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The multimode characteristics of vertical cavity surface emitting laser (VCSEL) sources lead to mode partition noise (MPN) impairing high-speed multimode fiber (MMF) links. In this letter, we propose a low-cost and straightforward MPN mitigation scheme by optimizing the launch condition between the VCSEL and the MMF. The dependence of the MPN on launch conditions is theoretically assessed. Simulation shows that the mode power redistribution induced by rearranging the launch condition has great potential to reduce the MPN. Experiments are carried out to demonstrate the MPN reduction. In our case, using a 15- $\mu \text{m}$ radial offset between the VCSEL and the MMF, we observe efficient noise suppression in both the frequency domain and the time domain.

In this article, we report on the asymmetry of intensity noise spectrum at millimeter-wave (mm-wave) heterodyne carriers. Passively mode-locked laser diode (PMLLD) is employed for a low phase noise mm-wave photonic generation using direct detection. This optical source produces an excess intensity noise known by laser mode partition noise (LMPN) in which its spectrum usually appears as symmetric double side-bands around the beat-note. The propagation over a dispersive medium such as optical fiber can modify the spectral behavior and profile of the LMPN. This article explores the impact of fiber transmission on the distortions of the LMPN in optical and electrical spectrum. Experimental results reveal, for the first time, that the LMPN symmetry is converted to an asymmetric deformation on the generated beating carrier. The mathematical model and numerical simulation are presented to give hints for analyzing this phenomenon. The findings of the simulations and measurements demonstrate the main role of second- and third-order fiber dispersion on the LMPN profile.

This chapter discusses the propagation effects, noise sources, and channel impairments for wireless communications, free-space optical communications, and fiber-optics communications. The key idea of the chapter is to derive the wave equation for a given medium from Maxwell’s equation and determine its solution subject to corresponding boundary conditions. After the introduction of the vector derivatives in orthogonal curvilinear, cylindrical polar, and spherical coordinate systems, we study vectorial nature of the light, derive Snell’s law of refraction from Maxwell’s equations, study total internal reflection, and explain the light confinement in step-index optical fibers. We also describe how arbitrary polarization state can be generated by employing three basic polarizing elements, namely, polarizer, phase shifter (retarder), and rotator. We then introduce the electromagnetic potentials to simplify the study of generation of electromagnetic waves, followed by antenna theory basics. We then discuss interference, coherence, and diffraction in optics. After that the detailed description of laser beam propagation effects over the atmospheric turbulence channels is provided, including the description of simulation models. In the section on wireless communication channel effects, we study path loss, shadowing, and multipath fading propagation effects. Both ray theory-based and statistical multipath wireless communication channel models are described. We then move to signal propagation effects in optical fibers and describe (1) fiber attenuation and insertion loss, (2) chromatic dispersion effects, (3) polarization-mode dispersion effects, and (4) fiber nonlinearities. Regarding the fiber nonlinearities, both Kerr nonlinear effects (self-phase modulation, cross-phase modulation) and nonlinear scattering effects, such as stimulated Raman scattering, are described. The generalized nonlinear Schrodinger equation is then described for both single-mode and few-mode fibers as well as the corresponding split-step Fourier algorithms to solve it. The following noise sources related to optical communication are described: mode partition noise, relative intensity noise, laser phase noise, modal noise, thermal noise, spontaneous emission noise, noise beating components, quantum shot noise, dark current noise, and cross talk. Finally, in section on indoor optical wireless communications, the channel models for both infrared and visible light communications are described.

The high-speed multimode optical interconnects based on vertical-cavity surface-emitting laser and multimode fiber (MMF) are severely constrained by band-limited devices, modulation nonlinearity, and laser induced noises such as relative intensity noise, mode partition noise, and fiber-induced noises such as chromatic dispersion and mode dispersion. The advanced digital signal processing technologies have been viewed as the inevitable tool to mitigate the physical limitations of electrical and optical components and the noise interactions during the transmission. In order to achieve multimode 100 Gbps/lane over 100-m transmission with the existing devices, a Volterra equalizer has been proven as a very effective equalization solution to deal with nonlinear impairments. However, the practical implementation of this nonlinear equalizer has been constrained by its tremendously high computation complexity. In this paper, we propose the threshold-based pruned retraining Volterra equalization (TRVE) to reduce the computation complexity, while maintaining the transmission performance. Multimode 100-Gbps/lane transmission over 100-m OM3 MMF has been experimentally demonstrated with up to 70.7% computation complexity reduction, while keeping the bit error rate under the 7% hard-decision forward error correction limit. In addition, the TRVE with $\ell _1$ -regularization is also proposed and experimentally verified to optimize the threshold selection.

