Scalability limitations of optical access and metro networks due to the polarization-dependent gain of semiconductor optical amplifiers

This article presents, for the first time, the derivation of approximate analytical formulae for the probability density function and the cumulative density function of the optical signal-to-noise ratio variation in optical local and metropolitan area networks due to the weakly polarization-dependent gain of cascaded semiconductor optical amplifiers. The cumulative density function is used to calculate the outage probability and derive specifications for the maximum allowable value of polarization-dependent gain per semiconductor optical amplifier in order to achieve a given network size.