This paper is devoted to an in-depth discussion of the Gaussian Noise (GN) model which describes non-linear propagation in uncompensated coherent transmission systems. Similar models and validation efforts are reviewed. Then, the main equations of the GN model are introduced. An intuitive physical interpretation of the equations and their features is proposed. The main characteristics of the non-linear interference (NLI) noise spectra that the GN model produces are discussed. To ease model exploitation, a new formulation in hyperbolic coordinates is proposed, which makes numerical integration faster. New approximate closed-form solutions are also provided. An extension of the GN model to distributed-amplification scenarios is introduced. NLI noise accumulation versus distance and bandwidth are studied in depth. Finally, the GN model implications as to system and networks design and optimization are discussed.

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The GN Model of Non-Linear Propagation in Uncompensated Coherent Optical Systems

Several approximate non-linear fiber propagation models have been proposed over the years. Recent re-consideration and extension of earlier modeling efforts has led to the formalization of the so-called Gaussian-noise (GN) model. The evidence collected so far hints at the GN-model as being a relatively simple and, at the same time, sufficiently reliable tool for performance prediction of uncompensated coherent systems, characterized by a favorable accuracy versus complexity trade-off. This paper tries to gather the recent results regarding the GN-model definition, understanding, relations versus other models, validation, limitations, closed form solutions, approximations and, in general, its applications and implications in link analysis and optimization, also within a network environment.

The GN-Model of Fiber Non-Linear Propagation and its Applications

We address perturbative models for the impact of nonlinear propagation in uncompensated links. We concentrate on a recently-proposed model which splits up the signal into spectral components and then resorts to a four-wave-mixing-like approach to assess the generation of nonlinear interference due to the beating of the signal spectral components. We put its founding assumptions on firmer ground and we provide a detailed derivation for its main analytical results. We then carry out an extensive simulative validation by addressing an ample and significant set of formats encompassing PM-BPSK, PM-QPSK, PM-8QAM, and PM-16QAM, all operating at 32 GBaud. We compare the model prediction of maximum system reach and optimum launch power versus simulation results, for all four formats, three different kinds of fibers (PSCF, SMF, and NZDSF) and for several values of WDM channel spacing, ranging from 50 GHz down to the symbol-rate. We found that, throughout all tests, the model delivers accurate predictions, potentially making it an effective general-purpose system design tool for coherent uncompensated transmission systems.

Modeling of the Impact of Nonlinear Propagation Effects in Uncompensated Optical Coherent Transmission Links

A cross-connect switch for fiber-optic communication networks employing a wavelength dispersive element, such as a grating, and a stack of regular (non-wavelength selective) cross bar switches using two-dimensional arrays of micromachined, electrically actuated, individually-tiltable, controlled deflection micro-mirrors for providing multiport switching capability for a plurality of wavelengths. Using a one-dimensional micromirror array, a fiber-optic based MEMS switched spectrometer that does not require mechanical motion of bulk components or large diode arrays can be constructed with readout capability for WDM network diagnosis or for general purpose spectroscopic applications.

Multi-wavelength cross-connect optical switch

Because the electroabsorption effect in semiconductor multiple quantum well material is approximately 50 times larger than in bulk semiconductors, significant interest has been generated in the use of MQW's in optical modulators Small high-speed devices have been made which show promise for external modulators in optical transmission systems, as well as for encoding and processing components in optical interconnect and signal processing systems The fact that these modulators are made from III-V semiconductors had led to interest in integration of these components with other active optoelectronic components Although most devices have operated with light of a wavelength of 085 mu m, recently much progress has been made in applying this technology to devices operating near 155 mu m The author reviews the work of the last few years in this field and indicates some future directions >

Multiple quantum well (MQW) waveguide modulators

A theoretical model is presented for analyzing the propagation of densely spaced WDM optical signals through a cascade of erbium-doped fiber amplifiers and single-mode optical fibers with nonuniform chromatic dispersion. By combining a numerical solution for the EDFA and an analytical expression for FWM components generated through the cascade, the model allows a realistic system analysis which includes gain peaking effect, amplified spontaneous emission accumulation and the effect of dispersion management on the four-wave mixing efficiency. The FWM power distribution at the end of the multi-amplifier transmission link is computed taking into account the phase relation between FWM light amplitudes generated within different sections of the link. The transmission of many WDM channels, evenly spaced around 1547.5 nm, has been analyzed for various dispersion management techniques and propagation distances. Numerical results point out the importance of such a model for a realistic design of WDM optical communication systems and networks. A proper choice of chromatic dispersion, amplifier characteristics, span length, input signal powers and wavelengths, combined with the use of gain equalizing filters, allows to maximize the transmission distance ensuring acceptable signal-to-noise ratio (SNR) and limited SNR variation among channels.

Modeling of four-wave mixing and gain peaking in amplified WDM optical communication systems and networks

We propose a volume holographic storage scheme, spatioangular multiplexing, which is a hybrid of both angular and spatial multiplexing. We describe the recording procedure, for a preliminary experiment in which 750 holograms were recorded (at room temperature) in a single photorefractive crystal of iron-doped lithium niobate and report the successful replay of all images with negligible cross talk and with an average diffraction efficiency of 0.5%.

Spatioangular multiplexed storage of 750 holograms in an Fe:LiNbO3 crystal

By placing the dispersion compensating fibre (DCF) first within each amplified span of a 10 Gbit/s standard fibre (SMF) dispersion-managed link the authors show, by numerical simulation, that the performance of such systems in terms of the Q factor is greater compared to systems positioning the DCF last. Examining their performance over 2000 km of standard fibre, it was found that the optimum channel power can be increased by 6 dB by having the DCF first.

Improved standard fibre performance by positioning the dispersion compensating fibre

We report the first demonstration of a novel optical logic device having an inverting characteristic which displays hard-limiting and optical gain of more than 10.

Novel nonresonant optoelectronic logic device

We propose a planar optical configuration for implementation of crossover interconnects. The planar overlay allows two-dimensional pixel arrays located on a wafer-scale integrated circuit to be interconnected in a compact and vibrationally robust configuration. By using an acute-angle microprism array with apex angles of 70.52 deg fabricated on a silicon substrate, we show the experimental result of the crossover interconnections. Some practical limits of the planar optical crossover interconnections are also discussed.

John E. Midwinter

Papers

Modeling of four-wave mixing and gain peaking in amplified WDM optical communication systems and networks

Spatioangular multiplexed storage of 750 holograms in an Fe:LiNbO3 crystal

Improved standard fibre performance by positioning the dispersion compensating fibre

Novel nonresonant optoelectronic logic device

Planar optical implementation of crossover interconnects.