Proposal and analysis of two-cavity Fabry-Perot structures based on fiber Bragg gratings

An all-fiber two-cavity Fabry-Perot (FP) configuration based on fiber Bragg gratings (FBGs) is proposed. The characteristics of transmission spectra for the two-cavity FP structure are theoretically analyzed and comprehensively modeled. The explicit expression of the transmission coefficient for the structures is derived. The general conditions for the lengths of two cavities and reflectivities of FBGs are presented to produce the single resonant transmission peak at the central wavelength in the FBG stop band. Based on the theoretical analysis, the transmission spectra of symmetric and asymmetric two-cavity FP structures are simulated, and the simulation results are discussed and explained qualitatively. The design guidelines of the device, including the choices of cavity lengths, grating lengths, and index modulation depths, are concluded. The results show that when the increasing of the cavity length of a single-cavity FP structure results in multiple resonant peaks in the stop band, the two-cavity FP structures of the same length can inhibit the secondary resonant peaks and keep the main peak without degrading the performance through appropriately designing the cavity lengths and FBGs. Finally, the fabrication error tolerances of the structures, including inaccurate cavity lengths and reflectivities of FBGs, are calculated and discussed.