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A mathematical framework is presented to study the evolution of multi-point cumulants in nonlinear dispersive partial differential equations with random input data, based on the theory of weak wave turbulence (WWT). This framework is used to explain how energy is distributed among Fourier modes in the nonlinear Schrödinger equation. This is achieved by considering interactions among four Fourier modes and studying the role of the resonant, non-resonant, and trivial quartets in the dynamics. As an application, a power spectral density is suggested for calculating the interference power in dense wavelength-division multiplexed optical systems, based on the kinetic equation of the WWT. This power spectrum, termed the Kolmogorov-Zakharov (KZ) model, results in a better estimate of the signal spectrum in optical fiber, compared with the so-called Gaussian noise model. The KZ model is generalized to non-stationary inputs and multi-span optical systems. [ABSTRACT FROM PUBLISHER]

This paper presents a new passive optical network (PON) architecture that applies an optical multicast capable switch (OMS) to direct wavelengths to a set of PON branches and enables them to share the transceivers in the central office (CO) on demand. The OMS is composed of fiber splitters and switching gates, and by controlling the on-off gates the wavelengths at the inputs can reach any outputs of the OMS. Through the OMS configuration, logical PONs are dynamically formed according to changing traffic patterns, and traffic is further scheduled in the time domain within each logical PON. The proposed network achieves network resource sharing without requiring tunable transceivers or wavelength filters, and without changing deployed network devices in the field or at the user end. Analysis and experimental study results show the efficiency of resource sharing and demonstrate the concept of resource sharing among PON branches. [ABSTRACT FROM AUTHOR]

Building on the Ethernet Passive Optical Network (EPON) and Gigabit PON (GPON) standards, Next-Generation (NG) PONs (i) provide increased data rates, split ratios, wavelengths counts, and fiber lengths, as well as (ii) allow for all-optical integration of access and metro networks. In this paper we provide a comprehensive probabilistic analysis of the capacity (maximum mean packet throughput) and packet delay of subnetworks that can be used to form NG-PONs. Our analysis can cover a wide range of NG-PONs through taking the minimum capacity of the subnetworks forming the NG-PON and weighing the packet delays of the subnetworks. Our numerical and simulation results indicate that our analysis quite accurately characterizes the throughput-delay performance of EPON/GPON tree networks, including networks upgraded with higher data rates and wavelength counts. Our analysis also characterizes the trade-offs and bottlenecks when integrating EPON/GPON tree networks across a metro area with a ring, a Passive Star Coupler (PSC), or an Arrayed Waveguide Grating (AWG) for uniform and non-uniform traffic. To the best of our knowledge, the presented analysis is the first to consider multiple PONs interconnected via a metro network. [ABSTRACT FROM AUTHOR]