0733-8724 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/JLT.2016.2581833, Journal of Lightwave Technology > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 1 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  ,   and   , 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 900nm VCSELs of known RIN which shows that the cross-correlation coefficient  ij is different for different mode pairs with a positive  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. Index Terms— 25Gbps MMF link, Mode Partition Noise for VCSEL-based optical links, Relative Intensity Noise, optical noise in VCSELs, optical communication, VCSEL-based MMF link, Spectrometry, short reach optical links, Mode competition, VCSEL transverse mode spatial overlap. I. INTRODUCTION THE recent interest in multilevel modulation formats for short reach optical links to support ever-increasing bandwidth requirements of datacenter applications requires a more careful assessment of the tighter impairment budget allocations [1]. Recent PAM-4 demonstrations at 50Gbit/s and higher have been reported using 850nm and 1060nm VCSELs for reaches up to 300m on standard OM4 and OM3 MMF [2], [3], [4] [5]. The performance of high-speed VCSEL-based PAM-4 optical links is mainly limited by dispersion and noise penalties. This S.Kota Pavan was with the Georgia Institute of Technology, Atlanta, GA 30318 USA. He is now with Texas Instruments, Dallas, TX 75243 USA ( e-mail: skotapavan@ti.com) Justin Lavrencik and S. E. Ralph are with the Georgia Institute of Technology, Atlanta, GA 30318 USA (404-894-5168; e-mail: stephen.ralph@ece.gatech.edu). Copyright (c) 2016 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to pubs-permissions@ieee.org. results from the inherent log   amplitude penalty (4.8dB for PAM-4) and the shorter symbol period compared to 10G. Furthermore the power-dependent VCSEL noise exacts a larger penalty when using PAM signaling [3], [4]. Noise impairment has two distinct aspects; 1) Random fluctuations in the composite power at the output of the VCSEL, i.e. the relative intensity noise (RIN) and 2) Correlations in the fluctuations of optical power among different VCSEL transverse modes due to mode competition [6]. These correlated fluctuations manifest as a random timing jitter after transport through the dispersive fiber due to the wavelength-dependence of the group velocity which is different for different VCSEL modes. This random jitter results in an additional amplitude variance at the optimal sampling instant, and is referred to as mode partition noise (MPN). Generally, RIN and MPN are treated as separate mechanisms without cross penalties [10]. Ogawa [7], [8] proposed, via simplifying assumptions, a simple model to estimate the variance due to MPN in optical links using single-transverse-mode Fabry-Perot (F-P) lasers with low RIN and having multiple longitudinal modes. This was later extended by Agrawal [9] to derive useful closed-form expressions for the power penalty due to MPN in single mode fiber (SMF) links under additional idealizing assumptions. This extended Ogawa-Agrawal (O-A) model has been adopted without modifications by the IEEE 802.3 standards group to estimate high-speed VCSEL-based MMF link performance [10], [11]. The different noise properties of VCSELs (compared to FP lasers) together with high-speed modulation challenges the assumptions of the O-A model which has been recently shown to be insufficiently accurate in describing the noise characteristics of VCSEL-based optical links [12], [13], [14]. The penalty estimations resulting from the simplifying assumptions of the O-A model are particularly inaccurate for next generation multi-level modulation links which are impacted significantly by MPN. Thus, there is now a need to improve on the existing O-A model for evaluating the effects of MPN in VCSEL-based links. Several attempts have been made recently to accurately model the MPN penalty for VCSEL-based links [11], [12], [13], [15]. A physics-based modeling of VCSEL noise that is based on the underlying rate equations, yet simple enough to be used within industry standards like the IEEE 802.3 is needed. VCSEL mode dynamics and thus noise characteristics differ from the longitudinal semiconductor lasers due to the unique New Model for Mode Partition Noise in VCSEL-MMF Links Based on Langevin-Driven Spatio-Temporal Rate Equations Sriharsha Kota Pavan, Member, IEEE, Justin Lavrencik, and Stephen E. Ralph, Senior Member, IEEE