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

Abstract

a b s t r a c tOptical 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.

Effect of spatial distribution of partial information on the accurate recovery of optical wave fields

“…The accumulated-overlapping case deserves additional scrutiny. In this case, for values of m 1 that are close to N ∕2 (more precisely, for m 1 > 32), the condition number hits the MATLAB precision limit ceiling around 10 16 , for all values of the fractional order a. We obtain condition numbers that do not hit the precision limit ceiling only for considerably uneven distributions (more precisely, for m 1 ≤ 32).…”

“…Planes perpendicular to the axis of propagation correspond to fractional Fourier domains (FRFDs) [3]. Furthermore, the same is true for all quadratic-phase systems [4], which are systems including an arbitrary sequence of lenses, sections of free space, and quadratic graded-index media [7][8][9][10][11][12][13][14][15][16]. Working with the FRT will allow us to approach the heart of the problem in its purest form and identify the main trends as clearly as possible, while the resulting important observations remain applicable to a broad class of systems of practical interest.…”