Homogeneous Vortex Solutions in Nonlinear Multicore Fiber with and Without Polarization Cross-Coupling

We study homogeneous vortex solutions in nonlinear multicore fibers with six periphery cores and one central core having two opposite polarizations using discrete nonlinear Schrodinger equation and Manakov equations for different discrete topological charges m = 0, 1, 2, 3. We compare the homogeneous solutions in the presence and absence of cross-coupling between the two opposite polarization fields. We also study their propagation dynamics by introducing a small random perturbation on the background of the homogeneous vortex solution numerically and then propagating them through a finite distance. Finally, we use linear stability analysis to find the gain spectrum and analyze the stability of the solutions.