  Building on the scientific understanding and technological infrastructure of
single-mode fibers, multimode fibers are being explored as a means of adding
new degrees of freedom to optical technologies such as telecommunications,
fiber lasers, imaging, and measurement. Here, starting from a baseline of
single-mode nonlinear fiber optics, we introduce the growing topic of multimode
nonlinear fiber optics. We demonstrate a new numerical solution method for the
system of equations that describes nonlinear multimode propagation, the
generalized multimode nonlinear Schrodinger equation. This numerical solver is
freely available, and includes a number of multimode fiber analysis tools. It
features a significant parallel computing speed-up on modern graphical
processing units, translating to orders-of-magnitude speed-up over the
split-step Fourier method. We demonstrate its use with several examples in
graded- and step-index multimode fibers. Finally, we discuss several key open
directions and questions, whose answers could have significant scientific and
technological impact.
