Scalable angular spectrum propagation

A scalable angular spectrum (SAS) algorithm with zoom capability for numerical propagation of scalar wave fields in homogeneous media is presented. The proposed method features three properties that distinguish it from existing methods: (1) It allows for propagation models where the destination pixel pitch is larger than the source pixel pitch, (2) it requires a computational complexity proportional to the cost of three successive fast Fourier transform (FFT) operations of the input field, and (3) it is valid for high numerical aperture (NA) propagation geometries. We find that our method approaches the precision of computationally far more expensive wave propagation models such as the angular spectrum method in conjunction with zero padding, as demonstrated on the canonical examples of diffraction from circular and square apertures under straight and oblique illumination. Finally, we discuss the validity of the proposed SAS method, derive practical bandlimit criteria, and state a limit for the propagation distance. The scalability, efficiency, and accuracy at high NA of our proposed wave propagation algorithm make it an attractive candidate for a large variety of forward and inverse modeling problems with the ability to apply automatic differentiation.