Semi-analytical methods for the efficient propagation of optical fields

The fast and accurate propagation of general optical fields in free space is still a challenging task. In this work we introduce three algorithms for the fast propagation of non-paraxial vectorial fields containing smooth but strong phase terms. Examples are fields with strong spherical, linear or astigmatic phase terms. Dependent on the shape of the smooth phase term different propagation operators have been developed. The main idea of all operators is the separation of the smooth phase term from the numerical propagation procedure. To this end the smooth phase term is not sampled but handled analytically. Then just the residual phase, for example the aberrations in case of a spherical smooth phase term, must be sampled which results in a drastically reduced numerical effort to propagate the field. We call such operators semi-analytical. For linear and spherical phase terms we demonstrate such operators. For general smooth phase terms we introduce in addition a lateral decomposition technique which allows the application of semi-analytical operators per subfield. Numerical results are presented which demonstrate the efficiency and the accuracy of the suggested propagation methods.