A new spatio-temporal 2D-FEM formulation applied to optical devices with cylindrical symmetry

A new and efficient spatio-temporal formulation based on the finite element method 2D is applied to simulate optical devices with cylindrical symmetry. One spatial coordinate r, radial component, and one temporal coordinate τ, transversal component, constitute the discretization domain. The propagation occurs along z-direction, being incremented by Crank-Nicholson scheme. The finite-element in conjunction with Galerkin´s method it´s been applied to discretizate the transversal domain and perfect matched layers (PML´s) are placed to truncate the transversal boundaries.