Propagation of electromagnetic fields between nonparallel planes

Optical systems can be understood as a sequence of homogeneous and inhomogeneous regions (free spaces and optical elements). In wave-optical engineering these regions are often analyzed separately using different physical approximations. The propagation of a wave within a homogeneous medium is well understood and described by different propagation integrals (for example by the angular spectrum of plane waves propagation, the Rayleigh Sommerfeld propagation and paraxial approximations following from these integrals). To allow a fast numerical evaluation of these integrals, typically Fast Fourier Transforms are used. If the propagation integrals are evaluated using Fast Fourier Transforms it follows automatically that start and end plane of the propagation have to be perpendicular to the optical axis. This can be a disadvantage if the complex amplitude of a propagating wave has to be calculated on a plane non parallel to the start plane of the propagation. Examples are the propagation of a wave to a screen which is tilted to the optical axis, the calculation of reflection of a wave on a tilted mirror and changing of the main propagation direction of a wave after a prism. The authors will demonstrate a modified propagation integral based on the angular spectrum of plane wave propagation that overcomes this limitation and allows a fast numerical evaluation using Fast Fourier Transforms. The advantage of the propagation method will be demonstrated on various examples.