An original approach to the solution of the nonlinear Schrödinger equation (NLSE) is pursued in this paper, following the regular perturbation (RP) method. Such an iterative method provides a closed-form approximation of the received field and is thus appealing for devising nonlinear equalization/compensation techniques for optical transmission systems operating in the nonlinear regime. It is shown that, when the nonlinearity is due to the Kerr effect alone, the order RP solution coincides with the order 2 + 1 Volterra series solution proposed by Brandt-Pearce and co-workers. The RP method thus provides a computationally efficient way of evaluating the Volterra kernels, with a complexity comparable to that of the split-step Fourier method (SSFM). Numerical results on 10 Gb/s single-channel terrestrial transmission systems employing common dispersion maps show that the simplest third-order Volterra series solution is applicable only in the weakly nonlinear propagation regime, for peak transmitted power well below 5 dBm. However, the insight in the nonlinear propagation phenomenon provided by the RP method suggests an enhanced regular perturbation (ERP) method, which allows the firstorder ERP solution to be fairly accurate for terrestrial dispersionmapped systems up to launched peak powers of 10 dBm.

Abstract-Sun et al.[1] succeeded in reducing the set of coupled first-order nonlinear partial differential equations determining the wavelength-dependent, time-varying amplifier gain into a single ordinary differential equation (ODE). In this paper, we further simplify the ODE bringing into greater evidence the physical meaning of the amplification process, and greatly enhancing the utility of the ODE as an analysis and design tool. We find that the gain dynamics of a doped-fiber amplifier are completely specified by its total number of excited ions r, whose time behavior is described by a simple first-order differential equation. We exploit this new understanding of amplifier gain dynamics: 1) to develop an equivalent circuit model for amplifier gain dynamics, 2) to identify that channel addition causes much faster transients than channel dropping in wavelength division multiplexing networks, and 3) to demonstrate that gain excursions can be significant in multichannel packet switching applications, which unlike timemultiplexed signals are characterized by bursts and lulls in communications. We are also able to revisit the most significant previously published results on both steady-state and dynamic analysis of doped-fiber amplifiers with a much more concise and more intuitive derivation.Index Terms-Doped-amplifier gain dynamics, EDFA, packet switching.

We investigate via experiments and simulations the statistical properties and the accumulation of nonlinear transmission impairments in coherent systems without optical dispersion compensation. We experimentally show that signal distortion due to Kerr nonlinearity can be modeled as additive Gaussian noise, and we demonstrate that its variance has a supra-linear dependence on propagation distance for 100 Gb/s transmissions over both low dispersion and standard single mode fiber. We propose a simple empirical model to account for linear and nonlinear noise accumulation, and to predict system performance for a wide range of distances, signal powers and optical noise levels.

The steady state behavior of regular two-connected multihoP networks in uniform traffic under hot-Pobto and a simple single-buffer deflection routing technique is analyzed for very high bit rate optical applications. Manhattan Street Network and ShuffleNet are compared in terms of throughput, delay, deflection probability, and hop distribution both analytically and network traffic. In a deflection routing network with equal link lengths, if the average statistics of the number of hops n are known, the packet rate can be obtained by conditioning On as 03 by simulation. It is analytically verified that this single-buffer P (e) = E~(e / n)~(n). (1) deflection routing technique recovers in both networks more n=l than 6O% of the throughput loss of hot-pohto with respect to For fixed n and fixed link length, the conditional enor rate store-and-forward when packets are generated with independent the average message length exceeds 20 packets. destinations. This gain, however, decreases to below 40% when depends On the 'pecific Optical for the network and is a point-to-point communication problem. Knowledge of the distribution of the number of hops P(n) is then necessary in network design to find the maximum bit U L~H O P packet-switching networks with regular two-rate and hence the maximum throughput achievable for a given M connected mesh topologies, such as Manhattan Street Offered load and physicd size Of the network. Network (MS) [l] and ShuffleNet (SN) [2], have been pro-This paper the steady state behavior Of twoposed for all-optical implementation at very high bit rates [3], connected mesh networks under deflection routing. The one-[4]. While in electronic networks buffering of hopping packets packet analytical appearing in [*], 191 for hot-potato at intermediate nodes is commonly used with conventional routing is reviewed and extended to the single-buffer memory store-and-forward routing, the Same is not true of all-optical configuration proposed in [6], which is particularly attractive networks, where the only fast optical memories avail-for optical implementation. Simulation results are provided to able are simple recirculating fiber delay loops which require Confirm the validity of the analytical models and stress the optical amplification, thus becoming impractical. Deflection consequences of violating some of the underlying assumptions. inate the need of optical amplifiers in the optical memory [6]. SN under various loads, for different network sizes, with no dramatic simplification is obtained with hotepotato buffers and with the above mentioned single-buffer memory. [71, which is a special of deflection routing where buffers Section I1 reviews deflection routing and summarizes some are not provided at all. topological properties of mesh networks whose interplay de-In these networks an all-optical path is provided between termines the global network behavior under deflection routing. source and destination, without intermediate regeneration of Section 111 describes node Operation and provides a detailed the...

Abstract-This paper presents a novel method based on a parametric gain (PG) approach to study the impact of nonlinear phase noise in single-channel dispersion-managed differentially phase-modulated systems. This paper first shows through Monte Carlo simulations that the received amplified spontaneous emission (ASE) noise statistics, before photodetection, can be reasonably assumed to be Gaussian, provided a sufficiently large chromatic dispersion is present in the transmission fiber. This paper then evaluates in a closed form the ASE power spectral density by linearizing the interaction between a signal and a noise in the limit of a distributed system. Even if the received ASE is nonstationary in time due to pulse shape and modulation, this paper shows that it can be approximated by an equivalent stationary process, as if the signal were continuous wave (CW). This paper then applies the CW-equivalent ASE model to bit-error-rate evaluation by using an extension of a known Karhunen-Loéve method for quadratic detectors in colored Gaussian noise. Such a method avoids calculation of the nonlinear phase statistics and accounts for intersymbol interference due to a nonlinear waveform distortion and optical and electrical postdetection filtering. This paper compares binary and quaternary schemes with both nonreturn-and return-to-zero (RZ) pulses for various values of nonlinear phases and bit rates. The results confirm that PG deeply affects the system performance, especially with RZ pulses and with quaternary schemes. This paper also compares ON-OFF keying (OOK) differential phase-shifted keying (DPSK) systems, showing that the initial 3-dB advantage of DPSK is lost for increasing nonlinear phases because DPSK is less robust to PG than OOK.Index Terms-Differential phase-shift keying (DPSK), differential quadrature phase-shift keying (DQPSK), Karhunen-Loéve (KL) transforms, nonlinear phase noise, parametric gain (PG).