Light diffraction in slab waveguide lenses simulated with the stepwise angular spectrum method.

A stepwise angular spectrum method (SASM) for curved interfaces is presented to calculate the wave propagation in planar lens-like integrated optical structures based on photonic slab waveguides. The method is derived and illustrated for an effective 2D setup first and then for 3D slab waveguide lenses. We employ slab waveguides of different thicknesses connected by curved surfaces to realize a lens-like structure. To simulate the wave propagation in 3D including reflection and scattering losses, the stepwise angular spectrum method is combined with full vectorial finite element computations for subproblems with lower complexity. Our SASM results show excellent agreement with rigorous numerical simulations of the full structures with a substantially lower computational effort and can be utilized for the simulation-based design and optimization of complex and large scale setups.