Multimode Nonlinear Fiber Optics: Massively Parallel Numerical Solver, Tutorial, and Outlook

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 Schrödinger equation. This numerical solver is freely available, implemented in MATLAB 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 conventionally-used 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.