Computation of diffracted fields for the case of high numerical aperture using the angular spectrum method

The angular spectrum (AS) method is a popular solution to the Helmholtz Equation without the use of approximations. In this work, new criteria on sampling requirements are derived using the Wigner distribution (WD). It is shown that for the case of high numerical aperture the conventional AS method requires a very large amount of zero-padding, making it impractical due to requirements on memory and computational effort. This work proposes the use of a modified AS algorithm that evaluates only non-zero components of the field. The results obtained from the WD combined with the modified AS algorithm enable an accurate and efficient field computation for cases where the conventional AS method cannot be implemented.