Analytical FWM Expressions for Coherent Optical Transmission Systems

Simplified, closed-form, mathematical expressions for four wave mixing (FWM) in coherent optical systems are derived. FWM is an important limitation in both coherent OFDM (CO-OFDM) and Nyquist-WDM systems. The effect is also important in networks deploying dispersion shifted fiber and/or based on very narrow channel spacing. In this work, 1) we improve the accuracy of the formalism in CO-OFDM systems by taking into account not only the contribution due to the power of the central carrier but also the contribution due to the spectral flanks as well as the guard band between channels and 2) we extend the formalism to work for flexgrid systems. The derived expressions can be used for a quick estimation of system performance and/or can be incorporated in routing algorithms that account for physical layer effects. The formalism for flexgrid systems is estimating the power of FWM with improved accuracy compared to existing models in the literature so it can be a key asset in dynamic resource allocation operations. Finally, the derived expressions are valid for both, uncompensated and dispersion managed systems.