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The fast and accurate propagation of general optical fields in free space is still a challenging task. Most of the
standard algorithms are either fast or accurate. In the paper we introduce without further physical approximations three new algorithms for the fast propagation of non-paraxial vectorial optical fields containing smooth
but strong phase terms. Dependent on the shape of the smooth phase term different propagation operators are
applied.
The first method for the efficient propagation of fields, which are containing smooth spherical phase terms,
is based on Mansuripur's extended Fresnel diffraction integral1 using fast Fourier Transformations. This concept
is improved by Avoort's parabolic fitting technique2 and the parameter space, for which the extended Fresnel
operator is numerically feasible, is discussed in detail. Furthermore we introduce the inversion of the extended
Fresnel operator for the fast propagation of non-paraxial fields into the focal region.
Secondly we discuss a new semi-analytical spectrum of plane waves (SPW) operator for the quick propagation of fields with smooth linear phase terms. The method is based on the analytical handling of the linear phase
term and the lateral offset, which reduces the required computational window sizes in the target plane.
Finally we generalize the semi-analytical SPW operator concept to universal shapes of smooth phases by de-
composing non-paraxial fields into subfields with smooth linear phase terms. In the target plane, all propagated
subfields are added coherently where the analytical known smooth linear phase terms are handled numerical
efficient by a new inverse parabasal decomposition technique (PDT).
Numerical results are presented for examples, demonstrating the efficiency and the accuracy of the three new
propagation methods. All simulations were done with the optics software VirtualLabTM.3
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