Angular spectrum representation of vector fields for supporting metasurface analysis and design

The angular spectrum method solves the vector Helmholtz equation for describing the propagation of the electric field rigorously. We present how the decomposition of the vector field by implementing intrinsic coordinates renders the propagation formulas analytically attractive by formulating analytical solutions for the propagated field. We investigate the validity range of different methods to calculate the projected focal spot: brute force integration, scalar angular spectrum decomposition and paraxial approximation. We combine our approach with the chirp Z transform to further extend the applicability range of the angular spectrum method and enable fine sampling of the focal spot beyond the limits of the fast fourier transform. The method can be applied to study focusing of highly converging light from aplanatic metalenses, such as immersion lenses for microscopy.