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Unformatted text preview: TECHNISCHE UNIVERSIT AT M UNCHEN, TECHNICAL REPORT, OCTOBER 2008 1 Analytical Calculation of the Number of Four-Wave-Mixing Products in Optical Multichannel Communication Systems Bernhard Goebel and Norbert Hanik Technical Report, May 21, 2008, updated October 27, 2008 Abstract In fiber-optic systems with multiple channels or subcarriers, any three channels create new signal components through the nonlinear process of Four-Wave-Mixing (FWM). For the first time, to our best knowledge, we calculate the number of these products for each frequency. The results can be useful for nonlinear system analysis of multiplexed fiber-optic communication systems. Index Terms Optical transmission, Fiber nonlinearity, Four- wave mixing. I. INTRODUCTION Three light waves at frequencies f i , f j and f k propagating through silica fiber can create new waves at frequencies f ijk = f i f j f k . This nonlinear process has its origin in the third-order material polarization and is commonly referred to as Four-wave-mixing (FWM) or Four-photon-mixing [1]. In multi-channel fiber-optic communication systems using Wavelength Division Multiplexing (WDM), FWM gives rise to interference between channels, thus decreasing the channel quality [2][6]. Similar distortions appear in channels that use subcarrier multiplexing, such as Orthogonal Frequency Division Multiplexing systems [7], [8]. Impairments due to FWM play a role in pseudo-linear transmission systems [9] as well as in parametric amplifiers [10], [11]. FWM products of the form f ijk = f i + f j f k (1) are of particular importance, as those products fall into the signal band. When chromatic dispersion is low and each channel has equal signal power, then each FWM product has equal power and the number of FWM products can be used directly to calculate the total FWM-induced noise power in each subband [7], [8]. In the presence of chromatic dispersion, the FWM noise power is reduced by the phase mismatch between the interacting subcarriers, and the variance of each FWM product depends on that phase mismatch [1], [4]. Determining the number of FWM products is a classical problem. In the context of intermodulation interference in radio systems, it has been described long before communi- cation over fiber was possible [12]. FWM impairments can be reduced by spacing the channels at unequal distances or by using only certain subchannels from an equal-spaced channel The authors are with Technische Universitat Munchen (TUM), Institute for Communications Engineering (LNT), D-80290 Munich, Germany. E-Mail: Bernhard.Goebel@tum.de. grid [13]. A method for determining the total number of FWM products in this general scenario based on Frequency Difference Triangle (FDT) sets has been proposed in [14], [15]. Chang et al. [15] use Frequency Difference Squares to determine the number of products falling on each subchannel and give an expression for this number in an equal-spaced system....
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This note was uploaded on 03/13/2011 for the course ELECTRICAL 605 taught by Professor Mugu during the Spring '08 term at University of Wisconsin - Fond du Lac.

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