The demand for high speed data transmission has increased rapidly over the past few years, leading to the development of the data center concept. Considering that vertical cavity surface emitting lasers (VCSELs) based optical interconnect is evolving to 100 Gb/s, relative intensity noise and mode partition noise are becoming significant, which cannot be equalized by conventional equalizers efficiently. On the other hand, optical fiber suffers from inter-symbol interference (ISI) and nonlinear channel response, making the equalization process even more challenging. Recently, several machine learning techniques have already been applied to recover signal from nonlinear distortions. However, previous experiments mainly focused on achieving low BER and have neglected the computational complexity. In this paper, we have designed a recurrent neural network (RNN) based equalizer. The equalizer is tested over a PAM-4 modulated VCSEL-MMF optical interconnect link, and shows BER performance improvement over equalizers based on ANN. A variant, Half-RNN, is also proposed and tested, whose computational complexity is 70% lower than ANN with similar BER performance. Our experiments provide guidance for designing neural network structure when using deep learning for equalization, justifying the significance of our work.

As global IP traffic demands are exponentially growing, the increase in sub-system and system level requirements for higher speeds and longer transmission distances from multi-mode fiber (MMF) based vertical-cavity surface-emitting laser (VCSEL) optical links are fundamentally inhibited by bandwidth limits due to inherent fiber dispersions as well as transmitter noise impairments. Noise variances such as spectral linewidth (Δ𝜆rms), relative intensity noise (RIN), mode noise (MN), mode partition noise (MPN), chromatic dispersion (CD), frequency chirp and reflection feedback etc., all have serious ramifications on signal-to-noise ratio (SNR) in degrading receiver sensitivity. In order to drive the systems to higher bandwidth levels, it is important to identify the source of noise impairments, and try to minimize them with optimum component designs that facilitate solutions to achieve high SNR at the receivers. In this contest the author propose a multipurpose effective refractive index (Δneff) model of VCSEL cavity to push data transmission of non-return zero (NRZ) based 100G SR4 to beyond eSR4 limits that can potentially offer stable industrial temperature narrow Δ𝜆rms and low RIN at chip level, low MPN in optical fiber, and high SNR at receiver, respectively. This simple and effective concept with further bandwidth, power and thermal budget improvements likely to have high potential for 850nm VCSEL use in PAM-4 based top of the rack (TOR)-leaf and leaf-spine 400G (SR8, SR4.2)/800G (SR16) Datacenter optical interconnects (DCI). The Δneff occurred from multilayer distributed Bragg reflector (DBR) stacks and quantum well active regions due to oxide layer is critical in fixing Δ𝜆rms of VCSELs as the data transmission distance is inversely proportional to Δ𝜆rms. The author discusses the impact of Δneff in creating narrow Δ𝜆rms and its benefit on low MPN in basic light transmitter units of NRZ 25.78125Gb/s and 28.05Gb/s transmissions of VCSELs in 100G eSR4 optical links with performance margin up to 400m in OM4 MMF at 85C with inexpensive power penalties at the receiver without equalization, pre-emphasis and error correction techniques.

In this letter, we study and demonstrate, for the first time, how chromatic dispersion causes laser mode partition noise at millimeter-wave (mm-wave) frequencies. A 60-GHz radio-over-fiber (RoF) transmission system employing an optical frequency comb is theoretically and experimentally investigated. Chromatic dispersion is a limiting factor in RoF systems, which induces power fading and phase noise on the resultant mm-wave beating carriers. Furthermore, experimental measurements in this letter show that when transmitting optical comb spectrum across kilometers of optical fiber, chromatic dispersion destroys partition noise compensation between modes. Therefore, the beat note carrier suffers from intensity noise impairments that degrade the system performance.

