  We consider a model nondispersive nonlinear optical fiber channel with
additive white Gaussian noise at large $\mathrm{SNR}$ (signal-to-noise ratio)
in the intermediate power region. Using Feynman path-integral technique we for
the first time find the optimal input signal distribution maximizing the
channel's per-sample mutual information. The finding of the optimal input
signal distribution allows us to improve previously known estimates for the
channel capacity. The output signal entropy, conditional entropy, and
per-sample mutual information are calculated for Gaussian, half-Gaussian and
modified Gaussian input signal distributions. We explicitly show that in the
intermediate power regime the per-sample mutual information for the optimal
input signal distribution is greater than the per-sample mutual information for
the Gaussian and half-Gaussian input signal distributions.
