Efficient multimode vectorial nonlinear propagation solver beyond the weak guidance approximation

In this paper, we present an efficient numerical model able to solve the vectorial nonlinear pulse propagation equation in circularly symmetric multimode waveguides. The algorithm takes advantage of the conservation of total angular momentum of light upon propagation and takes into account the vectorial nature of the propagating modes, making it particularly relevant for studies in ring-core fibers. While conventional propagation solvers exhibit a computational complexity scaling as 𝑁4mode$N_{\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}}^4$$N_{{\rm mode}}^4$, where 𝑁mode$N_{\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}}$${N_{{\rm mode}}}$ is the number of considered modes, the present solver scales as 𝑁3/2mode$N_{\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}}^{3/2}$$N_{{\rm mode}}^{3/2}$. As a first example, it is shown that orbital angular momentum modulation instability processes take place in ring-core fibers in realistic conditions. Finally, it is predicted that the modulation instability process is followed by the appearance of breather-like angular structures.