KEYWORDS: Diffraction, Fiber Bragg gratings, Error analysis, Diffraction gratings, Near field, Far-field diffraction, Near field diffraction, Ultraviolet radiation, Near field optics, Fourier transforms
The phase mask is a diffractive optical element that is widely used for fabricating the fiber Bragg gratings (FBGs) for telecom and sensing applications. We analyze the near field diffraction of the phase mask with periodic phase-shift errors, e.g., stitching errors. Our analysis shows that the stitching errors generate sidelobe peaks beside the main diffraction orders of the phase mask. Experiments in the far-field diffraction prove the analysis results, so that we can estimate the e-beam writing field size by the far-field diffraction. We obtain the diffraction near field distribution using the Talbot formula, which explains, for the first time at our best knowledge, how the stitching errors are transferred into the FBG with the same periodicity during the side-writing process. We find out that the noise energy in the near field varies with the phase mask to fiber spacing. An optimal spacing can be found and used in order to reduce the stitching error related sidelobes in the FBG spectrum.
We propose a model for the stitching errors in the phase mask, that allows computing the near field of diffraction. We show that the noise field associated to the stitching errors has some periodicity, which can be imprinted into the fiber Bragg gratings resulting in sidelobe noise in the spectrum. This noise effect varies as a function of phase mask-fiber spacing.
The rigorous coupled-wave analysis and our experimental measurements show optimal values of the phase retardation and duty cycle of the phase mask to minimize zero and even diffracted orders, that are more precise than that usually used according to the scalar theory of diffraction. Under an oblique incidence, we optimize the phase mask with three parameters: phase retardation, duty cycle, and refractive index, that results in a perfect sinusoidal interference field with high diffraction efficiency for writing the fiber Bragg grating.
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