Physical properties of optical fiber sidetap grating filters: free-space model

Presents theoretical and experimental results on the wavelength properties of sidetap grating filters written in single-mode optical fibers. A simple theoretical model based on Fraunhofer diffraction and antenna theory is used, modified to take into account the longitudinal variation of the incident field. Expressions are derived for the filter attenuation and bandwidth, and good agreement is demonstrated with experiment. The results show that the shape of the attenuation spectrum does not change with the filter length or index modulation, but that the magnitude of the attenuation increases with both parameters. The results also show that the effect of decreasing the fiber core-cladding index difference is to increase the peak attenuation and reduce the filter bandwidth. The existence of a strict longitudinal phase-matching condition is shown to cause asymmetry in the shape of the spectrum. Comparison with the properties of bulk sidetap gratings shows there to be a shift in the peak wavelength and apodization of the filter sidelobes. A simple diagram for the design of sidetap filters is presented for the first time.