In this work, four fast and rigorous methods for the simulation of light propagation in a homogenous medium are introduced. It is shown that in free-space propagation, the analytical handling of smooth but strong phase terms is very efficient in reducing the computational effort. Therefore, the angular spectrum of plane waves (SPW) operator is reformulated to handle linear, spherical, and general smooth phase terms without limiting the application of the fast-Fourier-transformation algorithm. Especially for nonparaxial field propagation, the proposed techniques can significantly reduce the required number of sampling points. Numerical results are presented to demonstrate the efficiency and the accuracy of the new methods.