In this paper, a 1310 nm InAlGaAs/InP multiple quantum well ridge waveguide FP laser with a built-in wavelength detuned band-pass filter has been fabricated and investigated in experiments. When compared to the reference FP laser fabricated in the same wafer, it is observed that the root-mean-square spectral width can be approximately reduced to half; and moreover, significant improvements on the transmission performances in terms of the power penalty at given transmission distance and the longest transmission distance at given bit error rate, have been achieved for the proposed laser at the same fabrication cost.

We present an analysis of pulse-amplitude modulation 4 (PAM) based multimode fiber (MMF) links using VCSELs at 850 and 1050 nm across a wide range of fiber profiles with effective modal bandwidth spanning from 2 to 10 GHz·km. We demonstrate speeds >51.56 Gbit/s over a set of standard OM3 and OM4 fibers with bit error rate (BER) 50 Gbit/s using PAM-4. We perform VCSEL characterization and through a comparison with our analytic link model, identify various link penalties including those due to the relative intensity noise and mode partition noise of the VCSEL.

The correlation properties of vertical-cavity surface-emitting laser (VCSEL) transverse modes determine the noise impairments of VCSEL-based high-speed MMF links. Relative intensity noise and mode partition noise originate from the distinct and aggregate fluctuations of the lasing transverse modes of VCSELs. These noise mechanisms are often the limitations in VCSEL-based optical links particularly 25 Gbaud and higher OOK and PAM-4 links and are an integral part of any link budget including those of the IEEE 802.3 and fiber channel T11.2 standards efforts. Here, we report the direct measurement of the correlation properties of high-speed VCSELs. We show that the corresponding computed mode partition noise (MPN) and relative intensity noise (RIN) powers are inconsistent with the conventional models used by standards groups yet are consistent with link measurements.

We present spectral-dependent electronic-photonic modeling of vertical-cavity surface-emitting laser (VCSEL)-multimode fiber (MMF) links for next-generation high-speed interconnects. The beam coupling processes, between the VCSEL and the MMF and between the MMF and the photodetector (PD), are discussed, with spectral-dependent three-dimensional launch conditions analyzed. The model accounts for fiber effects on the transmission performance, specifically modal attenuation, dispersion, mode mixing, and mode partition noise. An advanced split-step small-segment (4-S) method simulates the signal evolution over the MMF with high accuracy and high efficiency. Experimental validation at 25 Gbps confirms the high accuracy of the VCSEL-MMF link model. The model reveals that larger radial offsets can further excite lower-order mode groups reducing the power distributed to higher-order groups when a tilted beam couples to the input fiber facet. With an optimized misalignment launch, the modal bandwidth is greatly improved by 3.8-fold compared to the conventional center launch. The model helps determine the optimum launch condition to improve link performance metrics such as transmission reach.

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.

The development of robust next generation multi-mode VCSEL-based optical links requires an accounting of all penalties in the link. While limitations from fiber bandwidth can be overcome to a significant extent using equalization and forward error correction, noise in the link cannot be equalized. Measurements show that mode partition noise depends on launch condition, and the noise penalty can be decreased using devices with small k factor. Time and frequency domain characterization of mode power fluctuations shows that they occur primarily at frequencies below 5 GHz. These findings guide the development of VCSELs for 25GBaud PAM4 and higher bit rate applications.

New applications in industrial, automotive and datacom applications require vertical-cavity surface-emitting lasers (VCSELs) operating at very high ambient temperatures at ultrahigh speed. We discuss issues related to high temperature performance of the VCSELs including temperature response and spectral properties. The influence of the gain-to-cavity wavelength detuning on temperature performance and spectral width of the VCSELs is discussed. Performance of the oxide-confined 850 nm VCSELs with increased temperature stability capable of operating at bit rates up to 25 Gbit/s at heat sink temperature of 150°C and 35Gbit/s at 130°C. Furthermore, opposite to previous studies of VCSELs with large gain-to-cavity detuning, which demonstrated strongly increased spectral width and a strong redistribution of the mode intensities upon current increase. VCSELs demonstrated in this work show good reproducibility of a narrow spectrum in a wide range of currents and temperatures. Such performance strongly improves the transmission distance over multi-mode fiber and can reduce mode partition noise during high speed operation.

