Abstract
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].
Highlights
The region of diffraction from a few wavelengths to hundreds of micrometers from the mask is of interest for microlithography
The side-writing of fiber Bragg gratings (FBGs) through a phase mask is a type of interference lithography
This paper provides a theoretical base for the new design of the multiple phase-shifted phase masks for phase-only sampled high channel-count FBGs [1,2]
Summary
The region of diffraction from a few wavelengths to hundreds of micrometers from the mask is of interest for microlithography. The scalar diffraction Talbot imaging and rigorous coupled-wave analysis have been used to analyze the near-field beyond the phase mask in order to ensure high performance of the FBGs [3,4,5,6,7,8]. The split of the phase shifts caused large roll-off errors in the multi-channel spectrum that can be corrected by new designs of the phase-shifted phase masks [1,2]. In this paper we analyze an ideal near-field diffraction of the phase masks with multiple phase-shifts in order to get a physical understanding of the phase-shift split. This paper provides a theoretical base for the new design of the multiple phase-shifted phase masks for phase-only sampled high channel-count FBGs [1,2]
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