Abstract:
This paper presents a numerical method for solving the nonlinear Maxwell's equations that govern wave propagation in a Kerr nonlinear medium, where a material's refractive index changes with the intensity of an applied electric field. The study employs a perturbation approach, which simplifies the complex nonlinear wave equation by representing the solution as a power series expansion. This transforms the problem into solving a set of more manageable linear wave equations, which are then solved numerically using the Vector Finite Element Method on a hexahedral mesh. To validate this algorithm, the authors first analyze a two-dimensional rectangular waveguide, comparing the computed solutions for TE0, TE1, and TE2 propagation modes against known exact nonlinear solutions and achieving good agreement. The validated method is then used to investigate the effects of a more intense optical field in a fully three-dimensional cylindrical optical fiber, where simulations show that the high intensity causes the wave to reshape and steepen as it propagates.
