Theoretical investigation on the characteristics of transmission spectra of the two-cavity Fabry-Perot structure based on fiber gratings for single-frequency fiber laser

The characteristics of transmission spectra of the all-fiber two-cavity Fabry-Perot (F-P) configuration based on fiber Bragg gratings (FBG) are theoretically analyzed and modeled. The explicit expression of the transmission coefficient for two-cavity F-P structures is derived. When the single resonant transmission peak is produced at the central wavelength in FBG stop band, the general conditions for the lengths of two cavities and reflectivities of FBGs are presented. Based on the theoretical analysis, the transmission spectra of symmetric and asymmetric two-cavity F-P structures are simulated, and the simulation results are discussed and explained qualitatively. The design guidelines of the device, including the choices of cavity length, grating length and index modulation depth， are put forword. The results show that, when the increasing of the cavity length of a single-cavity F-P structure results in multiple resonant peaks in the stop band, the two-cavity F-P structures of the same length can suppress the secondary resonant peaks and keep the main peak unaffected without degrading the performance through appropriately designing the cavity lengths and FBGs.