Energy Conservation in Optical Fibers with Distributed Brick-Walls Filters

A band-pass filtering scheme is proposed to mitigate spectral broadening and channel coupling in the Nonlinear Schr\"odinger (NLS) fiber optic channel. The scheme is modeled by modifying the NLS Equation to include an attenuation profile with multiple brick-wall filters centered at different frequencies. It is shown that this brick-walls profile conserves the total in-band energy of the launch signal. Furthermore, energy fluctuations between the filtered channels are characterized, and conditions on the channel spacings are derived that ensure energy conservation in each channel. The maximum spectral efficiency of such a system is derived, and a constructive rule for achieving it using Sidon sequences is provided.