Parabasal field decomposition and its application to non-paraxial field propagation

We propose a parabasal field decomposition of non-paraxial fields, which enables various operations on such fields which are otherwise not feasible because of too high numerical effort. It is useful to distinguish between two basic cases of non-paraxial fields: 1) The field can be sampled without problems in the space domain but it is very divergent because of small features. A Gaussian beam with large divergence is an example. In this case the propagation of the field typically causes too high numerical effort and is not feasible. 2) The field possesses a smooth but strong phase function, which does not allow its sampling in space domain. Spherical, cylindrical and astigmatic waves with small radius of curvature are examples. In this case all operations which require a field sampling cannot be applied. For both cases a parabasal field decomposition is suggested which overcomes the problems. By separating linear phase factors from the parabasal fields the sampling effort is reduced drastically. This technique is applied to propagate non-paraxial fields.