Near-field diffraction of irregular phase gratings with multiple phase-shifts

A phase-step in a phase mask is not copied into the substrate but is split into two half-amplitude phase-shifts in the near-field because of the presence of an additional interference fringe system of the two beams diffracted from the two grating sections separated by the phase-step. In the case of multiple phase-shifts, the split phase-shifts from two adjacent phase-steps can crossover in the propagation without interfere. This paper contributes to understanding the near-field diffraction of irregular phase gratings with multiple phase-shifts, and provides a theoretical base for designing multiple phase-shifted phase masks for high channel-count phase-only sampled fiber Bragg gratings [1,2].