Optimal representation and processing of optical signals in quadratic-phase systems

• We derive the optimal sampling grid for signals in quadratic-phase systems.
• The grid allows non-redundant representation with the minimum number of samples.
• The longitudinal spacing is uniform with respect to the fractional Fourier order.
• The grid reflects the fundamental structure of optical propagation.
• The grid constitutes a robust basis for accurate and efficient computation.

Optical fields propagating through quadratic-phase systems (QPSs) can be modeled as magnified fractional Fourier transforms (FRTs) of the input field, provided we observe them on suitably defined spherical reference surfaces. Non-redundant representation of the fields with the minimum number of samples becomes possible by appropriate choice of sample points on these surfaces. Longitudinally, these surfaces should not be spaced equally with the distance of propagation, but with respect to the FRT order. The non-uniform sampling grid that emerges mirrors the fundamental structure of propagation through QPSs. By providing a means to effectively handle the sampling of chirp functions, it allows for accurate and efficient computation of optical fields propagating in QPSs.