELs of known RIN which shows that the cross-correlation coefficient ${{\boldsymbol{R}}_{{\rm{ij}}}}$ is different for different mode pairs with a positive ${{\boldsymbol{R}}_{{\rm{ij}}}}$ between 1 and 3 modes. This validates the new model predictions, while contradicting the O–A model assumptions when applied for VCSEL-based links.