Scattering modeling by a nonlinear slab: Exact solution of the full vector problem

We investigate the scattering of light by a nonlinear, anisotropic slab under conical incidence and arbitrary polarization, within the framework of Maxwell's equations, where the nonlinearities are described by nonlinear susceptibility tensors. We develop a fully tensorial numerical method, free from standard simplifications such as the undepleted pump approximation or scalar field assumptions, based on an iterative scheme where each step is solved via the finite element method. The two-dimensional problem is reduced to one dimension by exploiting symmetry arguments. Energy considerations are also addressed. Several numerical experiments involving a potassium titanyl phosphate (KTP) slab and a lithium niobate $({\mathrm{LiNbO}}_{3})$ photonic crystal are presented, including cases with incident TE and TM waves, as well as a rotation-based study highlighting the anisotropic capabilities of our numerical model. This work provides a practical and general tool to help the optics research community overcome the limitations of existing models. It may facilitate the design of more advanced experiments to test nonlinear optical theories or improve nonlinear devices.