Laser noise has been of high interest for many years, both in the context of fundamental physics and for a variety of laser applications. This chapter is meant to be an introduction into the area of laser noise. It focuses on single-frequency lasers, which have been studied in most detail and deserve significant attention for various reasons, including the fact that their understanding also greatly facilitates the understanding of more complicated situations — for example, in mode-locked lasers. A common situation is that a solid-state laser is pumped with a high-power semiconductor laser diode, with the latter exhibiting significant mode partition noise. Even if the total power of the semiconductor laser is fed into the solid-state laser, the resulting intensity noise of the solid-state laser can be significant, because the degree of pump absorption can significantly vary across the spectrum of the pump diode, so that the absorbed pump power fluctuates more than the total incident pump power.

The correlation properties of vertical-cavity surface-emitting laser (VCSEL) transverse modes determine the noise impairments of VCSEL-based high-speed links. The cross-correlation statistics between VCSEL mode pairs and the autocorrelation statistics for each VCSEL mode are directly measured using real-time 40GSs synchronous observations of spatially separated modes. Anticorrelation was found to be different for different mode pairs along with some positive correlations between modes, contradicting the assumptions of the IEEE model for mode partition noise in VCSEL multimode fiber links. These correlation results are used to estimate the mode partition parameter $k_{\mathrm { {mpn}}}$ yielding different values of $k_{\mathrm { {mpn}}}$ for the same VCSEL at the same bias, again in contrast with the IEEE model assumption.

Mode partition noise (MPN) of the laser employed at the transmitter can significantly degrade the transmission performance. In the paper, we introduce a simulation model of MPN in vertical cavity surface emitting laser (VCSEL) and simulate transmission of pulse amplitude modulation (PAM) and carrierless amplitude phase (CAP) signals in multimode fiber (MMF) link. By turning off other effects, like relative intensity noise (RIN), we focus solely on the influence of MPN on transmission performance degradation. Robustness of modulation and equalization type against MPN is studied.

International audience; We propose the use of Manchester encoding in conjunction with balanced detection to overcome the mode partition noise (MPN) limit of quantum-dash Fabry-Perot mode-locked lasers (QD-MLLs) used as multi-wavelength sources in short-reach applications. The proposed approach is demonstrated for a 10-mode laser, each carrying a 10-Gb/s signal. We show that bit-error-rate floors as high as 1e-4 when traditional non-return-to-zero (NRZ) modulation is employed with a single-ended detection scheme can be pushed below 1e-9 thanks to the introduction of Manchester encoding together with balanced detection. The benefit of the scheme could be attributed to the spectral shift of the Manchester spectrum, resulting in a smaller overlap with the high-relative intensity noise (RIN) region present at low frequencies, and the use of balanced detection. We clarify the origin of the performance improvement through comparisons of single-ended and balanced detection and the use of a RIN emulation technique. We unambiguously show that the use of balanced detection plays the leading role in MPN mitigation enabled by Manchester modulation.

We numerically study the effect of carrier grating originated by standing wave pattern on the multi-mode dynamics of semiconductor lasers toward the generation of optical frequency combs. The numerical analysis shows that, due to the localization of the carriers in the quantum dot (QD) active region, the carrier grating guarantees the simultaneous lasing of several optical lines with low mode partition noise, whereas this behavior is not observed in quantum well (QW) lasers because of the carrier diffusion in the active layer.

Modulation rates of VCSELs within multimode fiber links are now 25Gbps as standardized by both IEEE and Infiniband. Yet the need continues to advance the serial data rates to 50Gbps and higher to more readily support 100Gbps links with manageable fiber count. At these higher modulation rates the multimode VCSEL dynamics cannot be accurately modeled as single mode sources coupled into a MMF modeled as a simple filter. Specifically, our recent experimental results demonstrate the limitations of the standard mode partition noise and relative intensity noise models. By direct measurement of VCSEL mode dynamics we have shown modal statistics to be comprised of a mix of both correlated and anti-correlated components with a correlation time of a few symbol periods at 100G. Through simulations and experiments we demonstrate that MPN is significantly over estimated in the standard modeling tools and that RIN is enhanced by fiber dispersive effects, an effect not currently captured by current standard modeling methods and potentially underestimated.

