Design of bidirectionally pumped fiber amplifiers generating double Rayleigh backscattering

Optimum pumping schemes for bidirectionally pumped distributed fiber amplifiers are evaluated that simultaneously minimize the beat noise between signal and amplified spontaneous emission, as well as between signal and double Rayleigh backscattering. A way of adding a constraint on signal power to describe operation in a strong Kerr fiber nonlinearity regime is included. We show that one can find an optimum Raman net gain, as well as a percentage of forward to total Raman pumping maximizing the signal-to-noise ratio at the end of a transmission line using bidirectionally Raman-pumped transmission fibers.