Theoretical analysis of transmission characteristics for all fiber, multi-cavity Fabry-Perot filters based on fiber Bragg gratings

The characteristics of transmission spectra for the all fiber, multi-cavity Fabry-Perot (FP) configuration based on fiber Bragg gratings (FBG) are theoretically analyzed and modeled. The general transmission matrix function for the structure with any number of cavities is derived, and explicit expression of the power transmission coefficient for symmetrical two-cavity FP is presented. The general conditions for flat-top single resonant peak at the central wavelength in FBG stop band are derived and verified in the numerical simulation section. The transmission peaks of single-cavity and two-cavity FP structures are compared and discussed, and results show that compared to the single-cavity FP, flatness of the top and steepness at the edge of transmission peak can be improved by introducing one more cavity. The resonant transmission peak properties of two-cavity structure are investigated in detail for various values of cavity length and FBGs with different reflection characteristics, and the design guidelines for transmission-type filters are presented. The results show that the steepness of peak slope can be improved by increase of FBG reflectivities, and these kinds of filters can be used as narrow-band single-channel selectors and multi-channel wavelength de-multiplexing by properly choosing the length of cavities and reflectivities of FBGs.