The generation and accumulation of random jitter (RJ) in channels using multimode fibers (MMF) and vertical cavity surface emitting lasers (VCSEL) is investigated. A novel theoretical model that accommodates mode partition noise (MPN) and modal-chromatic dispersion interaction (MCDI) for the length dependence of RJ in VCSEL-MMF channels is developed. The proposed model requires a few channel parameters such as length, MPN coefficient, spectral width of the source, and a new parameter for describing the modal-chromatic interaction. Simulation predictions are verified by experiments.

When light generated by a multimode laser diode travels through a wave-length-sensitive element, such as an unbalanced interferometer, the mode partition noise might be converted into intensity noise, significantly increasing the intensity of the total optical noise at its output. In this work, it is shown that the mode partition noise converted into intensity noise by an unbalanced interferometer may be stabilized, and two approaches to achieve this intensity noise level control are demonstrated. A suitable very stable optical white noise source is also presented as an application of the intensity noise level control system stabilized at a maximum.

International audience; This paper examines the impact of laser mode partition noise (LMPN) during optical heterodyning process. The system presented here employs a passively mode-locked laser diode (PMLLD) as a multi-mode source for millimeter-wave (mm-wave) generation. A comprehensive theoretical and experimental study of LMPN at low frequency and, for the first time, in mm-wave frequency band is demonstrated. Simulations are presented to investigate the distribution of mode partition noise across optical modes. LMPN appears as an impairment in performance on a radio-over-fiber (RoF) communication system by increasing the intensity noise when the number of optical modes detected by a photodiode (PD) is limited. The effect of LMPN for various number of modes is demonstrated by coherent and incoherent receivers, and it is shown that 25 dB degradation in signal power occurs due to noise when not all modes are detected. Index Terms-Error vector magnitude (EVM), laser mode partition noise (LMPN), millimeter-wave (mm-wave), optical heterodyne, passively mode-locked laser diodes (PMLLD), phase noise, radio-over-fiber (RoF), relative intensity noise (RIN).

We investigate reduction of mode partition noise of a spectrally sliced Fabry-Perot laser diode (FP-LD) for application to seeded DWDM systems. The proposed scheme for the noise reduction incorporates a fiber-based Mach-Zehnder interferometer (MZI) and a reflective semiconductor optical amplifier (RSOA). The MZI enables to reduce a relative intensity noise (RIN) more than 3 dB with better noise distributions. Experimental results of 10-Gb/s signal transmission exhibit a considerable bit-error-rate (BER) reduction by three orders of magnitude at the given received power. After the noise reduction, the FP-LD is applied to a 10-Gb/s DWDM system as a seed-light-source. In a local-seeding scheme, return-to-zero (RZ) and carrier-suppressed (CS)-RZ signal formats are compared as a function of transmission distance. Furthermore, a back-reflection induced impairment is evaluated in a remote-seeding scheme. We also count the number of useable channels to show the feasibility of DWDM transmission. (C) 2016 Optical Society of America

We develop a complete theoretical model to explain the interaction of modal and chromatic dispersion in optical channels based on vertical cavity surface emitting lasers and multimode fibers. We propose an original formalism to estimate the magnitude of this interaction on the channel bandwidth and mode partition noise power penalty within traditional communication system link models. Simulation results are experimentally validated.

In this paper we investigate and quantify the dynamic behavior of the mode partition noise variance. We found that the mode partition noise variance is largest at the bit boundaries and depends on the slope (edge transition times) of the signal in links with one propagating fiber mode. In multimode fibers we show similar dependence, although the mode partition noise is reduced because fiber mode groups mix the chromatically dispersed laser modes responsible for mode partition noise.

