  The throughput of submarine transport cables is approaching fundamental
limits imposed by amplifier noise and Kerr nonlinearity. Energy constraints in
ultra-long submarine links exacerbate this problem, as the throughput per fiber
is further limited by the electrical power available to the undersea optical
amplifiers. Recent works have studied how employing more spatial dimensions can
mitigate these limitations. In this paper, we address the fundamental question
of how to optimally use each spatial dimension. Specifically, we discuss how to
optimize the channel power allocation in order to maximize the
information-theoretic capacity under an electrical power constraint. Our
formulation accounts for amplifier physics, Kerr nonlinearity, and power feed
constraints. Whereas recent works assume the optical amplifiers operate in deep
saturation, where power-conversion efficiency (PCE) is high, we show that given
a power constraint, operating in a less saturated regime, where PCE is lower,
supports a wider bandwidth and a larger number of spatial dimensions, thereby
maximizing capacity. This design strategy increases the capacity of submarine
links by about 70% compared to the theoretical capacity of a recently proposed
high-capacity system.
