Impact of Polarization- and Mode-Dependent Gain on the Capacity of Ultra-Long-Haul Systems

Motivated by the recent interest in single-mode semiconductor optical amplifiers and multimode erbium-doped fiber amplifiers, we present a unified, comprehensive treatment of the effect of polarization- and mode-dependent gain (PDG and MDG) on the capacity of ultra-long-haul transmission systems. We study the problem using simulations of a multisection model, including the effects of PDG or MDG and polarization mode dispersion (PMD) or modal dispersion. We also analytically derive exact expressions for the capacity distribution of PDG-impaired single-mode systems. In agreement with previous work, we find that PDG and MDG cause fluctuations in capacity, which reduces average capacity and may cause outage. We show that the multimode systems studied, with at least $D = 14$ spatial/polarization modes, have sufficient modal diversity and frequency diversity to strongly suppress capacity fluctuations and reduce outage probability so that the outage capacity approaches the average capacity. We show that single-mode systems, by contrast, inherently provide low modal and frequency diversity, making them more prone to outage. To alleviate this problem, frequency diversity can be increased by artificially inserting PMD. Finally, we quantify the PDG/MDG requirements of optical amplifiers to ensure that the average capacity is close (within a 1-2 dB effective SNR loss) to the theoretical optimum. We show that these PDG/MDG requirements are stringent, especially considering the minimum-mean-square error linear equalizers implemented in typical multiple-input multiple-output receivers.