In this paper, we propose a new method to mitigate the mode partition noise (MPN) in VCSEL-MMF based links by using wavefront shaping technique. The noise characteristic of the VCSEL-MMF links is theoretically studied and the impacts of coupling coefficients between VCSEL and MMF on the MPN and the system performance are investigated via simulation and experiment. The simulation results show that for 25-Gb/s OOK signal after 300-m MMF transmission, five orders of magnitude improvement of BER can be observed and the standard deviation of the received signal, which is the characterization of the MPN, is reduced for about an order when wavefront shaping is applied. With the help of wavefront shaping, we show that the DSP complexity has been profoundly reduced in order to achieve reliable 56-Gb/s and 112-Gb/s PAM-4 transmission by simulation. We perform experiment for 25-Gb/s OOK signal transmission over 300-m OM3 MMF with the launching optical power of -4 dBm to the fiber. About 1-dB power penalty improvement has been achieved at 7% FEC threshold after 300-m MMF transmission and the noise in the eye diagram is mitigated. The results of our simulation and experiment show the effectiveness of wavefront shaping to mitigate the MPN, therefore reduce the DSP complexity and improve transmission performance for the VCSEL and MMF based high speed short reach optical interconnects.

We experimentally demonstrate the performance analysis of burst-mode receivers (BMRx) in a 622 Mb/s 20-km gigabit-capable passive optical network (GPON) uplink. Our receiver features automatic phase acquisition using a clock phase aligner (CPA), and forward-error correction using (255, 239) Reed-Solomon (RS) codes. The BMRx provides instantaneous (0 preamble bit) phase acquisition and a packet-loss ratio (PLR) < 10?6 for any phase step (±2? rads) between consecutive packets, while also supporting more than 600 consecutive identical digits (CIDs). The receiver also accomplishes a 3-dB coding gain at a bit-error rate (BER) of 10?10. The CPA makes use of a phase picking algorithm and an oversampling clock-and-data recovery circuit operated at 2× the bit rate. The receiver meets the GPON physical media dependent layer specifications defined in the ITU-T recommendation G.984.2 standard. We investigate the PLR performance of the system and quantify it as a function of the phase step between consecutive packets, received signal power, CID immunity, and BER, while also assessing the tradeoffs in preamble length, power penalty, and pattern correlator error resistance. We also study the impact of mode-partition noise in the GPON uplink in terms of the effective PLR and BER coding gain performance of the system. In addition, we demonstrate how the CPA and the RS(255, 239) codes can be used in tandem for dynamic burst-error correction giving reliable BERs in bursty channels.

High performance, inexpensive light sources are needed for the advancement of wavelength division multiplexed (WDM) photonic access networks. In this paper, the unique features of multiwavelength modelocked semiconductor lasers are demonstrated with an emphasis on possible integration into access networks. An evaluation of multiwavelength passive, active, and hybrid modelocking reveals that hybrid modelocking is optimum for the suppression of mode partition noise as well as coherence tailoring in multiwavelength lasers. Low-distortion propagation of 10 channeltimes5 GHz multiwavelength pulses through multimode fiber is achieved. Intracavity gain flattening enables the simultaneous generation of 6 GHz pulse trains into 168 parallel wavelength channels for a 1 THz aggregate pulse rate from a single laser source. This work conveys the potential for semiconductor laser modelocking to produce multiple telecommunications wavelengths for data transmission and auxiliary functions in photonic networking

We propose and demonstrate a reduction of mode partition noise of an F-P LD using a fiber-based Mach-Zehnder interferometer (MZI). Injection-locked dual F-P LDs suppress polarization dependence to reduce a noise power by 3-dB.

Mode partition noise (MPN) can become the dominant limitation in 850 nm VCSEL-based multi-mode fiber (MMF) links at high data rates. Fluctuations in the partition of energy between the transverse modes of the VCSEL combined with the chromatic dispersion in the fiber leads to intensity noise at the receiver. The impact of MPN on non-equalized and equalized links has been studied with a numerical model of the VCSEL and MMF. The MPN in 25 Gb/s VCSELs has been investigated by examining noise in individual mode groups isolated using a thin film Fabry-Perot filter. The measured k factor below 0.15 should enable links significantly longer than 100 m at 25 Gb/s and higher data rates.

Cross-correlations between VCSEL transverse modes are measured using 40GSps synchronous observations of spatially separated modes. Positive correlation and anti-correlation behaviors are observed as well as low, distinct k mpn , contrary to assumptions of the IEEE model.