New basis for rotationally symmetric nonparaxial fields in terms of spherical waves with complex foci

A scheme for computing rotationally-symmetric nonparaxial monochromatic scalar fields is proposed, based on a new orthonormal basis of solutions of the Helmholtz equation given by combinations of spherical waves focused at imaginary points. These basis fields are found through a mapping of the angular spectra of the multipolar basis over the sphere of directions. The convergence of the basis can be optimized by an appropriate choice of the location of the imaginary focus. The new scheme is tested for the case of converging spherical waves of different numerical apertures, with and without aberrations.